X-Planes: Convair X-6

The Convair X-6 was never built. It is the first article in this series about an aircraft that did not exist, and the interesting thing about it is not the absence but the residue, because the programme that would have produced it ran for fifteen years, spent about a billion dollars, and left a technical record larger than that of most aircraft in this series that flew. This article is the seventh in the X-Planes series, following the X-1, the X-2, the X-3, the X-4, and the X-5. The National Advisory Committee for Aeronautics, abbreviated NACA throughout and reconstituted in 1958 as the National Aeronautics and Space Administration, abbreviated NASA, contributed cycle analysis. The Atomic Energy Commission and the Air Force supplied the money and the reactors.

The keystone question is whether a reactor can be flown. The answer is yes, and one was, and the aircraft that carried it proved that the answer did not matter.

The Research Question

The keystone is whether the mass of shielding a reactor requires can be carried by an aircraft that still has a reason to fly.

The attraction is enormous and easy to state. Fission releases about two million times more energy per unit mass than combustion, so an aircraft that heats its air with a reactor, burning no fuel, is not range-limited in any sense a designer of the 1940s would recognize. Writing the energy released per kilogram of uranium-235 fissioned against the lower heating value of kerosene,

\[E_{\text{fission}} \approx 8.2 \times 10^{13} \ \text{joules per kilogram}, \qquad E_{\text{chem}} \approx 4.3 \times 10^{7} \ \text{joules per kilogram} \tag{1}\]

The first of those follows from the energy released per fission event and the mass of the nucleus that supplies it,

\[E_f \approx 200 \ \text{MeV} = 3.20 \times 10^{-11} \ \text{joules}, \qquad E_{\text{fission}} = \frac{E_f \, N_A}{M_{235}} \tag{2}\]

gives a ratio of

\[\frac{E_{\text{fission}}}{E_{\text{chem}}} = 1.9 \times 10^{6} \tag{3}\]

The rate at which a reactor must consume nuclei to hold a given power follows immediately,

\[\dot{N}_f = \frac{P}{E_f} \tag{4}\]

so a hundred megawatt core is fissioning

\[\dot{N}_f = \frac{10^{8}}{3.20 \times 10^{-11}} = 3.12 \times 10^{18} \ \text{nuclei per second} \tag{5}\]

and that number, rather than the power, is what determines everything difficult about the aircraft, because each of those events emits radiation as well as heat.

A strategic bomber of the period consumed fuel by the tens of tonnes. The same energy delivered by fission is measured in grams. The figure of merit that governs a conventional bomber collapses. Endurance for a fuel-burning aircraft is the fuel divided by the flow required, that flow being the thrust-specific fuel consumption, abbreviated TSFC, multiplied by the thrust,

\[t_{\text{endurance}} = \frac{m_{\text{fuel}}}{\text{TSFC} \times F} \tag{6}\]

and for a nuclear aircraft that consumption is not small but effectively zero,

\[\text{TSFC} = \frac{\dot{m}_{\text{fuel}}}{F} \longrightarrow 0 \quad \Longrightarrow \quad t_{\text{endurance}} \longrightarrow \text{limited by something else} \tag{7}\]

The quantity that had bounded every bomber ever built stops bounding anything, and the binding constraint moves to the crew, the lubricating oil, and the reactor. The mission this bought was a bomber that could remain airborne for weeks at a time, holding a target at risk continuously without needing to surge to reach it. The Army Air Forces began a project on Nuclear Energy for the Propulsion of Aircraft in May of that year, abbreviated NEPA.

The objection is equally easy to state. A reactor at power is an intense source of gamma rays and neutrons, and the crew must survive the flight. Shielding is dense material, dense material is heavy, and the aircraft must carry all of it all of the time. The keystone is therefore not whether a reactor can produce the thrust, which was never seriously in doubt, but whether what must be wrapped around it leaves an aircraft worth building.

A second constraint enters through the same door and deserves stating early. A reactor sustains itself when the neutron population reproduces, and the criticality condition states this as

\[k_{\text{eff}} = \frac{\text{production}}{\text{absorption} + \text{leakage}} = 1 \tag{8}\]

and leakage grows as a core is made small. For a bare core the non-leakage probability is approximately

\[P_{\text{NL}} \approx \frac{1}{1 + B^{2} M^{2}}, \qquad B^{2} = \left( \frac{\pi}{R} \right)^{2} \ \text{for a sphere} \tag{9}\]

with $M^2$ the migration area. An aircraft reactor must be compact, compact cores leak, and leaked neutrons must be paid for with enrichment or with a reflector. A compact aircraft core is therefore driven toward highly enriched fuel. That raises a proliferation concern as well as an engineering one, and no other aircraft in this series shares it.

That framing was understood at the outset. The Stever 1948b convened at the Massachusetts Institute of Technology in 1948 to assess feasibility, and its verdict, that the thing was possible but would take fifteen years and a great deal of money, turned out to be very nearly right in duration and wrong only in supposing that the endpoint would be reached. The study was thorough in a way its one-line summary conceals. It produced numbered reports on aircraft and on aircraft configuration, recorded a meeting with Boeing, assessed something as specific as the tolerance of aerial reconnaissance film to nuclear radiation, and was indexed well enough that the index survives as a document in its own right. It also established the comparison baseline, since Shoults 1948 examined the ability of chemically propelled aircraft to complete the same missions, so the question that eventually killed the programme was asked at the beginning and answered wrongly. The analysis of the mission case ran alongside, including studies of nuclear aircraft for antisubmarine warfare where endurance rather than speed is the whole of the requirement, and the performance parameters that would govern any such aircraft. Configuration studies followed in quantity. Hutton et al. 1952 compares fourteen nuclear-powered airplanes against one another. Documents of that kind exist only when a subject has passed from speculation into engineering.

Programme Origin

The institutional history is a sequence of transfers, and each transfer is a symptom.

Project NEPA began on 28 May 1946 under the Army Air Forces and ran as a study effort until May 1951. Its 1947 funding is given in one account as ten million dollars, and the Comptroller General puts the cost of the whole project at about twenty-one million. It was then replaced by the joint Atomic Energy Commission and Air Force programme called Aircraft Nuclear Propulsion, abbreviated ANP. The quarterly progress reports begin in that period and continue, in an unbroken series, for a decade. The programme pursued two propulsion architectures in parallel, the first sign that nobody was confident which would work.

The direct air cycle was assigned to General Electric at Evendale, Ohio. It is a turbojet with the combustor replaced by a reactor core. Air leaves the compressor, passes through the core, is heated by fission, and expands through the turbine. It is mechanically simple and thermodynamically direct, and its working fluid passes through the reactor and comes out radioactive.

The indirect cycle went to Pratt and Whitney at Middletown, Connecticut. A liquid metal or molten salt loop carries heat from the core to a heat exchanger, and the air is heated there without ever entering the core. It is cleaner and it costs a temperature drop across the exchanger, an entire secondary loop with pumps and radiators, and the mass of all of it. The circulating fuel reflector-moderator reactor was its central concept.

Under project MX-1589 Convair was to modify two B-36 airframes. One would carry a reactor to measure shielding, and one would become the X-6. The B-36 was chosen because it was the largest aircraft available, and that reason governs this article throughout. Its gross mass of about 186,000 kilograms over a wing of 443 square metres gives

\[\frac{W}{S} = \frac{186{,}000 \times 9.80665}{443} = 4.12 \times 10^{3} \ \text{newtons per square metre} \tag{10}\]

at an aspect ratio of

\[A = \frac{b^{2}}{S} = \frac{70.1^{2}}{443} = 11.1 \tag{11}\]

describing a high-aspect-ratio, lightly loaded aeroplane built for endurance and therefore the right starting point for a mission defined by staying airborne. Follow-on aircraft would have used the swept-wing YB-60. The X-6 entry gives its powerplant as General Electric X-40 engines, which were J53 turbojets modified for nuclear heating, drawing on a P-1 reactor, whereas the J47 entry names as the X-6 engine the J47-derived X39 that ran in the Heat Transfer Reactor Experiments.

The first airframe was built and flown. The second was not, because the Air Force cancelled the X-6 work at Convair in 1953.

Sizing From First Principles

The keystone relationship is the shield mass, and it can be derived from the reactor power and the geometry with nothing more exotic than an exponential.

How Much Power the Aircraft Needs

Start with the thrust. Take a B-36 at its maximum takeoff weight of about 186,000 kilograms, an upper bound on its weight in cruise, flying at a lift-to-drag ratio near eighteen, so the thrust required is

\[F = \frac{W}{L/D} = \frac{186{,}000 \times 9.80665}{18} = 1.01 \times 10^{5} \ \text{newtons} \tag{12}\]

At an assumed cruise speed of 200 metres per second, close to the B-36’s maximum speed and about twice its listed cruising speed of 103 metres per second, the propulsive power is

\[P_{\text{prop}} = F V = 1.01 \times 10^{5} \times 200 = 20.3 \ \text{megawatts} \tag{13}\]

and the thermal power the reactor must supply follows from the overall efficiency of the propulsion system,

\[P_{\text{thermal}} = \frac{P_{\text{prop}}}{\eta_{\text{overall}}}, \qquad \eta_{\text{overall}} = \eta_{\text{thermal}} \, \eta_{\text{propulsive}} \tag{14}\]

which for a turbojet of the period is near 0.20, giving

\[P_{\text{thermal}} = \frac{20.3}{0.20} = 101 \ \text{megawatts} \tag{15}\]

About a hundred megawatts of thermal power is a substantial power reactor by any standard and was an enormous one to propose putting in an aeroplane in 1950. The figure is not sensitive to the assumptions in any way that matters, since an efficiency of 0.25 gives 81 megawatts and 0.30 gives 68, and the listed cruising speed would roughly halve it, which the logarithmic shield dependence derived below turns into less than a centimetre of lead.

The fuel consumption that power implies is the promise made concrete. At a hundred megawatts for a hundred hours,

\[m_{\text{U-235}} = \frac{P \, t}{E_{\text{fission}}} = \frac{10^{8} \times 3.6 \times 10^{5}}{8.2 \times 10^{13}} = 0.44 \ \text{kilograms} \tag{16}\]

against the 837 tonnes of kerosene that would deliver the same energy. A nuclear bomber burns less than half a kilogram of fuel on a hundred-hour mission. Every difficulty in this article is the price of that number.

What the Reactor Emits

A reactor at power produces prompt fission gammas, fission product decay gammas, and fast neutrons, all in quantities proportional to the fission rate and therefore to the power. Taking about eight of the two hundred megaelectronvolts per fission as escaping gamma energy,

\[P_\gamma \approx 0.04 \, P = 4.0 \ \text{megawatts} \tag{17}\]

which at a mean photon energy near one megaelectronvolt is a source strength of

\[S_\gamma = \frac{P_\gamma}{\bar{E}_\gamma} = \frac{4.0 \times 10^{6}}{1.60 \times 10^{-13}} = 2.50 \times 10^{19} \ \text{photons per second} \tag{18}\]

and the neutron source follows from the yield per fission,

\[S_n = \nu \, \dot{N}_f = 2.4 \times 3.12 \times 10^{18} = 7.49 \times 10^{18} \ \text{neutrons per second} \tag{19}\]

Both scale linearly with the power, and the next two sections turn on that fact.

The dose rate at distance $r$ from a shielded source is governed by an exponential attenuation with a buildup correction,

\[\dot{D}(r, x) = \frac{k \, P}{4 \pi r^{2}} \, B(\mu x) \, e^{-\mu x} \tag{20}\]

in which $x$ is the shield thickness, $\mu$ the linear attenuation coefficient of the shield material, and $B$ the buildup factor accounting for photons that scatter into the beam rather than being removed from it. That factor is not a fudge but a computed quantity. Auslender 1957 obtains it for layered configurations by Monte Carlo, the method still used. The corresponding neutron quantity is the effective removal cross-section tabulated by Chapman and Storrs 1955, and Eggen et al. 1961 supplies the fast-neutron spectrum and dose-rate calculations that convert a flux into a dose. The quantities behind these coefficients were measured or computed under this programme or its immediate neighbours. Neither quantity is a settled constant, and both remain active research subjects. Buildup factors are still being computed to greater depth and by new methods, with Sun et al. 2025b carrying Monte Carlo evaluation to a hundred mean free paths, Kang and Zu 2026 and Yang et al. 2026b replacing the tabulations with learned models, and Hashim et al. 2026 treating the multilayer case this article’s divided shield requires. On the neutron side, Soliman 2025 treats the energy dependence of the removal cross-section, which the single-value treatment above hides. Jiaju et al. 2025 approach cross-section generation as a computational discipline. The factor $k$ collects the source spectrum and the conversion from fluence to dose.

Two features of that expression govern the result. The distance term is a power law and the shield term is an exponential, and an exponential wins every argument it is in.

The starting figure decides the shield, so it comes first. Unshielded at ten metres the photon fluence rate is

\[\varphi = \frac{S_\gamma}{4 \pi r^{2}} = \frac{2.50 \times 10^{19}}{4 \pi \times 100} = 1.99 \times 10^{16} \ \text{per square metre per second} \tag{21}\]

and the dose rate follows from the energy fluence and the mass energy-absorption coefficient of tissue,

\[\dot{D} = \varphi \, \bar{E}_\gamma \left( \frac{\mu_{en}}{\rho} \right)_{\text{tissue}} = 1.99 \times 10^{16} \times 1.60 \times 10^{-13} \times 3.09 \times 10^{-3} \tag{22}\] \[\dot{D} = 9.8 \ \text{grays per second} \tag{23}\]

Ten grays per second, when about five grays is a median lethal whole-body dose. One second of exposure at ten metres from an unshielded hundred megawatt core kills the crew. The shield must reduce that number, and stating it makes clear why the programme could not economize.

Solving for the thickness required to hold the dose at a limit $\dot{D}_0$,

\[x = \frac{1}{\mu} \ln \left( \frac{k \, P \, B}{4 \pi r^{2} \dot{D}_0} \right) \tag{24}\]

For lead at photon energies around one megaelectronvolt the mass attenuation coefficient is about 0.070 square centimetres per gram, so with a density of 11.34 grams per cubic centimetre,

\[\mu = 0.070 \times 11.34 = 0.794 \ \text{per centimetre} \tag{25}\]

giving a tenth-value layer of

\[x_{1/10} = \frac{\ln 10}{\mu} = \frac{2.303}{0.794} = 2.90 \ \text{centimetres} \tag{26}\]

so every 2.9 centimetres of lead removes ninety percent of what reaches it.

The mission, not taste, sets the attenuation demanded. Allowing the crew fifty millisieverts over a hundred-hour flight sets a rate limit of

\[\dot{D}_0 = \frac{0.05}{100} = 5 \times 10^{-4} \ \text{grays per hour} \tag{27}\]

against an unshielded rate of $3.54 \times 10^{4}$ grays per hour, so

\[\mathcal{A} = \frac{\dot{D}_{\text{unshielded}}}{\dot{D}_0} = \frac{3.54 \times 10^{4}}{5 \times 10^{-4}} = 7.1 \times 10^{7} \tag{28}\]

and with a buildup factor of ten the thickness is

\[x = \frac{\ln \left( \mathcal{A} B \right)}{\mu} = \frac{\ln \left( 7.1 \times 10^{8} \right)}{0.794} = \frac{20.4}{0.794} = 25.7 \ \text{centimetres} \tag{29}\]

Twenty-six centimetres of lead, and that is the gamma shield alone. That is the number the programme spent fifteen years trying to reduce.

Neutrons need a different material and are attenuated by a removal cross-section rather than by a photon coefficient,

\[\varphi_n(x) = \varphi_n(0) \, e^{-\Sigma_R x} \tag{30}\]

with $\Sigma_R$ near 0.095 per centimetre for lithium hydride, the aircraft shield material of choice because it supplies hydrogen at low density and captures the moderated neutrons in lithium without emitting a penetrating capture gamma. Waldrop 1958 treats it explicitly as a mobile neutron shield, so the aircraft requirement appears there as a material specification, and specimens were irradiated and tested, with two of the test series documented separately. The hydride family more broadly is surveyed in Cernak 1960a. For comparison the heavy alternative, structural concrete, is characterized by Blizard and Miller 1958, and its unsuitability for an aircraft is a matter of density, not of physics. The unshielded fast neutron dose rate at ten metres works out to some $7.5 \times 10^{5}$ sieverts per hour, so the attenuation required is $1.5 \times 10^{9}$ and

\[x_n = \frac{\ln \left( 1.5 \times 10^{9} \right)}{0.095} = 222 \ \text{centimetres} \tag{31}\]

Two and a quarter metres of lithium hydride. The two shields are not simply additive, since lead scatters neutrons inelastically and lithium hydride attenuates photons, so a layered design achieves both requirements in less material than the sum. The sum nevertheless remains an upper bound, and the true figure lies between the lead alone and the two together.

The Result That Decides the Programme

One property of the exponential is easy to miss, and it turns out to decide the argument. Because thickness depends on the logarithm of the power, increasing the reactor power barely thickens the shield,

\[\Delta x = \frac{1}{\mu} \ln \left( \frac{P_2}{P_1} \right) \tag{32}\]

Going from one megawatt to a thousand, a factor of a thousand in power, costs

\[\Delta x = \frac{\ln 1000}{0.794} = 8.7 \ \text{centimetres} \tag{33}\]

of additional lead. The shield is not a cost proportional to the reactor. It is a large fixed overhead that a bigger reactor barely increases. That single fact determines which aircraft can be nuclear and which cannot, and it does so in the opposite direction from intuition. A small nuclear aircraft is not easier than a large one. It is impossible, because it must carry nearly the same shield with far less aircraft to carry it.

The Optimum Separation

Distance is the other lever and it trades against structure. Putting the reactor further from the crew reduces the dose as $r^{-2}$ and therefore permits a thinner shield, but the fuselage that holds them apart adds mass.

Take a shadow shield of area $A$ covering the forward face of the reactor, with the crew compartment at distance $r$. Holding the crew dose fixed and solving the attenuation relation for thickness gives

\[x(r) = \frac{1}{\mu} \left[ \ln \left( \frac{k P B}{4 \pi \dot{D}_0} \right) - 2 \ln r \right] \tag{34}\]

so the shield mass falls logarithmically with separation,

\[m_{\text{shield}}(r) = \rho_s A \, x(r) = C - \frac{2 \rho_s A}{\mu} \ln r \tag{35}\]

while the structure needed to span that distance grows linearly at $\lambda$ kilograms per metre,

\[m_{\text{struct}}(r) = \lambda r \tag{36}\]

The total has an interior minimum. Differentiating and setting to zero,

\[\frac{d m_{\text{total}}}{d r} = -\frac{2 \rho_s A}{\mu r} + \lambda = 0 \quad \Longrightarrow \quad r^{*} = \frac{2 \rho_s A}{\mu \lambda} \tag{37}\]

Evaluating with lead at 11,340 kilograms per cubic metre, a forward hemisphere of 1.5 metre radius giving $A = 14.1$ square metres, $\mu = 79.4$ per metre, and a fuselage structural mass of 400 kilograms per metre,

\[r^{*} = \frac{2 \times 11{,}340 \times 14.1}{79.4 \times 400} = 10.1 \ \text{metres} \tag{38}\]

About ten metres of separation is optimal, and a B-36 fuselage is 49 metres long. The airframe is large enough to hold the optimum comfortably, and that explains further why this aircraft was chosen and not a smaller one. The NB-36H carried the reactor in a bomb bay aft of the crew, who sat in the nose, so the aircraft used that geometry.

The Number That Ends the Argument

With the separation chosen and the thickness computed, the shield mass follows,

\[m_{\text{shield}} = \rho_s A x = 11{,}340 \times 14.1 \times 0.257 = 4.11 \times 10^{4} \ \text{kilograms} \tag{39}\]

or 41 tonnes of lead, which against a gross weight of 186 tonnes is

\[\frac{m_{\text{shield}}}{m_{\text{gross}}} = \frac{41{,}100}{186{,}000} = 0.221 \tag{40}\]

Twenty-two percent of the aircraft is gamma shielding, and adding the neutron layer computed above takes the upper bound to

\[\frac{m_{\text{Pb}} + m_{\text{LiH}}}{m_{\text{gross}}} = \frac{41{,}100 + 24{,}500}{186{,}000} = 0.353 \tag{41}\]

The comparison that matters is not with the gross weight but with the payload, since a B-36 carried a maximum bomb load of about 39,000 kilograms,

\[\frac{m_{\text{shield}}}{m_{\text{payload}}} = \frac{41{,}100}{39{,}000} = 1.05 \tag{42}\]

The gamma shield alone weighs slightly more than the entire bomb load, and the full shield weighs about 1.7 times it. A nuclear bomber buys unlimited range by giving up the payload that made the range worth having, and that sentence is the programme in one line. The trade is not fatal in principle, since a larger aircraft dilutes a fixed shield mass. It is fatal in practice because the aircraft that dilutes the shield adequately is one nobody wanted to buy.

This was understood at the time. Shield optimization was a named research subject with a literature by 1953, shield weights were tracked as a programme metric, and the effect of the shield on the centre of gravity posed a design problem serious enough to warrant its own study. Shield synthesis was pushed to the point of formal minimum-weight optimization, and the computational tools were built in-house, with shield analysis programs and their successors developed for the task.

Divided Shielding and the Trick That Was Not Enough

The shield mass above assumes shielding the reactor. There is a cheaper arrangement and the programme used it.

A divided shield puts part of the material at the reactor and part around the crew. The reactor shield need only cover the solid angle subtended by the crew compartment, and the crew shield handles radiation that reaches the crew by other paths, principally scattering from the surrounding air. Writing the total as a sum,

\[m_{\text{total}} = \rho_s A_r x_r + \rho_c A_c x_c \tag{43}\]

subject to the constraint that the direct and scattered contributions together meet the dose limit,

\[\dot{D}_{\text{direct}} \left( x_r \right) + \dot{D}_{\text{scatter}} \left( x_r, x_c \right) \le \dot{D}_0 \tag{44}\]

the optimum divides the material between the two according to the relative areas. Forming the Lagrangian and differentiating with respect to each thickness gives the condition that the marginal dose reduction per unit mass be equal in both shields,

\[\frac{1}{\rho_s A_r} \frac{\partial \dot{D}}{\partial x_r} = \frac{1}{\rho_c A_c} \frac{\partial \dot{D}}{\partial x_c} \tag{45}\]

and because each partial derivative carries its own exponential, the condition reduces to a relation between the two thicknesses and the ratio of areal masses,

\[\mu_r x_r - \mu_c x_c = \ln \left( \frac{\rho_c A_c \, \mu_r}{\rho_s A_r \, \mu_c} \right) \tag{46}\]

Because the reactor shadow shield can be small in area while the crew compartment shield must wrap a larger volume, the division is not obvious in advance. This is the calculation Blizard 1953 set out and that the deGanahl et al 1954 and the AC-series power plant shield calculations applied to particular configurations. Solving it for a real layered geometry required machinery, and the programme built it, with an IBM 704 shielding program and a multilayer gamma flux code among the results. The supporting measurements are extensive, covering centreline dose rates from source planes of different area, gamma heating within a shield, the nuclear and physical properties of a graphite reactor shield, and duct penetration experiments at the Convair ground test reactor, the last of which addresses a problem every real shield has, the pipes and cables that must pass through it. A comparable ground installation is treated in Meem and Fairbanks 1956.

The scattered term is the reason the trick has a floor. Radiation that leaves the reactor in any direction can scatter off the surrounding air and arrive at the crew from outside the shadow, an effect that grows with air density and therefore falls with altitude. The effect of altitude and flight speed on shielding requirements was studied for that reason. The scattered contribution can be written in the same form as the direct one but with the air acting as the scattering medium, so that it scales with the density along the path,

\[\dot{D}_{\text{scatter}} \propto \rho_{\text{air}}(h) \, \frac{S_\gamma}{4 \pi r^{2}} \, f_{\text{geom}} \tag{47}\]

and the atmosphere thins exponentially with altitude,

\[\rho_{\text{air}}(h) = \rho_0 \, e^{-h / H}, \qquad H \approx 8.4 \ \text{kilometres} \tag{48}\]

so climbing from sea level to twelve kilometres reduces the scattered term by

\[\frac{\rho(12{,}000)}{\rho_0} = e^{-12/8.4} = 0.24 \tag{49}\]

A shadow shield alone is insufficient in an atmosphere. The aircraft must fly high to make its shielding lighter, a coupling between the flight condition and the structural mass that no conventional aircraft has, and it means the shield cannot be sized without first choosing the cruise altitude.

Material choice attacked the same problem from the other end. Gamma attenuation wants high atomic number and density, and neutron attenuation wants hydrogen. Lithium hydride supplies hydrogen at low density and captures neutrons in the lithium without producing a penetrating capture gamma, which makes it very nearly the ideal aircraft neutron shield, and its properties were characterized in detail under the programme. The investigation of metallic hydrides as moderators, reflectors, and shields pursued the same family.

Dependent Systems

The Direct Cycle and What It Does to the Air

Passing the working fluid through the core is simple and it has a consequence.

The thrust of a turbojet follows from the momentum change,

\[F = \dot{m} \left( V_e - V_0 \right), \qquad V_e = \sqrt{2 c_p T_4 \left[ 1 - \left( \frac{p_0}{p_4} \right)^{\frac{\gamma - 1}{\gamma}} \right]} \tag{50}\]

and the heat the reactor must add to reach turbine inlet temperature $T_4$ from compressor discharge temperature $T_3$ is

\[P_{\text{thermal}} = \dot{m} \, c_p \left( T_4 - T_3 \right) \tag{51}\]

The cycle behind them is a Brayton cycle whose thermal efficiency depends on the compressor pressure ratio alone in the ideal case,

\[\eta_{\text{th}} = 1 - \left( \frac{1}{\pi_c} \right)^{\frac{\gamma - 1}{\gamma}}, \qquad T_3 = T_2 \, \pi_c^{\frac{\gamma - 1}{\gamma}} \tag{52}\]

Nothing in either relation cares where the heat came from. The reactor is a heat source with a temperature limit, as a combustor is, and the design problem is to get $T_4$ as high as the turbine will tolerate.

That is where the difficulty lies. A combustor reaches flame temperatures far above what the turbine can take and the design problem is dilution. A reactor must reach turbine inlet temperature in its own fuel elements, which must therefore run hotter than the air they are heating. The margin needed follows from the convective heat transfer at the element surface,

\[q'' = h \left( T_w - T_{\text{air}} \right), \qquad \mathrm{Nu} = \frac{h D_h}{k} = 0.023 \, \mathrm{Re}^{0.8} \mathrm{Pr}^{0.4} \tag{53}\]

and the total surface the core must present follows from the power and the achievable flux,

\[A_{\text{fuel}} = \frac{P_{\text{thermal}}}{q''} \tag{54}\]

so a core transferring a hundred megawatts at a megawatt per square metre needs a hundred square metres of heated surface packed into something like a cubic metre, a power density of

\[\frac{P}{V} \approx 100 \ \text{megawatts per cubic metre} \tag{55}\]

That power density is demanded by an aircraft’s intolerance for volume. For a 1950s turbine tolerating something like 1150 kelvin at inlet, the fuel element surface must exceed that, and a fuel element at that temperature in a fast air stream is a materials problem of the first order. An entire literature was built on it, from Level 1962 through high-temperature work reported at the ANP materials meetings. Element development ran continuously, with Conway 1956, Butterfield 1956, Conn et al. 1957, and the shaped-wire study of Tribus 1955 representing the range of approaches tried. Inspection became a separate discipline in Marjon 1957, measuring the element temperature required thermocouples that would survive the environment, and Collins and McGurty 1960 covers the cladding alloys. The fuel element is where an aircraft reactor differs most from a power reactor, because it must be light, must run hotter, and must present a hundred square metres of surface to a fast air stream without shedding any of itself into the exhaust. What it does shed is the subject of Wilks 1959.

The modern answer to that problem is to encapsulate the fuel rather than to clad it, and the coated particle is where high-temperature reactor fuel went. Zheng et al. 2026 compute the interaction between such particles and the matrix holding them, Liu and Liu 2025 and Poschmann et al. 2025 model their performance including the departures from sphericity that real manufacture produces, and Peng et al. 2025 model the coupled irradiated thermal and mechanical behaviour of the elements, with the transmutation products that change the properties over life in Paul et al. 2025 and the multi-scale coupling problem in Zhang et al. 2026d. Gas-cooled cores of the kind the programme also examined continue in Chong and Sagara 2026 and Owston 2025.

Pushing air through that core costs pressure, and pressure lost between compressor and turbine is thrust not produced. The core acts as a duct with friction,

\[\frac{\Delta p}{p} = f \frac{L}{D_h} \frac{\rho V^{2}}{2 p} \tag{56}\]

and the fractional thrust penalty follows the fractional pressure loss closely for a turbojet, so a five percent core pressure drop is roughly a five percent thrust penalty on top of everything else. The programme measured this instead of estimating it. Segaser 1948, among the earliest documents in the record, determines pressure drop factors through typical fuel element channels. Chandler et al. 1957 finds that surface oxidation of the elements increases the loss, a degradation mechanism with no combustor analogue. The temperature rise of the fluid passing the elements is computed by Woods 1954. A combustor adds heat at nearly constant pressure because it is an open volume. A reactor core is a heat exchanger and behaves like one.

The air itself becomes radioactive. Natural argon is 0.93 percent of the atmosphere and argon-40 captures a neutron to become argon-41, a gamma emitter with a 110 minute half-life. The activity produced scales with the neutron flux, the residence time, and the mass flow,

\[A_{41} = \sigma_c \, \phi \, N_{40} \left( 1 - e^{-\lambda t_{\text{res}}} \right) \tag{57}\]

so a direct-cycle aircraft trails a plume of activated air behind it continuously. The programme studied this. It also means that a fuel element failure releases fission products directly into the exhaust, a different and much less tolerable proposition. The nuclear aircraft safety analysis programme existed to bound these questions, and Menegus and Ring 1958 takes the case of a crash, computing the accidental dispersion of reactor materials and the distance that must be controlled around it. That calculation has no counterpart elsewhere in this series, because no other aircraft in it could contaminate the ground it fell on. Connor 1960 sets out aerospace nuclear safety as a discipline, and the reactor community’s own accident literature, including a maximum credible accident analysis and an account of a zero power reactor accident, supplied the methods.

The fact that matters most in this section is that the direct cycle nuclear turbojet was tested. The Heat Transfer Reactor Experiments at the Idaho site ran a reactor coupled to turbojet engines on the ground and produced thrust from fission. HTRE-1, HTRE-2, and HTRE-3 form the series, with the hazards analysis preceding them and the operation manuals describing the assembly. The programme reached the point of a working nuclear turbojet on a test stand. Thornton and Blumberg 1961 report that the HTREs fulfilled their test goals, in a paper published the year the programme was cancelled.

They also had an accident. The HTRE No. 3 nuclear excursion has a dedicated summary report, and its existence is a reminder that this was a reactor programme with reactor risks conducted at aircraft schedules.

The Indirect Cycle and What It Costs

Keeping the air out of the core costs a temperature drop and a great deal of hardware.

An intermediate loop introduces a heat exchanger between the reactor and the air, and a heat exchanger of effectiveness $\varepsilon$ delivers

\[T_{4} = T_3 + \varepsilon \left( T_{\text{reactor}} - T_3 \right) \tag{58}\]

so the reactor must run hotter than the turbine inlet by the amount the exchanger cannot recover,

\[T_{\text{reactor}} - T_4 = \left( 1 - \varepsilon \right) \left( T_{\text{reactor}} - T_3 \right) \tag{59}\]

Effectiveness is bought with surface area, through the number of transfer units,

\[\mathrm{NTU} = \frac{U A_{\text{HX}}}{\left( \dot{m} c_p \right)_{\min}}, \qquad \varepsilon = 1 - e^{-\mathrm{NTU}} \ \text{for a large capacity ratio} \tag{60}\]

so that pushing effectiveness from 0.9 to 0.95 raises the required area by about thirty percent,

\[\mathrm{NTU} = -\ln \left( 1 - \varepsilon \right) : \quad 2.30 \longrightarrow 3.00 \tag{61}\]

An effectiveness of 0.9 with a compressor discharge at 600 kelvin and a required turbine inlet of 1150 kelvin demands a reactor outlet of

\[T_{\text{reactor}} = T_3 + \frac{T_4 - T_3}{\varepsilon} = 600 + \frac{550}{0.9} = 1211 \ \text{kelvin} \tag{62}\]

sixty kelvin hotter than the direct cycle needs, with the exchanger mass added on top. The mass penalty of a heat exchanger scales with the heat transferred and inversely with the temperature difference driving it,

\[m_{\text{HX}} \propto \frac{P_{\text{thermal}}}{U \, \Delta T_{\text{lm}}} \tag{63}\]

so demanding high effectiveness, which means small $\Delta T$, makes the exchanger large exactly when the mass budget is already spent. The loop that feeds it costs power as well,

\[P_{\text{pump}} = \frac{\dot{m}_{\text{coolant}} \, \Delta p_{\text{loop}}}{\rho_{\text{coolant}} \, \eta_{\text{pump}}} \tag{64}\]

which for a liquid metal at aircraft flow rates is not negligible and which must be supplied from the same reactor, reducing the thrust available by the amount it consumes. The Pratt and Whitney circulating fuel reflector-moderator reactor, whose first volume sets out the design, and the lithium-cooled reactor experiment represent the state that programme reached, which never approached flight hardware. Merriman and Chase 1955 gives the critical mass and power relationship for a reflector-moderated sodium-cooled configuration.

The cycle space was searched more widely than the two named architectures suggest. Schwartz 1952 analyses inert gas cooled reactors for supersonic application, Schwartz 1953 investigates a sodium vapour compressor jet, Alvis and Chessman 1957 examines a gas generator and free turbine arrangement, and the ramjet variants appear in Boppart 1957 and Szekely 1961, with the radiator such a vehicle needs in Larson 1958a. A direct-cycle steam-cooled reactor was even examined for merchant ships in Falkenberry et al. 1959, which shows how far the architecture was carried once it existed. Weights, dimensions, and radiation patterns for a single installation appear in Gaffin 1959. The engine performance studies are extensive, with Larson 1958c, Larson 1958b, advanced characteristics for supersonic aircraft, and nuclear JT-11 turbojet performance all by the same author, alongside the ANP powerplant data compilation that closes the series.

The NACA contribution sits here. Humble et al. 1950 give a preliminary analysis of three cycles for nuclear aircraft propulsion, Doyle 1951 and Doyle 1948 work a mercury-vapour intermediate cycle, and Cavicchi et al. 1959 design a subsonic nuclear logistic aircraft around a helium-cooled reactor. The state of the art was summarized by Finger and Rom 1962 and in the proceedings of the nuclear propulsion conference the same year, by which point the subject had already moved to space.

Decay Heat and the Aircraft That Cannot Be Parked

Shutting down a reactor stops the fission but not the heat.

Fission products continue to decay after shutdown, and the thermal power follows an empirical law of the Way-Wigner form,

\[\frac{P_{\text{decay}}(t)}{P_0} \approx 0.066 \, t^{-0.2} \tag{65}\]

with $t$ in seconds after shutdown. Evaluating for a hundred megawatt core,

\[P_{\text{decay}}(1 \ \text{s}) = 6.6 \ \text{MW}, \qquad P_{\text{decay}}(1 \ \text{h}) = 1.28 \ \text{MW}, \qquad P_{\text{decay}}(1 \ \text{day}) = 0.68 \ \text{MW} \tag{66}\]

An hour after landing the reactor is still producing more than a megawatt. What that means if the cooling stops can be written down directly. With no heat removal the core heats adiabatically,

\[\frac{dT}{dt} = \frac{P_{\text{decay}}(t)}{m_{\text{core}} \, c_{p,\text{core}}} \tag{67}\]

and for a five tonne core of specific heat 500 joules per kilogram kelvin at the one-hour decay power,

\[\frac{dT}{dt} = \frac{1.28 \times 10^{6}}{5000 \times 500} = 0.51 \ \text{kelvin per second} \tag{68}\]

or 31 kelvin per minute, so a core sitting at 1000 kelvin reaches a melting point near 1700 kelvin in

\[t_{\text{melt}} \approx \frac{700}{0.51} = 1.4 \times 10^{3} \ \text{seconds} = 23 \ \text{minutes} \tag{69}\]

Twenty-three minutes from a cooling failure to a melted core, an hour after the aircraft has landed. In a direct-cycle aircraft the cooling medium is the air flowing through the engines, so the airflow must be maintained on the ground, after shutdown, indefinitely, or the core melts. A nuclear aircraft cannot simply be parked. It requires ground equipment to sustain core cooling, and the mass of heat that must go somewhere is comparable to a large industrial furnace running continuously in a hangar.

The time integral makes the point sharper. Total energy released after shutdown up to time $T$ is

\[E_{\text{decay}} = \int_0^{T} 0.066 \, P_0 \, t^{-0.2} \, dt = \frac{0.066 \, P_0}{0.8} T^{0.8} \tag{70}\]

which for a day comes to 73 gigajoules, an average of 850 kilowatts sustained around the clock. No other aircraft in this series carries an operational burden of that kind, and it persists whether or not the aircraft ever flies again. Reactor coolant flow optimization for the Aircraft Shield Test Reactor is the programme’s version of this problem, and the modern treatments of decay heat removal and long-term cooling during transients show it never went away.

Radiation and the Aircraft Itself

The crew is not the only thing that must survive the reactor.

Dose accumulates in materials as well as people, and the failure modes differ. Organic materials cross-link or embrittle, semiconductors accumulate lattice damage and charge, and lubricants polymerize. The accumulated dose at a component is the integral of the local rate over the mission,

\[D_{\text{component}} = \int_0^{t_{\text{mission}}} \dot{D}(\mathbf{r}, t) \, dt \tag{71}\]

The damage mechanism in a solid is displacement rather than ionization, and it is measured in displacements per atom accumulated over the fluence,

\[\text{dpa} = \sigma_d \int_0^{t} \varphi_n \, dt = \sigma_d \, \Phi_n \tag{72}\]

so a component’s life is set by a fluence limit rather than by a dose rate,

\[t_{\text{life}} = \frac{\Phi_{n,\text{limit}}}{\varphi_n} \tag{73}\]

and because the components are distributed through the airframe rather than concentrated in one shielded volume, they cannot all be behind the shadow shield. The work therefore had to develop Fries 1958 and an entire design practice for electronic systems intended to work in nuclear aircraft, restated the following year as a major influence on such designs. The material behaviour underneath it was catalogued systematically. Radiation damage to elastomers, lubricants, fabrics, and plastics is a title that conveys the breadth of the problem, with plastic laminates, organic lubricants and polymers, and the behaviour of fuels and lubricants in dynamic test equipment under irradiation treated separately, and a bibliography of effects on aluminium, elastomers, and lubricants collecting the rest. Control system components have their own damage study, the field held semiannual symposia, and the results were gathered into a handbook. An aircraft is mostly organic materials and precision mechanisms, and a reactor is hostile to both.

That subject became an industry once electronics moved into space, and the mechanisms the ANP engineers were discovering empirically now have names and models. Displacement damage in semiconductors is reviewed by Ha and Kim 2025, single-event effects and the hardening practices that answer them by Aguiar and Martinella 2026 and Liu et al. 2025, with circuit-level hardening in Kumar et al. 2025 and the charge transport underneath it in Mendes and Tomal 2025. The problem the programme met in a bomber is the problem a satellite designer now meets in orbit. It is answered by radiation hardening as an engineering discipline, and the programme’s work is an early instance of it.

The Crew and Their Permitted Dose

The dose limit, the boundary condition on the shield calculation, is a choice and not a physical constant.

Mission dose is the product of rate and duration,

\[D_{\text{mission}} = \dot{D} \, t_{\text{mission}} \tag{74}\]

so an endurance mission is precisely the case where a modest dose rate becomes unacceptable. The mission that justifies the aircraft is the mission that makes its shielding hardest. A four-hour sortie at a given dose rate is a quarter of the dose of a sixteen-hour one, and nuclear propulsion was argued for flights measured in days.

The limit was not merely an engineering parameter to the programme either. A medical advisory panel was convened under NEPA. Among its subcommittee reports sits an evaluation of the psychological aspects of asking aircrew to fly a reactor. Such a document is unusual in an aeronautical record, and it indicates how the problem was understood at the time. The somatic effects were pursued in parallel. Leverett and Beasley 1960 investigates lens opacity in personnel operating a portable reactor, cataract being the effect that appears first at doses below those that produce anything else measurable.

Choosing $\dot{D}_0$ therefore chooses the shield mass, through the logarithm,

\[m_{\text{shield}} \propto \ln \left( \frac{1}{\dot{D}_0} \right) \tag{75}\]

The sensitivity is best written as a derivative, since that is the quantity a programme manager would want,

\[\frac{\partial m_{\text{shield}}}{\partial \ln \left( 1 / \dot{D}_0 \right)} = \frac{\rho_s A}{\mu} = \frac{11{,}340 \times 14.1}{79.4} = 2.01 \times 10^{3} \ \text{kilograms per e-fold} \tag{76}\]

so each factor of $e$ in permitted dose is worth two tonnes, and because the dependence is logarithmic, accepting ten times the dose saves only one tenth-value layer of material, which is 2.9 centimetres of lead and about four and a half tonnes on the geometry above. Relaxing the crew dose limit by a factor of ten buys back about two and a half percent of the aircraft. The asymmetry matters, because it means the programme could not have been rescued by accepting a more dangerous aircraft. The exponential that makes shielding effective also makes it insensitive to how much risk one is willing to impose on the crew.

The Flight Test Record

One aircraft flew and it was not the X-6.

The NB-36H, a B-36H-20-CF with serial 51-5712 that had been damaged by a tornado at Carswell Air Force Base on 1 September 1952, was rebuilt as the Nuclear Test Aircraft. It carried the Aircraft Shield Test Reactor, abbreviated ASTR, a one megawatt reactor of about 16,000 kilograms, hung in a bomb bay on a hook so it could be lowered into a shielded pit between flights. Water served as moderator and coolant and dumped its heat overboard through water-to-air exchangers, and in that sense the NB-36H entry calls the reactor air-cooled. The reactor never powered the aircraft. Its purpose was to be a source, and the aircraft’s purpose was to measure what that source did to a crew compartment and to the equipment around it.

The crew section was rebuilt in lead and rubber at a mass reported as eleven tons in one account and twelve in another, with leaded glass in the windows. The aircraft flew 47 times between 17 September 1955 and March 1957, accumulating 215 flight hours of which the reactor was operated during 89.

The dose the crew accumulated is computable from the reported operating time and is the quantity the exercise existed to bound,

\[D_{\text{crew}} = \dot{D}_{\text{shielded}} \, t_{\text{reactor}} = \dot{D}_{\text{shielded}} \times 89 \ \text{hours} \tag{77}\]

so an allowance of fifty millisieverts across the whole programme sets the shielded rate at

\[\dot{D}_{\text{shielded}} = \frac{0.05}{89} = 5.6 \times 10^{-4} \ \text{sieverts per hour} \tag{78}\]

That rate is the design point the crew shield was built to, and the flights were flown to confirm it.

The measurements are the programme’s most valuable output and they are documented. The reactor was calibrated, its fast neutron spectra measured, and it was operated in conjunction with the Tower Shielding Facility so that airborne results could be compared against a ground installation where the geometry was known exactly. The Tower Shielding Facility required its own critical experiments and a conceptual design study, and multilayer shield experiments ran alongside. Comparing measured against calculated dose was the point, since a shield design method validated against flight is worth more than one that is not.

What the flights established is that the shielding worked. The crew was protected from the reactor’s radiation. What they also established, and what mattered more, is that this was true for a one megawatt source in an aircraft that carried nothing else, and that the shield for a hundred megawatt propulsion reactor would be the mass computed above.

The NB-36H was scrapped, the X-6 was never built, and the programme was cancelled in March 1961.

Comparison With Ground Prediction

The X-6 inverts the usual relationship, because there was no flight against which to check the prediction, and the prediction is all there is.

For every other aircraft in this series the interesting question is where the ground facilities were wrong. Here the ground facilities are the entire record. The Aircraft Reactor Experiment, the Heat Transfer Reactor Experiments, the Tower Shielding Facility, and the NB-36H measurements form a body of validated engineering that was never assembled into an aeroplane, and on a fair assessment the prediction was largely right and the programme was cancelled for reasons the prediction supported instead of contradicting.

One check is available, and it should be performed, because nowhere else in this article can the derivation be tested against hardware that existed. Apply the shield calculation to the ASTR in the NB-36H rather than to a propulsion reactor.

The source is a hundred times weaker and the separation is greater, so the unshielded rate at the crew station scales as

\[\dot{D}_{\text{ASTR}} = \dot{D}_{100} \left( \frac{P_{\text{ASTR}}}{P_{100}} \right) \left( \frac{r_{100}}{r_{\text{ASTR}}} \right)^{2} = 9.84 \times \frac{1}{100} \times \left( \frac{10}{15} \right)^{2} \tag{79}\] \[\dot{D}_{\text{ASTR}} = 0.044 \ \text{grays per second} = 157 \ \text{grays per hour} \tag{80}\]

Holding the crew to fifty millisieverts across the 89 hours of reactor operation demands

\[\mathcal{A} = \frac{157}{5.6 \times 10^{-4}} = 2.8 \times 10^{5}, \qquad x = \frac{\ln \left( 2.8 \times 10^{6} \right)}{0.794} = 18.7 \ \text{centimetres} \tag{81}\]

The NB-36H’s crew section was lined with lead and rubber as a whole, but the direct beam from a reactor behind the crew falls on its rear face, so the area taken here is the compartment cross-section and not its surface. Taking six square metres,

\[m = \rho_s A x = 11{,}340 \times 6.0 \times 0.187 = 1.27 \times 10^{4} \ \text{kilograms} \tag{82}\]

Against a reported crew shield of eleven to twelve tons. Repeating the calculation with the far more permissive occupational allowance of the 1950s, about 0.3 sieverts, gives 16.4 centimetres and 11.2 tonnes. The two bracket the reported figure when its tons are read as metric tonnes. The method used throughout this article reproduces the one aircraft in it that flew. That agreement is the closest thing to validation available for a programme that never built its aeroplane, and the propulsion-reactor numbers above deserve to be taken seriously because of it.

The one place where flight added something the ground could not is the air-scattering term. A reactor on a tower over a field is not a reactor at altitude in a moving aircraft, and the scattered dose depends on the density and geometry of the air around the source. The NB-36H therefore flew instead of sitting on a stand, and Edwards 1954 accordingly addresses altitude and flight speed as well as geometry.

The deeper comparison is between what the programme predicted about itself and what happened to it. The Lexington Project in 1948 said fifteen years and at least a billion dollars. The programme ran fifteen years, spent about a billion dollars, and was cancelled. The feasibility study was correct about the cost and the schedule and wrong only in assuming that a correct cost and schedule would be paid.

What the Data Changed

The aircraft was never built and the programme’s output was substantial. Making that case is the purpose of this article.

The most durable result is a reactor. The Aircraft Reactor Experiment, abbreviated ARE, run at Oak Ridge in 1954, was the world’s first molten salt reactor, using a circulating fluoride salt as both fuel and coolant. It was designed for a high power density and a high outlet temperature, as an aircraft requires, and it ran successfully. A molten salt core also runs near atmospheric pressure.

That combination merits a number, because it accounts for the whole of the concept’s appeal and explains why the concept outlived the aircraft. A water-cooled reactor must be pressurized to keep its coolant liquid, and the saturation pressure climbs steeply with temperature,

\[p_{\text{sat}}(T) \approx p_c \exp \left[ \frac{\Delta H_{\text{vap}}}{R} \left( \frac{1}{T_c} - \frac{1}{T} \right) \right] \tag{83}\]

so a pressurized water reactor at 600 kelvin sits near 15.5 megapascals while a molten fluoride salt at 1000 kelvin has a vapour pressure below a kilopascal, a ratio of

\[\frac{p_{\text{PWR}}}{p_{\text{salt}}} \approx 1.5 \times 10^{4} \tag{84}\]

The vessel mass follows the pressure directly, since a thin spherical shell of radius $R$ holding pressure $p$ at allowable stress $\sigma$ requires

\[t = \frac{p R}{2 \sigma} \quad \Longrightarrow \quad m_{\text{vessel}} = 4 \pi R^{2} \rho t = \frac{2 \pi \rho \, p R^{3}}{\sigma} \tag{85}\]

A molten salt core carries a second property that mattered less to the aircraft than it does now. Because the fuel is dissolved in the coolant, thermal expansion of the salt removes fuel from the core, so the reactivity feedback is strongly negative,

\[\alpha_T = \frac{\partial k_{\text{eff}}}{\partial T} < 0, \qquad \delta k = \alpha_T \, \delta T \tag{86}\]

and a power excursion is self-limiting without any control action at all. The pressure vessel mass is proportional to the pressure, so a molten salt reactor’s vessel is four orders of magnitude lighter than a water reactor’s at the same size. For an aircraft that is decisive, and for a ground station it is merely attractive, yet attractive was enough for the idea to survive in a place it was not invented for. Its operation and Bettis et al. 1957b document the experiment, the hazards summary preceded it, the components of its fused-salt and sodium circuits are described in detail, and it was disassembled and examined afterward. Oak Ridge’s aircraft nuclear power plant designs give the surrounding context.

The pivot from aircraft to civilian power is visible in the record as it happens. McPherson 1957 is titled Molten Salts for Civilian Power and appeared while the aircraft programme was still running, Briant and Weinberg 1957 argues molten fluorides as power reactor fuels, Grimes et al. 1958 sets out the chemistry, and by MacPherson 1960c the concept is being evaluated for a ten-year plan that has nothing to do with aeroplanes. The people who built a reactor for an aircraft spent the late 1950s explaining that it would be more useful somewhere else, and they were right.

That reactor is the ancestor of a technology now under active commercial development. The molten salt reactor is a serious contemporary subject, and the modern literature is treated below. An aircraft programme that produced no aircraft produced a reactor concept that outlived it by seventy years and is being commercialized as this is written. That is not a consolation prize. It is a better return than most flown programmes achieve.

The second consequence is a design discipline. Shielding analysis as a computational activity, radiation-hardened components, and the practice of validating shield codes against measurement are all recognizable as ANP outputs. When nuclear propulsion returned as a subject it returned for space and not for air, and it inherited these tools directly. The Nuclear Engine for Rocket Vehicle Application programme, abbreviated NERVA, and its nuclear thermal rocket successors, the radiation shielding weight problem in space, and the symposia on protection against radiations in space are the same discipline redirected. That redirection was already under way while ANP ran. Schreiber 1956 describes the Los Alamos nuclear rocket programme that became Rover and then NERVA. The crewless branch left a paper trail too, and the Pluto programme progress reports document the nuclear ramjet in period.

The Soviet effort was watched. Butz 1959 gives an open-literature assessment of Soviet nuclear plane concepts written while both programmes were live. For the American side, the institutional summary is Air Force Nuclear Propulsion. The Plum Brook hazards work shows the transition in progress at NASA.

The third is a negative result that was correct. No crewed aircraft has since been built around air-breathing nuclear propulsion, and the one later air-breathing nuclear vehicle publicly claimed, the Russian Burevestnik cruise missile, carries no crew. The Soviet Union flew its own testbed, the Tu-95LAL, and reached the same conclusion. The Project Pluto nuclear ramjet, which dispensed with the crew and therefore with most of the shield, is the exception that proves the rule, since removing the crew removes the constraint this article is about.

The Contemporary Literature

Cluster	Records
Shielding materials, space shielding and reactor shields in general	897
Nuclear ramjets, rockets and space reactors	870
Molten salt and circulating fuel reactors	836
Compact, mobile and modular reactors	549
Hydrogen, synthetic fuel and other routes to long range	490
Attenuation physics, buildup and radiation transport	414
Decay heat, kinetics and reactor safety	400
Shield design, optimisation and weight	348
Reactor fuel, cooling and the wider nuclear literature	301
The nuclear aircraft and its programme record	260
Radiation effects on materials, components and electronics	217
Crew dose and the human limit	65
Similarity, information and the design of experiments	6
Total	5,653

The subject did not end. It moved, and it split into three descendants that no longer resemble one another.

Molten Salt Reactors

The Aircraft Reactor Experiment’s direct line is now a substantial commercial and academic field. Holcomb 2025 treats thermal-spectrum molten salt breeder fuel cycles, McFarlane 2024 argues that the fuel cycle rather than the reactor is the hard part, and Creasman et al. 2024 compute fuel depletion for a molten salt demonstration reactor. Modelling work includes Fischer and Bureš 2024, whose subject is the Molten Salt Reactor Experiment, the ARE’s successor at Oak Ridge, and Mochizuki 2024a on load following. The chemistry that makes a circulating fuel salt difficult is pursued by Cheng et al. 2025 on noble metal fission product aggregation and Niu et al. 2024 on extracting molybdenum-99 from fuel salt, with Yilmaz et al. 2025a on thorium fuelling and Mishra et al. 2024b supplying an irradiated fuel salt data library. Dunkle and Bogetic 2026 address accident behaviour. The physical properties of the salts themselves, which the Oak Ridge chemists established by measurement, are now being computed from first principles by Li et al. 2026b. Jiang et al. 2026 study the tritium that a fluoride salt inevitably generates, and Liu and Chen 2026 follow the salt outside the reactor entirely, as a lubricant. Reactor kinetics with a circulating fuel, where the delayed neutron precursors leave the core before they decay, is a peculiarity of this reactor type that the ARE encountered first and that Chen et al. 2025b still treat. A 1954 aircraft reactor experiment is the origin of all of it.

Shielding

The shield-mass problem this article derives is now solved computationally instead of empirically, but it is the same problem. Ahmed 2026a reviews neutron shielding mechanisms and materials, Liu et al. 2026a present a dual-stage shielding optimization method, and Huang et al. 2025b optimize the shield of a heat pipe cooled reactor, a compact mobile reactor and so the same class of problem as an aircraft. Lee and Cho 2025 address the question this article calls the boundary condition, namely how to set the radiation target level that the rest of the design then follows from.

The modern statement of the problem replaces the closed-form estimate used above with a constrained optimization over a layered geometry,

\[\min_{\mathbf{x}} \ \sum_{j} \rho_j A_j x_j \quad \text{subject to} \quad \dot{D}\left( \mathbf{x} \right) \le \dot{D}_0, \quad x_j \ge 0 \tag{87}\]

with the dose evaluated by transport rather than by an attenuation law. Transport makes the problem tractable to solve well and intractable to solve by hand. The gain over a hand estimate comes from letting the layer thicknesses vary independently and from exploiting the fact that each material attenuates both radiations,

\[\dot{D} \left( \mathbf{x} \right) = \dot{D}_\gamma \prod_j B_j e^{-\mu_j x_j} + \dot{D}_n \prod_j e^{-\Sigma_{R,j} x_j} \tag{88}\]

the coupling this article set aside when it treated the lead and the lithium hydride separately and called their sum an upper bound.

Shielding materials are being developed at a rate the programme would have envied, and the search is now for composites that combine attenuation with structure rather than for a single dense element. Ozdemir et al. 2025 develop a ternary gamma-shielding composite, Sayyed et al. 2025, Gomaa and El-Tayebany 2026, and Yavuzkanat and Şahmaran 2026 evaluate glass systems where the shielding and the structural role are the same material, and Jiang 2025 pursues carbon-bearing neutron shields, in which the lithium hydride idea reappears with the hydrogen bound differently. Facility-scale optimization appears in Syarip et al. 2025 and Sunil 2025.

Materials work continues along the lines the programme opened. Bhardwaj et al. 2024 fabricate neutron-absorbing metal hydride ceramic matrix composites, a modern form of the same hydride shield, and Stone et al. 2024, Khan et al. 2025a, and Sekkat et al. 2026 develop composite and additively manufactured shields. Han et al. 2025a and Han et al. 2025c address space reactor shielding, with Oğul et al. 2026 treating a small modular reactor. The crewed-vehicle version of the problem, the X-6’s problem with the source moved outside, appears in DeWitt and Benton 2024 on secondary proton buildup, Matthiä and Berger 2024 on lunar surface exposure, and Yıldırım and Opçin 2026 on multilayer composites.

Nuclear Propulsion Where the Shield Is Affordable

Nuclear propulsion survived in the two places where the constraint this article derives does not bind, namely vehicles with no crew and vehicles where nothing else will do.

Space is the second case. Alnuaimi and Kim 2026 assess a liquid uranium-manganese nuclear thermal rocket, Guilbaud et al. 2024 restudy the KIWI-B-4E core from the Rover programme with modern methods, and Aueron and Thomas 2024 examine electric-pump-fed nuclear thermal propulsion. Nuclear electric systems appear in Ma et al. 2026 and mission studies in Ancona et al. 2025. Duan et al. 2026 analyse the reactivity safety of an air-cooled nuclear thermal propulsion reactor, the direct air cycle returning under a different name for a different vehicle.

Surface and orbital power is a further branch, and Smith et al. 2026a analyse a Kilopower-class reactor for lunar use while Zhang et al. 2026f model the heat pipe startup such a system depends on. Marine propulsion never stopped, and Delgarm et al. 2025 optimize a naval plant while Kim and Lee 2026 explicitly modernize the ML-1 architecture, which was a transportable military reactor contemporary with ANP. Every one of those applications shares the X-6’s constraint and relaxes exactly one part of it, since a lunar reactor has no crew nearby, a ship can carry the shield, and a transportable reactor need not fly.

The microreactor is the other descendant, and it inherits the X-6’s real problem, a reactor that must operate away from the infrastructure a power station enjoys. Parisi and Arafat 2026 describe the MARVEL microreactor, Domingos et al. 2026 and Rangel et al. 2026 treat fuel choices including designs avoiding enriched uranium, and Abdussami et al. 2025, Kim and Macfarlane 2026, and Shobeiri et al. 2025 weigh the economics that decide whether any of it happens. Accident source terms and tolerant fuels are Sun et al. 2025d and Elkhawas et al. 2025, with materials in Islam and Haque 2025 and Lan et al. 2024. The proliferation dimension, which the X-6 raised by requiring highly enriched fuel in a compact core and which no other aircraft in this series raises at all, is treated by Mitsuboshi and Sagara 2025 for small modular reactors, Bolukbasi and Margulis 2026a through fuel cycle composition, and Chong and Sagara 2025 through burnup strategy. Isotope production as a use for the flux appears in Chandler et al. 2025.

What Took Its Place in Aviation

The question the X-6 was built to answer, how to fly without carrying the energy as chemical fuel, is live again and is being answered differently.

Hydrogen is the leading candidate and it shares a structural character with nuclear propulsion, in that the energy is cheap and the container expensive. Li 2024 reviews hydrogen-powered aircraft, Jagtap et al. 2024 and Wahler et al. 2025 work the conceptual design and the aerostructural trade, Sasi et al. 2025 treat hydrogen and ammonia turbofans, Lu et al. 2025 recover exhaust heat in a cryogenic installation, and Zhang et al. 2026a address crashworthiness, the hydrogen version of the question the nuclear aircraft safety programme asked about dispersing a core. Batteries are the other candidate, and keeping the cells of an aircraft battery in balance is a research subject, as Peng et al. 2024a show. The hydrogen case is surveyed by Gopalasingam et al. 2025, the tank and its ballast consequences are codesigned by Antonakis and Glenis 2026, the thermodynamics of the stored liquid are treated by Li et al. 2026c, and the drop-in alternative that avoids the tank entirely is the synthetic fuel of Bardon et al. 2025 and Quiroz et al. 2025. The same argument is being had at sea, where the mass penalty is affordable, in Liu and Fu 2025.

The mission itself has also been answered without any of this. The X-6 existed to keep an aircraft airborne indefinitely, and that requirement is now met by vehicles with no crew to shield and very little mass to lift. Jung et al. 2025 analyse the endurance of a solar-powered high-altitude unmanned aircraft, which achieves persistence by having almost no energy demand rather than by carrying an enormous energy supply, with the structural problems such an airframe meets instead in Sampath and Kattimani 2025. A programme that spent a billion dollars to remove the fuel constraint was eventually answered by removing the crew and most of the aircraft, a solution nobody in 1946 would have accepted and nobody in 2026 finds surprising.

Every one of these is a fixed-overhead problem of the kind this article derives for the shield. The general form can be written down, and the X-6 is one instance of it. Let an aircraft carry a fixed installation of mass $m_{\text{fix}}$ that enables a mission but performs no work during it. The payload available is what remains,

\[m_{\text{payload}} = m_{\text{gross}} - m_{\text{empty}} - m_{\text{fix}} - m_{\text{consumed}} \tag{89}\]

and the configuration is viable only while that difference is positive and large enough to justify the aircraft,

\[\frac{m_{\text{fix}}}{m_{\text{gross}}} < 1 - \frac{m_{\text{empty}}}{m_{\text{gross}}} - \frac{m_{\text{payload,min}}}{m_{\text{gross}}} \tag{90}\]

For hydrogen the fixed installation is the tank, characterized by a gravimetric index,

\[\eta_g = \frac{m_{\text{H}_2}}{m_{\text{H}_2} + m_{\text{tank}}} \quad \Longrightarrow \quad \frac{m_{\text{tank}}}{m_{\text{H}_2}} = \frac{1 - \eta_g}{\eta_g} \tag{91}\]

so an index of 0.35 costs 1.86 kilograms of tank per kilogram of fuel while an index of 0.7 costs 0.43, and the entire commercial argument turns on which end of that range is achievable. A cryogenic tank, like a shield, has a mass that does not shrink in proportion to the mission and that must be carried whether or not it is doing anything at that moment. The X-6’s arithmetic is a special case of a general pattern in aircraft design, and recognizing it as such is worth more than the aircraft would have been.

Shielding materials, space shielding and reactor shields in general

The largest cluster, and the shield considered as a material. Concrete, glass, metal hydride, polymer composite and heavy-metal shields, the general reactor shielding texts, and the shielding of crewed spacecraft. 95 titles concern shielding glasses and 74 concretes, mortars, cements or bricks, which is the shield treated as a materials subject rather than as a design weight.

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2020] [Stamatelatos 1975] [Stamatelatos and La Bauve 1978] [Stamatelatos and LaBauve 1977] [Stankovic 1970] [Stein et al. 1967] [Stephens 1965] [Stephens 2006] [Stern 1953] [Stevens 2022] [Stewart and Buykx 1988a] [Stewart and Buykx 1988b] [Stewart et al. 2024b] [Stone et al. 2024] [Study of Plasma Radiation 1967] [Study of Plasma Radiation 1968] [Study the Space Radiation 2024] [Stults and Karpius 2021] [Subbaiah and Sunny 2001] [Sun et al. 2025c] [Sutherland 1964] [Suvorov and Fedorenko 1969] [Svikis 1963] [Svikis 1964] [Swami et al. 2020] [Sweeney and Fry 1986] [Synthesis Structure and Gamma-Ray 2024] [Szilvasi 1965a] [Szymendera 1965] [Tanaka et al. 1972b] [Technical Specifications 1978] [Technical Specifications 1982] [Technical Specifications 1986] [Terlizzi and Labouré 2022] [Terlizzi and Labouré 2023] [Tharwat et al. 2024] [Thiele 1967] [Thiele and Bunch 1968] [Thomsen] [Thomsen et al. 2015] [Thomson and Schwab 1969] [Tobias 1980a] [Tobias 1980b] [Tochilin 1970] [Tomlinson et al. 1962] [Torczynski and Gross 1988] [Toto 2026] [Townsend 2005] [Townsend et al. 1989] [Tripathi et al. 2008] [Trubey 1974] [Trubey 1982] [Tsoulfanidis 1982] [Tsoulfanidis 1984] [Tsypin 1967] [Tsypin et al. 1965] [Tuscharoen and Kaewkhao 2014] [Tveten 1971] [Uematsu and Yamamura 1974] [Umemura et al. 1993] [Unagar et al. 2025] [Unlu and Ozkara 2026] [National Institute of Standards and Technology 1994] [Urabe et al. 2003] [Van Houten 1967] [Varghese et al. 2023] [Vernon 1957] [Verschuur 1971] [Veselkin et al. 1969c] [Veselkin et al. 1969b] [Veselkin et al. 1969a] [Veselkin et al. 1974] [Vinayak et al. 2024] [Vira et al. 2023] [Voskresenskii et al. 1974] [Wagner et al. 1988] [Waldrop 1958] [Wang 1997] [Wang et al. 2013a] [Wang et al. 2015b] [Wang et al. 2016a] [Wang et al. 2021] [Washburn et al. 2014] [Washburn et al. 2015] [Wattar 2024] [Watts 1969] [Weber 1963] [Welch 1961b] [Welch 1961a] [Welch 1963] [Welch 1971] [Welch 1974] [Welch et al. 1961] [Wells and Warman 1973] [Werneth et al. 2013] [Westbrook and DeVore 1995] [Weyland et al. 1979] [Wilson et al. 2003] [Winroth et al. 2020] [Wishau et al. 2003] [Witherspoon 1965] [Wrapp 2018] [Wrights 1975] [Wu et al. 2019a] [Wu et al. 2020b] [x-Ray and Gamma-Ray Shielding 1966] [xiao and Li 2023] [Xu et al. 2016] [Yamamoto and Tsuchiya 1962] [Yan et al. 2025] [Yang et al. 2026a] [Yanko and Ginn 1961] [Yannitell 1989] [Yannitell and Coughlin 1988] [Yarar and Bayülken 1994] [Yastrebinsky et al. 2021] [Yavuzkanat and Şahmaran 2026] [Yıldırım and Opçin 2026] [Yinusa et al. 2024] [Yinusa et al. 2026] [Yorgun 2026] [Youell et al. 1964] [Yvars et al. 1975] [Yılmaz et al. 2021] [Zagar and Ravnik 2002] [Zaitsev et al. 1964] [Zali et al. 2017] [Zapp 2007] [Zaritsky et al. 2011] [Zebardast and Saray 2025] [Zeisser 1964] [Zeitlin 2019] [Zeitlin 2020] [Zeitlin 2021] [Zhang et al. 2017] [Zhang et al. 2020c] [Zhang et al. 2020a] [Zhang et al. 2025b] [Zhang et al. 2025c] [Zhang et al. 2026c] [Zhao et al. 2024] [Zhou et al. 2024] [Zohuri 2022] [ÇAĞLar 2025] [Özdemir 2020] [Özdemir and Yılmaz 2018] [Özdemir et al. 2017] [Ølgaard 1959] [Ünal and Durmuş 2025] [Şengül and Akkurt 2024] [Žagar et al. 2004]

Nuclear ramjets, rockets and space reactors

The descendant in which the shield is affordable. Nuclear thermal rockets and the Rover and NERVA engines, nuclear electric propulsion, the Kilopower and fission surface power reactors, and the Tory nuclear ramjet reactors of Project Pluto. 394 titles concern the nuclear thermal rocket and 154 nuclear electric propulsion, against 45 on the nuclear ramjet, the air-breathing engine the article treats as the exception that proves the rule.

870 records. [A Plan to Qualify 1993] [Division of Reactor Development, AEC 1962] [Ailman et al. 1966] [Akyuzlu et al. 2020] [Al Zaman and Monira 2023] [Alawneh et al. 2022b] [Aldemir et al. 2004] [Allen 1993b] [Allen et al. 1991] [Allen et al. 1992] [Allen et al. 1993a] [Allen et al. 1993b] [Alnuaimi and Kim 2026] [Alnuaimi et al. 2024] [Ambrus et al. 1984] [Ames and Lutz 2021] [Amiri et al. 2007] [An Historical Collection 1992] [Anderson et al. 2023] [Angeliu et al. 2006] [Angeliu et al. 2007] [Angelo and Buden 1982] [Anghaie and Harris 1993] [Anghaie et al. 1993] [Anish et al. 2018] [Arias 2016] [Ashe and Otting 1993] [Atkins and Lillie 1983] [Pluto Program Bi-Monthly Progress 1957] [Atwell 2005] [Aueron and Thomas 2019] [Aueron and Thomas 2024] [Badavi et al. 2010a] [Badavi et al. 2010b] [Ballard 2006] [Banjac and Heger 1994] [Bannova and Gulacsi 2024] [Barattino 1985] [Barbieri and Lampert 1961] [Barghouty 2007] [Barnett 1991] [Barrett 1964] [Barth and Pike 2022] [Bartine and Engle 1982] [Bauer and McLafferty 1968] [Beale 1961] [Beck 1993] [Beck et al. 1992] [Beck et al. 1993] [Bednarczyk 1989] [Belair et al. 2013] [Belian and Jones 2024] [Bender and Stahl 2023] [Benensky et al] [Bennett 1989] [Bennett 1991a] [Bennett 1991b] [Bennett 1992] [Bennett and Miller 1992] [Benton et al. 2012a] [Benton et al. 2012b] [Berg and Disney 2004] [Berman 1987] [Berman 1992] [Beveridge 1968] [Beveridge 2016] [Bhattacharyya 1993] [Bhattacharyya 2002] [Bhattacharyya 2011] [Bilardo 2026] [Bleeker 1993a] [Bleeker 1993b] [Bloomfield and Sovie 1991] [Bokor et al. 1991] [Bokulic et al. 1993] [Boppart 1957] [Borowski 1988] [Borowski 1994] [Borowski 2003] [Borowski et al. 2012] [Borowski et al. 2014] [Bowman et al. 2007] [Boyer 1972] [Boylston et al] [Brengle et al. 1993] [Briggs et al. 2016] [Brooks et al] [Brown 1965] [Brown and Coates 1966] [Bucknell 2015] [Buden 1990] [Buden 1992b] [Buden 1992c] [Buden 1992a] [Buden and Angelo 1981] [Buden and Garrison 1984] [Buden et al. 1993b] [Buden et al. 1993a] [Budnick 1965] [Buksa and Houts 1992] [Buksa et al. 1991] [Bulman 2011] [Bulman and Neill 2000] [Bulman et al. 2001] [Bulman et al. 2002] [Burns and Johnson 2020] [Burns et al. 2022b] [Busby et al. 2007] [Bussard 1956] [Bussard 1958] [Bussard 1961] [Byers 1991] [Bythrow et al. 1993] [Caffrey] [Caffrey 2016] [Caffrey 2018] [Caffrey et al. 2015] [Calderoni 2024] [Cameron and Herbert 1993] [Capo 1962] [Carpenter 1972] [Carter and Bunch 1987] [Casal 1970] [Casal and Pitts 1971] [Cataldo and Borowski 1998] [Gulf Radiation Technology, San Diego, Calif. et al. 1970] [Chaiken 2019] [Chapter 15. Futuristic Systems 2020] [Charmeau et al. 2009] [Cheu et al. 2024] [Clark 1991d] [Clark 1991c] [Clark 1991a] [Clark 1991b] [Clark and Miller 1991] [Clark et al. 1992a] [Clark et al. 1993a] [Clark et al. 1993b] [Clark et al. 1994] [Cline et al] [Clough et al. 2006] [Connor 1960] [Cook 2005] [Coomes and Dagle 1990] [Coomes and Dagle 1991] [Coomes and Dagle 1992] [Coomes et al. 1985] [Coomes et al. 1986] [Coomes et al. 1988] [Cooper 1960] [Cooper 1968] [Corban and Wagner 1993] [Corliss and Schwenk 1971] [Corrington 1968] [Craft and King 2010] [Craft et al. 2009] [Craven et al. 2014] [Culbreth and Gonzalez 2019] [Culver and Rochow 1993] [Culver et al. 1992] [Curran et al. 1990] [Czaplewski] [Dagle et al. 1992b] [Dagle et al. 1992a] [Dailey et al. 1990] [Dailey et al. 1992] [Damerval 1970] [Davis 1965] [Davis 1984] [DeHart 2021a] [DeHart 2021b] [DeHart 2022] [DeHart et al. 2022] [DeHart et al. 2023] [DeHart et al. 2025] [Deininger and Nock 1990] [Deininger and Vondra 1987] [Determan et al. 1983] [DeWitt and Benton 2024] [Difilippo 1994] [Dill et al. 1991] [Disney et al. 1970] [Ditz and Shukay 1961] [Doherty 1991] [Doherty 1992] [Doherty 1993a] [Doherty 1993b] [Doherty and Holcomb 1993] [Doherty et al. 1991] [Downey et al. 2004] [Downey et al. 2005] [Duan et al. 2023] [Duan et al. 2026] [Duchek et al] [Dudkin et al. 1992] [Dudzinski and Borowski 2002] [Dugan and Diaz 1988] [Dugan et al. 1993] [Dujarric et al. 2013] [Duke and Houghton 1966] [Durham 1968] [Durham 1969] [Durham et al. 1991] [Dyson et al] [Dyson et al. 2008] [Edelbaum 1963] [Edens et al. 2020] [Ehresman and Gunn 2003] [El-Genk 2010] [El-Genk 2023] [El-Genk 2024] [El-Genk and Hoover 1993] [El-Genk and Metzger 1994] [El-Genk and Xue 1992b] [El-Genk and Xue 1992a] [El-Genk et al. 1992] [El-Genk et al. 1993a] [El-Genk et al. 1994a] [Electric Thrusters for Transportation 2004] [Elliott 2006] [Emrich 1993] [Emrich 2014] [Emrich 2016d] [Emrich 2016h] [Emrich 2016f] [Emrich 2016g] [Emrich 2016b] [Emrich 2016e] [Emrich 2016a] [Emrich 2017] [Emrich 2023d] [Emrich 2023e] [Emrich 2023g] [Emrich 2023b] [Emrich 2023f] [Emrich 2023i] [Emrich 2023h] [Emrich 2023a] [Emrich and Kirk 2006] [Emrich and Young 1992] [Emrich et al. 2012] [Emrich et al. 2015] [Engle et al. 1971b] [Engle et al. 1971a] [English 1991] [Ernest 1982] [Ernst 1981] [’ Eyes ‘ 1958] [Fang et al. 2022b] [Farbman and Thompson 1975] [Feller and Joyner 1999] [Felten and Dunn 1993] [Fensin et al. 2006] [Ferg 1973] [Finger 1965] [Finger 1969] [Finnigan 1959] [Finnigan 1960b] [Finnigan 1960a] [Finnigan 1962] [Fittje et al. 2015] [Floyd et al. 2019] [Forsley et al] [Forsley et al. 2022] [Fortini and Tuffias 1993] [Friedlander 1966] [Friesen 1995] [Frisbee and Hoffman 1993] [Frisbee et al. 1991] [Frisbee et al. 1993] [Frisbee et al. 1994] [Frischauf and Hamilton 2004] [Frischauf et al. 2006] [Frye et al. 2005] [Funk and Lombardo 1968] [Gabriel and Helms 1970] [Gabriel and Helms 1974] [Galecki and Patterson 1987] [Gallup 1990] [Garrison and Nock 1982] [Gatsonis et al. 1993] [Gedeon and Morey 1987] [George 1991] [George 1993] [Ghossein et al. 2026] [Gibson and Schmitz 2020] [Gibson et al. 2014] [Gibson et al. 2017] [Gibson et al. 2018a] [Gibson et al. 2018b] [Gibson et al. 2020] [Glenn and Bulman 1999] [Goldberg 1964] [Graves 1972] [Grier et al] [Guilbaud et al. 2024] [Gunn 1989] [Gunn 1990] [Gunn and Hundal 1994] [Gunn et al. 1993] [Gustafson 1993] [Hack et al. 1990] [Hadley 1959] [Hadley 1963] [Haffner 1965] [Haffner 1969] [Hall and McCann 1986] [Hallet 1966] [Hamilton et al. 2023] [Hamilton et al. 2024] [Hampel 1960] [Hampel 1962] [Hampel and Goldberg 1962] [Hampel and Moran 1962] [Han et al. 2025a] [Harnack et al] [Harris et al. 2017] [Harrison et al. 2017] [Harter and DeHart 2025] [Harty and Brengle 1993] [Haslett 1994] [Haslett 1995] [He et al. 2022b] [Hehn 1968] [Heidet et al. 2020] [Heilbronn and Townsend 2001] [Helton et al] [Herner et al] [Hetterich 2006] [Hew et al. 2018] [Higgins et al. 2021c] [Higgins et al. 2021b] [Hill et al. 1966] [Hill et al. 1993] [Hollstein 1963] [Holman and Pierce 1986] [Holmes and Calomino 2022] [Holmes et al] [Homan et al. 1993] [Horton 1966] [Houts et al. 1999] [Houts et al. 2012] [Houts et al. 2013] [Houts et al. 2014] [Houts et al. 2015b] [Houts et al. 2015a] [Houts et al. 2017] [Houts et al. 2019] [Howard 2017] [Howard 2020] [Howard and Ruggles 2020] [Howarth and Retallick 1962] [Howarth and Retallick 1963] [Howe et al. 1991] [Howe et al. 2021] [Hsieh and Koenig 1977] [Hsieh et al. 1973] [Huang and Steyn 1969] [Huang and Steyn 1970] [Hula 2015] [Infographic 2019] [Ingber and Higdon 1968] [Ingber and Higdon 1969] [Irwin and Tinker 2005] [Isenberg et al. 1987] [Ivanenok and Wett 1993] [Jack 1963] [Jaffe et al. 1963] [Jaffe et al. 1988b] [Jiao et al. 2023] [Johnson 1968] [Johnson 1969] [Johnson 1993] [Johnson and Rom 1962] [Johnson et al. 1993] [Jolly et al. 2015] [Jones] [Jones 2023] [Jones and Sauer 1984] [Jones and Wells 1962] [Jordan and Woodsum 1967] [Joyner et al. 2007] [Kajimura et al. 2008] [Kaldon and Smith 2024] [Kalyan Raj I. and Parks 2019] [Kalyan Raj I. and Parks 2020] [Kammash 1992] [Kammash and Galbraith 1993] [Kammash and Tang 2006] [Kane and Wells 1965] [Kapernick and Dixon 2008] [Karns et al. 1993] [Keaton and Tubb 1986] [Kendall 1972] [Kesten and Krascella 1967] [Khan and Parlos 1989] [Khan et al. 2024] [Khan et al. 2025b] [Khatry and Aydogan 2017] [Kim 2015] [Kim et al. 2026a] [King and de Holanda Mencarini 2022] [King and Marshall 1997] [King et al. 2006] [Kirk et al. 2008] [Klein 1991] [Klein 2004] [Klein and Lewis 1992] [Klein et al] [Klein et al. 2021] [Kluever and Pierson 1994] [Knight et al. 1981] [Krauthamer et al. 1995] [Krecicki and Kotlyar 2022] [Krecicki and Kotlyar 2023] [Krecicki et al. 2022] [Kruger 1991] [Kumar et al. 2020] [Labib and King 2015] [Laboure et al. 2022] [Laboure et al. 2023] [Labouré et al. 2023] [McLafferty 1965] [McLafferty 1966] [McLafferty 1967] [McLafferty 1969a] [McLafferty 1969b] [Lal and Locke 2021] [Lambertini 2026] [Langrod and Carniglia 1961] [Langston et al] [Lanin 2012a] [Lanin 2012b] [Lanzerotti 2004] [Larin 1962] [Larson 1958a] [Larson 1958d] [Larson et al] [Latham 1967] [Latham et al. 1965] [Lawdensky and Culbreth 2018] [Lawrence 2005] [Lawrence and Powell 1995] [Lee et al. 2022a] [Leifer et al. 1991] [Lenard 2024] [Lengweiler 1963] [Lenox 2023] [Levinsky et al] [Levinsky et al. 2026] [Lewis et al. 2022] [Li et al. 2023e] [Li et al. 2023c] [Liley and Duneer 1967] [Lim and Lee 2022] [Lim and Lee 2023] [Lin and Youinou 2020] [Litchford et al. 2007] [Liu 1971] [Liu et al. 2022a] [Lombrozo 1992] [Lopez Honorato et al. 2023] [Lorenz and Kellman 1964] [Ludewig et al. 1991] [Ludewig et al. 2006] [Lutz 2021] [Ma et al. 2026] [Machemer et al] [Madeleine Charlot et al. 2023] [Maise 2006] [Maldonado 2023] [Maldonado and Levinsky 2025] [Maldonado et al. 2025] [Mankins et al. 1987] [Manzella et al] [Marjon 1963b] [Marshall 1997] [Marshall et al. 1994] [Martin 2016] [Martin and Cline 2025] [Martin et al] [Mason 2006] [Mason et al] [Mason et al. 2017] [Masser 1971] [Matthews and Chidester 1993] [Matthiä and Berger 2024] [Mauk et al. 1993] [Maya et al. 1991] [Maya et al. 1993] [McClure and NASA 2018b] [McClure and NASA 2018a] [McClure et al. 2014] [McClure et al. 2020] [McCurdy et al. 2014] [McGuire et al. 2006] [McKissock and Bloomfield 1989] [McKissock and Bloomfield 1990] [McKissock and Bloomfield 1994] [McLafferty 1970] [McLaren and Ragheb 2010] [Meidinger and Martin 2017] [Merkle 1959] [Merkle 1961] [Meschini and Cammi 2022] [Metzger et al. 2005] [Miao et al. 2022] [Miller 1962] [Milner et al. 2024] [Minovitch 1972] [Mintz 1965] [Mitchell 1993] [Mitchell et al. 2015] [Mohamed 2025] [Mohr 1963] [Mondt 1981] [Mondt and Prickett 1973] [Mondt et al. 1974] [Moriarty 1993b] [Moriarty 1993a] [Morley and El-Genk 1993a] [Morley and El-Genk 1993b] [Morley and El-Genk 1994a] [Morley and El-Genk 1994b] [Morley and El-Genk 1995] [Morley et al. 1994] [Morris 1978] [Morrison 2021] [Morton et al. 1964] [Mowery et al] [Moyer 1962] [Moyer and Goldberg 1965] [Moyer et al. 1960] [Moyer et al. 1964] [Mudd et al. 2022] [Mughabghab et al. 1993] [Mughabghab et al. 1997] [Mulqueen et al. 2007] [Murray et al. 1969] [Myers et al. 2024] [Preliminary Hazards Summary 1963] [Nagorski 1981] [Nagorski and Boain 1981] [Nakagawa et al. 2003] [Naudet et al. 2025] [Nealy et al. 1991] [Nelson and Simpson 2006] [Nelson et al. 2021b] [Nikitaev et al] [Nikitaeva 2020] [Nikitaeva and Thomas 2021] [Nikitaeva and Thomas 2022] [Nikitaeva and Thomas 2023] [Nikitaeva et al] [Nikitaeva et al] [Nikolaev et al. 1993] [Noca et al. 2001b] [Noca et al. 2001a] [Nock and Garrison 1982] [Nowicki et al. 2025] [Nowicki et al. 2026] [Nuclear Electric Propulsion Mission 1973] [Nuclear Electric Propulsion NEP 1984] [Pope 2021] [Nuclear Rocket Propulsion Systems 1962] [Nuclear Rockets and Ramjets 1962] [Nuclear-Thermal-Rocket Propulsion Systems 2008] [O’Brien et al. 2012] [O’Neal 1962] [Oleson et al] [Oleson et al. 2021] [Olsen et al. 1991] [Ondeck et al] [Orphan et al. 1972] [Overholt 1993b] [Overholt 1993a] [Palac et al. 2009] [Palac et al. 2010] [Palac et al. 2016] [Palaszewski et al. 1989] [Palmer 1981] [Palomares] [Palomares and Werner 2023] [Palomares et al] [Palomares et al] [Palomares et al] [Palomares et al. 2020] [Palomares et al. 2022] [Paniagua and Sandler 1993] [Paniagua et al. 2008] [Parcher and Sims 2005] [Parma et al. 1993] [Paschall 1993] [Patel 2015] [Patel et al. 2016] [Patton et al. 2002b] [Patton et al. 2002a] [Pawlik and Phillips 1976] [Pawlik and Phillips 1977] [Paydar et al. 2023] [Peakman and Gregg 2020] [Peakman and Lindley 2023] [Peecook and Stone 1992] [Peecook and Stone 1993] [Peelle 1967a] [Peelle 1967b] [Peery 1993] [Pelaccio and El-genk 1994] [Pelaccio et al. 1991b] [Pelaccio et al. 1991a] [Pelaccio et al. 1993c] [Pelaccio et al. 1993a] [Pellacio et al. 1993] [Performance of Nuclear-Electric Propulsion 1961] [Peschka 1964] [Petrosky et al. 1993] [Pheil 2006] [Phillips and Koenig 1978] [Phillips and Pawlik 1978] [Pierce 1991] [Pingel et al] [Pingel et al] [Pingel et al. 2023] [Pluta and Murata 1991] [Poeth 2005] [Polansky et al. 1994] [Polzin and Houts] [Postlehwait et al. 2005] [Poston 2021c] [Poston 2021a] [Poston 2021b] [Poston et al. 2002] [Poston et al. 2008] [Powell 1993] [Powell et al. 1993] [Pratt et al. 2021] [Presby] [Preston-Thomas 1958] [Prickett and Spera 1972] [Prickett and Stearns 1973] [Principles of Nuclear Rocket 2016] [Principles of Nuclear Rocket 2023] [Pu et al. 2023] [Pulsed Thermionic Converter Study. 1976] [Putzu 2026] [Qi et al. 2022] [Qualls and Hancock 2011] [Qualls and Werner 2017] [Quinteros et al. 2023] [Raab 1963] [Rader et al. 2019] [Ramsthaler and Schnitzler 1990] [Randolph and Polk 2004] [Rao et al. 2022] [Reck et al. 1991] [Reetz 1965] [Retallick and Pierce 1962] [Review of Reactor Confi 2008] [Reynolds 1963b] [Reynolds 1964] [Riley et al. 2026] [Robinson et al. 1972] [Rodean 1962] [Rodriguez et al] [Rodriguez et al] [Rogers et al. 1972] [Roler et al. 1993] [Rom 1964] [Rom 1968] [Rosaire 2022] [Rosaire et al. 2023] [Rosen 1962] [Rothman 1962] [Rovang and Marko 1993] [Rubin and Gardner 1961] [Rubiolo et al. 2024] [Ruddy et al. 2005] [Russak 1964] [Ryan and Borowski 2014] [Sackheim and Houts 2000] [Saenger 1964] [Sahin 1979] [Salah et al. 1970] [Santos and Guimarães 2025] [Sasmal et al] [Sasmal et al] [Sauer 1993] [Schaeperkoetter et al. 2025] [Schaff 1967] [Schaupp and Sawyer 1972] [Schmidt and Decker 1960] [Schmidt et al. 1993] [Schnitzler 2012] [Schnitzler 2014] [Schnitzler and Borowski 2012] [Schoenfeld et al. 2008] [Schreiber 1956] [Schreiber 1959] [Schreiber 1969] [Schriener and El-Genk 2014a] [Schriener and El-Genk 2024] [Schrock 1959] [Schroll 2024] [Schroll and Frederick 2024] [Schulthess et al. 2022] [Schulthess et al. 2023] [Searight et al. 2022] [Segna et al. 1992] [Selcow et al. 1993b] [Selcow et al. 1993a] [Selected Data from NERVA 2023] [Sercel and Krauthamer 1986] [Shah 1993] [She et al. 2023] [Shechtman 2004] [Shehzad et al. 2026] [Shen 1963] [Shengquan and Jicai 1990] [Shipers and Allen 1992] [Shipers and Brockmann 1992] [Shipers and Brockmann 1993] [Shipers et al. 1993] [Shooman and Sforza 1993] [Siamidis 2006] [Silva and Byers 1980] [Silverman et al. 1985] [Simpson 1967] [Sims and Parcher 2005] [Sivakumar and Palmtag 2026] [Slaba et al. 2013] [Smith and Stonehill] [Smith et al] [Smith et al] [Smith et al] [Smith et al. 2013] [Smith et al. 2022] [Smith et al. 2023] [Smith et al. 2026a] [Smith et al. 2026b] [Soffer and Wright 1973] [Space Reactors 2013] [Spacecraft Electrostatic Radiation Shielding 2008] [Spencer 2024] [Spincourt 1966] [St. Leger-Barter 1963] [Stanley 1991] [Stark et al] [Stearns 1975] [Steiner et al. 2021] [Stetson 1993] [Stewart 2019] [Stewart and Schnitzler 2007] [Stewart and Schnitzler 2008] [Stewart et al. 2020] [Stiger 1965] [Stone 1992] [Stone 1993] [Stone 1994] [Stone and Sovey 1992] [Stone et al] [Stone et al. 1993b] [Stonehill et al] [Stonehill et al] [Stonehill et al. 2024] [Streetman and Graves 1963] [Stubbs 1962] [Stubbs and Kim 1993] [Stubbs et al. 1993] [Sukumaran et al. 2023] [Sukumaran et al. 2024] [Sullivan] [Sumner et al] [Sung and Farron 1962] [Suzuki 1993] [Swint 1993] [Taylor and Emrich 2016] [Taylor et al. 2015] [Taylor et al. 2018b] [The Development of Nuclear 1993] [Thom et al. 1977] [Thomas et al] [Thomas et al. 2021] [Thomas et al. 2024] [Thomas et al. 2025] [Thompson et al. 1993b] [Thompson et al. 1993a] [Thoms 1975] [Tinker et al] [Tournier and El-Genk 2005] [Towle 1961] [Townsend et al. 2005] [Trammell et al. 2013] [Trammell et al. 2015] [Tripathi and Nealy 2007] [Tripathi and Nealy 2008a] [Tripathi and Nealy 2008b] [Tucker et al. 2020] [Tucker et al. 2023] [Turkel 1972] [Uzel and Ozyildirim 2017] [Vafapour et al. 2024] [Valdes et al. 2026] [Valentine 1962] [VanDyke et al. 2002] [Velidi and Guven 2020] [Velio and Décline 2024] [Venchiarutti 1965] [Venetoklis 1995] [Venneri and Kim 2016] [Veselka and Fradeneck 2024] [Vicente et al. 1989] [Vitiv 2026] [Voevodina et al. 2015] [Volkoff and Womack 1967] [von Ubisch 1960] [Voss 1984] [Voss and Reynolds 1994] [Vuolo et al. 2017] [Wagner 1993] [Walter 1962] [Walter 1964] [Walton and Malloy 1991] [Walton et al. 1992] [Wang and He 2013] [Wang et al. 2013b] [WANL R-202 Presentation 1975] [Warren et al] [Watson 1994] [Watson et al. 2024] [Weintraub 1961] [Weintraub 1962] [Welch 1967] [Welch 1972] [Wen et al. 2022] [Wen et al. 2023] [Werner 2014] [Werner et al. 2008] [Werner et al. 2011] [Westenhofer and Shi 2026] [Westrom 1966] [Wetzel and Solomon 1994] [Wheatley 1968] [White et al. 2003] [Widgeon Paisner et al. 2024] [Widmer 1963] [Widmer and Brown 1966] [Williams et al. 2005a] [Wilson 1975] [Wilson et al] [Wilson et al. 2002] [Wilson et al. 2009] [Wilson et al. 2025a] [Wood and Thomas 2021] [Woodrow 1987] [Woodsum 1972] [Wright and Lipinski 2003] [Yasui 1961] [Yee et al. 1986] [Yen 1993] [Yi et al. 2026] [Youchison et al. 2006] [Youinou 2025] [Youinou et al. 2020] [Young et al. 1993] [Zhang et al. 2011] [Zhang et al. 2020d] [Zhang et al. 2024a] [Zhu et al. 2025] [Zubrin 1992] [Zubrin and Decher 1991]

Molten salt and circulating fuel reactors

The Aircraft Reactor Experiment’s direct line. The Molten Salt Reactor Experiment, breeder studies, fuel salt chemistry, circulating-fuel kinetics, safeguards and the commercial designs now in development. 521 of its 836 records date from 2015 or later, and 108 name the Molten Salt Reactor Experiment itself, the aircraft reactor’s successor at Oak Ridge.

836 records. [A Review Paper 2024] [Abalin et al. 1995] [Abou-Jaoude et al. 2021c] [Abuqudaira et al. 2023] [Abuqudaira et al. 2024b] [Abuqudaira et al. 2024a] [Abuqudaira et al. 2025] [Adamski 1970b] [Adamski 1970a] [Adamson and Taboada 1967] [Adler 1970] [Aigner 2000] [Aizawa et al. 2024] [Aji 2014] [Alekseev et al. 1999] [Allibert et al. 2023] [Alseaidan et al. 2024] [Alzaabi and Peterson 2022] [Anderson and Sabharwall 2012] [Andersson et al. 2023] [Andreades and Peterson 2017] [Andrews and McFarlane 2023] [Andrews and Myhre 2022] [Andrews et al. 2021b] [Andrews et al. 2021a] [Arcella et al. 1966] [Arregui-Mena et al. 2023] [Ashraf et al. 2019] [Ashraf et al. 2020] [Aufiero et al. 2014] [Aufiero et al. 2017] [Bae et al. 2019] [Baes 1965] [Baes 1973] [Baes 1974] [Bahri et al. 2017] [Bailey and Tunnell 1954] [Bajorek and Diamond 2018] [Ball 1966] [Ball and Kerlin 1965] [Bandini 1988] [Barthold 1966] [Barthold 1967] [Bauman et al. 1971] [Beall and Guymon 1965] [Beall et al. 1961] [Beeny 2019] [Beeny 2021] [Beeny 2022] [Belles and Flanagan 2018] [Belles et al. 2018a] [Belles et al. 2018b] [Beneš and Konings 2012] [Beneš and Konings 2013] [Beneš and Konings 2020] [Beneš and Souček 2020] [Bentzinger et al. 1998] [Berg and Buijs 2023] [Besmann and Schorne-Pinto 2021] [Besmann et al. 2024] [Bettis 1961] [Bettis and Bauman 1970] [Bettis and McDonald 1964] [Bettis et al. 1972b] [Bettis et al. 1972a] [Betzler 2021] [Betzler et al. 2016a] [Betzler et al. 2016c] [Betzler et al. 2016b] [Betzler et al. 2017e] [Betzler et al. 2017c] [Betzler et al. 2017b] [Betzler et al. 2017a] [Betzler et al. 2017d] [Betzler et al. 2018b] [Betzler et al. 2018a] [Betzler et al. 2019c] [Betzler et al. 2019b] [Betzler et al. 2019a] [Bhattacharya et al. 2026] [Bigelow and Greenstreet 1957b] [Bigelow and Greenstreet 1957a] [Bogetic et al. 2016] [Bolisetti et al. 2022] [Bolukbasi and Margulis 2025] [Bolukbasi and Margulis 2026b] [Bostelmann et al. 2021] [Briant and Weinberg 1957] [Briggs 1964] [Briggs 1969] [Briggs 1972] [Broc et al. 1983] [Brovchenko et al. 2012] [Brown et al. 2016b] [Brown et al. 2016a] [Brown et al. 2019] [Bull Ezell et al. 2019] [Burke 2024] [Burman and Uziel 1995] [Burman et al. 1998] [Burnett 2022] [Busby et al. 2019] [Caire and Roure 2007] [Calderoni and Cabet 2012] [Calegario et al. 2024] [Campbell and Cathers 1959] [Cantor 1968] [Cantor 1973] [Cao et al. 2016b] [Cao et al. 2016a] [Cao et al. 2025] [Caprais] [Carbajo et al. 2017] [Carberry and Petrovic 2021] [Carberry and Petrovic 2023] [Carlberg et al. 2009] [Carter 1968] [Carter and Alexander 1961] [Carter and Borrelli 2020a] [Carter and Borrelli 2020b] [Carter and Carter 2022] [Carter et al. 2022] [Cervi et al. 2019] [Chandler and Bolt 1969] [Chandler and Bolt 1970] [Chapter 9. Molten Salt 2020] [Chen and Brooks 2024] [Chen and Brooks 2025] [Chen et al. 2024b] [Cheng et al. 2025] [Chirayath et al. 2025] [Chisholm et al. 2020b] [Chisholm et al. 2020a] [Cho et al. 2009] [Choi and Mohammad Jaradat 2023] [Choice of Fuel Salt 2023] [Christian and Mahler 2026] [Christian et al. 2024c] [Christian et al. 2024a] [Christian et al. 2024b] [Chvala et al. 2017] [Cioncolini and Iacovides 2015] [Cipiti 2018] [Clarno et al. 2023] [Coleman 1999b] [Coleman 1999a] [Collins et al. 2017b] [Collins et al. 2017a] [Compere et al. 1975] [Core-Moderated Circulating Fuel Reactor 1957] [Cornejo et al. 2021] [Couet et al. 2023] [Creasman et al. 2023a] [Creasman et al. 2023b] [Creasman et al. 2024] [Crowley and Rose 1967] [Csom et al. 2002] [Cul et al. 2001] [Cunningham et al. 1957] [Da-Lin et al. 2008] [Dai 2017b] [Dai 2017a] [Davidson et al. 2018] [Davidson et al. 2019] [Davidson et al. 2021] [Davidson et al. 2023] [Davidson et al. 2024] [Degtyarev and Ponomarev 2012] [Degtyarev et al. 2015] [DeGuire and Ragusa 2024] [Del Cul et al. 2000] [Delpech and Gerard 2008] [Detkina et al. 2022] [Development Status of Molten-Salt 1972] [Development Work on Molten-Salt 1970] [Diaconeasa et al. 2025] [Diamond 2018] [Diamond et al. 2018] [Dillon 1973] [Diniz et al. 2020] [Diniz et al. 2022] [Dion et al. 2021a] [Dion et al. 2021c] [Dion et al. 2021b] [Direct Support 1970] [Dudnikov et al. 2015] [Dulla et al. 2006] [Dulla et al. 2013] [Dumaire et al. 2022] [Dunkle and Bogetic 2026] [Dunkle et al. 2022] [Dunkle et al. 2023a] [Dunkle et al. 2023b] [Dunkle et al. 2025a] [Dunkle et al. 2025b] [Dwijayanto and Harto 2023] [Dykin and Pázsit 2016] [Elhareef and Wu 2024b] [Elhareef and Wu 2024c] [Elhareef and Wu 2024a] [Elhareef and Wu 2025] [Elhareef et al. 2025a] [Elhareef et al. 2025b] [Elzohery et al. 2026] [Emam et al. 2026] [Emrich 2005] [Engel and Steffy 1971] [US Atomic Energy Commission (AEC) et al. 1965] [Engel et al. 1970] [Engel et al. 1979a] [Engel et al. 1979b] [Engel et al. 1980] [Enlund 1953] [Ergen 1953a] [Ergen 1953b] [Ergen 1954] [Ergen 1956] [Ergen 1958] [Erickson and Yoshioka 2024] [Eslinger et al. 2021] [Evaluation of the Molten 1972] [Evaluation of the U.S. 1997] [Evans 2024b] [Ezell et al. 2018] [Ezell et al. 2021] [Fang et al. 2020] [Fang et al. 2022a] [Fang et al. 2024] [Faugeras 1975] [Faugeras et al. 1975] [Faulkner and Petrovic 2024] [Fei et al. 2019a] [Feng and Cao 2021] [Feng et al. 2019] [Holcomb 2023d] [Fierro Lopez et al. 2023] [Findlay et al. 2025b] [Findlay et al. 2025a] [Fischer and Bureš 2024] [Fischer and Bureš 2023] [Flanagan et al. 2018] [Flanders and Blecher 1963] [Fleck 1955] [Fluoride Salt Advanced High-Temperature 2016] [Forsberg 2002] [Forsberg 2004a] [Forsberg 2004c] [Forsberg 2004b] [Forsberg 2006b] [Forsberg 2006c] [Forsberg 2007b] [Forsberg and Curtis 2014] [Forsberg et al. 2003] [Forsberg et al. 2019] [Fratoni et al. 2020] [Frederix and Komen 2023] [Fredrickson 2022] [Fredrickson et al. 2018] [Freile et al. 2021b] [Freile et al. 2021a] [Fuerst et al. 2021] [Fuerst et al. 2024] [Fujikura and Aizawa 2025] [Furukawa 1974] [Gabbard 1970] [Gaitanis et al. 1962] [Gallaher 1971] [Gallego et al. 2019] [Gardner et al. 2023] [Garrett et al. 2025] [Gat 1997] [Gat and Dodds 1993] [Gat and Dodds 1997] [Gat and Engel 1992] [Gat and Engel 1993] [Gat et al. 1991] [Gat et al. 1992] [Gates et al. 2019a] [Gehin and Powers 2014] [Gehin and Powers 2016] [Gehin et al. 2011] [Gelbard 2021] [Gelbard et al. 2022] [Gelbard et al. 2023] [Geringer et al. 2018] [German et al. 2016] [German et al. 2022] [Gilliam et al. 2002] [Glass et al. 2020] [Glass et al. 2021] [Goetz et al. 2021] [Goetz et al. 2022] [Gorton et al. 2022] [Goryachenko 1966] [Goryachenko 1970] [Goryachenko et al. 1970] [Graham et al. 2019] [Graham et al. 2021] [Greenwood 2018] [Greenwood and Betzler 2018a] [Greenwood and Betzler 2018b] [Greenwood and McMurray 2020] [Greenwood et al. 2016] [Greenwood et al. 2018] [Greenwood et al. 2019a] [Greenwood et al. 2019b] [Grenon 1974] [Grenon and Geist 1971] [Grimes 1964] [Grimes 1970] [Grimes et al. 1958] [Guo et al. 2017] [Guymon and Haubenreich 1969] [Haghighi et al. 2002] [Hale et al. 2014] [Hartanto et al. 2023b] [Hartanto et al. 2023a] [Hartanto et al. 2024a] [Hartanto et al. 2024b] [Hartmann and Paviet 2022] [Harto 2012] [Haskin et al. 2023] [US Atomic Energy Commission (AEC) and Haubenreich 1965] [Haubenreich and US Atomic Energy Commission (AEC) 1967] [Haubenreich 1969] [Haubenreich 1970] [Haubenreich 1973] [Haubenreich and Engel 1970] [Haubenreich and Richardson 1970] [Haubenreich et al. 1975] [He et al. 2015] [He et al. 2018] [Heidet et al. 2016] [Henderson and Ragan 1967] [Hiatt 2025] [Higgins et al. 2021a] [Hightower 1975b] [Hightower 1975a] [Hightower 1976b] [Hightower 1976a] [Hightower and McNeese 1975] [Hightower and McNeese 1976] [Hightower et al. 1971] [Hines and Melin 2022] [Hirose 2020] [Ho et al. 2023] [Hoffman et al. 2025] [Hogue et al. 2021a] [Hogue et al. 2021b] [Hogue et al. 2024] [Hogue et al. 2025a] [Hogue et al. 2025b] [Hogue et al. 2026] [Holcomb 2023a] [Holcomb 2023c] [Holcomb 2023b] [Holcomb 2024a] [Holcomb 2024b] [Holcomb 2024c] [Holcomb 2025] [Holcomb and Owusu-Achampong 2023] [Holcomb and Retamales 2025] [Holcomb and Tano 2025] [Holcomb et al. 2018b] [Holcomb et al. 2018a] [Holcomb et al. 2019b] [Holcomb et al. 2019a] [Holcomb et al. 2020] [Holcomb et al. 2021] [Holcomb et al. 2022a] [Holcomb et al. 2022b] [Holcomb et al. 2022c] [Holcomb et al. 2024] [Homogeneous Circulating Fuel Reactor 1955] [Horan 2021] [Houtzeel and Dyer 1972] [Hu et al. 2020] [Hu et al. 2025] [Huang et al. 2024a] [Huang et al. 2025a] [Hub 1956] [Huddar et al. 2018] [Humrickhouse and Fuerst 2020] [Identification and Evaluation 1996] [Ignat’ev et al. 2018] [Ivory et al. 2024] [Jaradat et al. 2020] [Jaradat et al. 2021] [Jaradat et al. 2024] [Jayaraman 2024] [Jenet 2024] [Jeong and Cho 2026] [Jeong and Shirvan 2021] [Jeong et al. 2022a] [Jerden et al. 2019] [Jia et al. 2025] [Jiang et al. 2020] [Johnson et al. 2020] [Johnson et al. 2021] [Johnson et al. 2022] [Kamei 2012] [Karcz et al. 2025] [Kasam and Shwageraus 2021] [Kaygisiz and Revankar 2023] [Kedl 1970] [Kedl 1972] [Keesling 2021] [Keiser 1977] [Keller and Franklin 1955] [Kempkes 1969] [Kerlin 1961] [Kerlin and Ball 1967] [Kerlin et al. 1971a] [Kerlin et al. 1971b] [Khaleb et al. 2024] [Khokhlov et al. 2009] [Kim et al. 2024b] [Kim et al. 2026b] [Kitcher 2020b] [Kloosterman 2017] [Kolar and Miraldi 1968] [Kophazi et al. 2006] [Koukolikova et al. 2017] [Kovacevic et al. 2021] [Kovacic et al. 2018] [Kraus et al. 2022] [Krepel and Ragusa 2024] [Krepel et al. 2006] [Krpan et al. 2025] [Krpan et al. 2026] [Kupriyanov et al. 2022] [Kópházi et al. 2009] [Křepel et al. 2014] [Lafreniere et al. 2025] [Larsen et al. 2023] [Larsen et al. 2024b] [Larsen et al. 2024a] [Leandro et al. 2018] [LeBlanc and Rodenburg 2017] [Lee and Kozlowski 2023] [Lee et al. 2019] [Lee et al. 2020d] [Lee et al. 2022d] [Lee et al. 2022c] [Lee et al. 2023a] [Lee et al. 2023c] [Lee et al. 2024a] [Lee et al. 2025b] [Lee et al. 2025d] [Lee et al. 2025a] [Leonard and Mandil 1951] [Leute et al. 2021] [Li and Tano Retamales 2025] [Li et al. 2018a] [Li et al. 2022b] [Li et al. 2023g] [Li et al. 2025a] [Li et al. 2026b] [Liu and Chen 2026] [Liu and Wang 2016] [Liu et al. 2016a] [Lo et al. 2022] [Lock 1956] [Lubbers 2019] [Lyu et al. 2026] [MacDonald 1951] [MacPhee 1958] [MacPherson 1960c] [MacPherson 1960a] [MacPherson 1960b] [MacPherson 1969] [MacPherson 1972] [MacPherson 1985] [Mardus-Hall et al. 2017] [Marone] [Marshall 2019] [Martin et al. 2017] [Maul 2018] [McCoy 1967] [McCoy 1971] [McCoy et al. 1969] [McCoy et al. 1970] [McDuffee et al. 2018] [McDuffee et al. 2022] [McFarlane 2024] [McFarlane et al. 2018] [McFarlane et al. 2019b] [McFarlane et al. 2019a] [McFarlane et al. 2019c] [McFarlane et al. 2020] [McGoff et al. 1959] [McMurray et al. 2018] [McMurray et al. 2020] [McMurray et al. 2021b] [McMurray et al. 2021a] [McNeese 1968] [McNeese 1970] [McNeese 1971b] [McNeese 1971a] [McNeese 1971e] [McNeese 1971d] [McNeese 1971c] [McNeese 1972a] [McNeese 1972d] [McNeese 1972b] [McNeese 1972c] [McNeese 1974] [McNeese 1975] [McNeese 1976] [McNeese and Ferris 1971] [McNeese et al. 1972] [McPherson 1957] [McWherter 1970] [Merk and Konheiser 2014] [Merk and Litskevich 2015] [Merle-Lucotte et al. 2006] [Messenger et al. 2012] [Messner et al. 2019] [Meyer et al. 1975] [Miller et al. 1999] [Mir et al. 2023a] [Mir et al. 2023b] [Mishra et al. 2024b] [Mishra et al. 2024a] [Mitchell et al. 2022] [Mochizuki 2020] [Mochizuki 2023] [Mochizuki 2024a] [Mochizuki 2024b] [Modeling and Simulation 2019] [Mohammad Jaradat and Ortensi 2023] [Mohammad Jaradat et al. 2024b] [Moir 2002] [Molten Salt Reactor Experiment 1996] [Molten Salt Reactors 2021] [Molten-Salt Reactor Experiment. 1968] [Molten-Salt Reactor Experiment. 1969] [Molten-Salt Reactor Experiment. 1970] [Molten-Salt Reactor Experiment. 1971] [None and US Atomic Energy Commission (AEC) 1962] [Molten-Salt Reactor Processing. 1967] [Molten-Salt Reactor Processing. 1971] [Molten-Salt Reactor Processing 1973] [Molten-Salt Reactor Processing Studies. 1970] [Molten-Salt Reactor Program. 1971] [Oak Ridge National Lab., Tenn. 1961] [Oak Ridge National Lab., Tenn. 1962a] [Author 1958b] [Author 1958a] [Author 1958c] [Author 1959b] [Author 1960c] [Oak Ridge National Lab., Tenn. 1964] [Author 1965a] [Author 1965b] [Author 1966] [Oak Ridge National Lab., Tenn. 1971a] [Oak Ridge National Lab., Tenn. (USA) 1973] [Oak Ridge National Lab., Tenn. (USA) 1975] [Oak Ridge National Lab., Tenn. 1962b] [Author 1962c] [Oak Ridge National Lab., Tenn. 1963] [Oak Ridge National Lab., Tenn. 1967b] [Oak Ridge National Lab., Tenn. 1967a] [Oak Ridge National Lab., Tenn. 1968] [Oak Ridge National Lab., Tenn. 1970] [Oak Ridge National Lab., Tenn. 1971b] [Oak Ridge National Lab., Tenn. 1972b] [Oak Ridge National Lab., Tenn. 1972a] [Author 1959c] [Author 1959d] [MOLTEN-SALT REACTORS. 1967] [Moon et al. 2023] [Morgan and Johnson 2019] [Moss and Carter 2025b] [Moss and Carter 2025a] [Muhlheim and Belles 2023] [Mui et al. 2021] [Mui et al. 2024] [Mui et al. 2025] [Mukherjee and Dash 2018] [Muránsky et al. 2019] [Nahari et al. 2026] [Nasr et al. 2025] [Nelson et al. 2021a] [New Kind of Homogeneous 1959] [Nguyen and Chen 2024b] [Nguyen and Chen 2024a] [Nguyen and Chen 2026] [Nguyen and Van Rooijen 2022] [Nguyen et al. 2023] [Niu et al. 2024] [Novikov 1966] [Numakura et al. 2011] [Numbers et al. 2024] [O’Brien et al. 2017] [Ocampo Giraldo et al. 2024] 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Compact, mobile and modular reactors

Reactors built to work away from a power station. Microreactors, heat pipe reactors, small modular reactors, the high-temperature gas-cooled line, the Army package power reactors and nuclear ship propulsion. 165 titles name a microreactor and 130 concern ships, submarines or naval propulsion, the two places where the article finds the X-6’s constraint relaxed.

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Hydrogen, synthetic fuel and other routes to long range

What answered the mission instead. Hydrogen-fuelled aircraft, synthetic and sustainable aviation fuel, aerial refuelling and the solar-powered long-endurance aircraft. 170 titles concern aerial refuelling or the tanker, 137 concern hydrogen and 127 concern solar-powered or long-endurance flight. Aerial refuelling is the arrangement the article credits with making unlimited range a matter of logistics rather than of propulsion.

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2024] [Trainelli 2026] [Tramposch et al. 2024] [Traub 2011] [Traub 2016] [Tripathi and Choubey 2025] [Troeltsch et al. 2020] [Tsukerman et al. 2017] [Tucker et al. 2007] [Tzoumakis et al. 2024] [Uddin and Pant 2021] [Vachon and Ray 2004] [Valasek et al. 2002] [Vendra] [Venkataramanan and Dogan 2004] [Verstraete 2013] [Victor 1990] [Voss et al. 2026] [Waddington et al. 2023] [Wagner et al. 2025] [Wahler et al. 2025] [Wang et al. 2007] [Wang et al. 2009b] [Wang et al. 2009a] [Wang et al. 2010a] [Wang et al. 2010b] [Wang et al. 2014] [Wang et al. 2019a] [Wang et al. 2020] [Wang et al. 2025b] [Wang et al. 2026d] [Wang et al. 2026f] [Wang et al. 2026a] [Weiser 2025] [Weiser and Ossmann 2022b] [Weiser and Ossmann 2022a] [Weiser et al. 2023b] [Weiser et al. 2023a] [Weiser et al. 2026] [Weiss 1973] [Weltz et al. 2021] [Wilkins et al. 2009] [Williams et al. 2005c] [Winterbottom et al. 2016] [Wise and Lavretsky 2009] [Wise et al. 2008] [Witcofski 1976] [Witcofski 1977] [Woehler et al. 2023] [Woodruff et al. 1979] [Wu 2023] [Wu et al. 2019b] [Wu et al. 2020a] [Wu et al. 2022b] [Qing-biao et al. 2013] [Xian-Zhong et al. 2013] [Xing et al. 2023b] [Xing et al. 2023c] [Xing et al. 2023a] [Xiongfeng et al. 2014] [Xu et al. 2015] [Xufeng et al. 2013] [Yakovlieva et al. 2023] [Yazar et al. 2025] [Yoon et al. 2018] [Young et al. 2005] [Youngblood and Talay 1982] [Yuan et al. 2024] [Yue et al. 2016] [Yue et al. 2019] [Zetina et al. 2013] [Zhang and Jiang 2023] [Zhang and Liu 2018] [Zhang et al. 2020b] [Zhang et al. 2024c] [Zhang et al. 2026a] [Zhang et al. 2026g] [Zhao et al. 2021] [Zhipu Jin et al. 2006] [Zhongjian Li et al. 2006] [Zhu et al. 2016] [Zhu et al. 2018]

Attenuation physics, buildup and radiation transport

The physics the attenuation law stands on. Buildup factors, removal cross sections, attenuation coefficients, duct streaming, skyshine, and point-kernel and Monte Carlo transport. 128 titles concern the buildup factor, which the article’s lead estimate takes as a single factor of ten and which this literature tabulates by energy, depth, material and geometry.

414 records. [Abdu Hamoud Al-khawlany et al. 2026] [Abu-rayan et al. 2026] [Adamu et al. 2026] [Aim-O et al. 2017] [Akar Tarım and Gürler 2018] [Akkurt et al. 2011] [Akman et al. 2022] [Akyildirim et al. 2017] [Al Huwayz et al. 2025] [Al-Ani and Jawad 2018] [Al-Buriahi and Tonguc 2019] [Al-Buriahi et al. 2026] [Al-Hadeethi et al. 2022] [Al-Muttairi and Kabir 2026] [Al-Taani and Hamad 2025] [Alabsy et al. 2021] [Alfuraih 2022] [Alhajali and Boush 2020] [Alharbi et al. 2025] [Alhindawy et al. 2024] [Alkarrani et al. 2024] [Almisned 2024] [Aloraini et al. 2023] [Alotibi et al. 2026] [Alrowaili et al. 2025] [Alrowaili et al. 2026] [Alsalmi 2026] [Alshammari et al. 2026] [Altowyan et al. 2021] [Alzahrani et al. 2024] [Anderson 1959] [Arbuzov 2024a] [Arbuzov 2024b] [Arbuzov 2025] [Assad et al. 1999] [Atak et al. 2015] [Attia et al. 2025] [Auslender 1957] [Avery and Curtis 1969] [Aye and Ko 2024] [Bacigalupi and Thinger 1968] [Badyaev et al. 1974] [Bakshi 2018] [Bantan et al. 2020] [Barbucci et al. 1988] [Barson 1965] [Basha et al. 2027] [Basu et al. 2019] [Basu et al. 2021] [Baykara et al. 2025] [Baykara et al. 2026] [Beeley et al. 2000] [Bindel et al. 2000] [Biswas et al. 2016] [Blizard and Miller 1958] [Blizard et al. 1968] [Blosser et al. 1958a] [Boahen et al. 2022] [Borodkin et al. 2007] [“Boron Rich Mortars 2021] [Bottino et al. 1969] [Bowman and Trubey 1958] [Bozek and Godlewski 1968] [Broder et al. 1973a] [Broder et al. 1973b] [Broder et al. 1975] [Burke and Beck 1974] [Burns 1994] [Burrell and Watts 1967] [Burrell and Watts 1968] [Burson and Summers 1964] [Byun and Yun 2015] [Calculation of the Effects 2023] [Capo 1959] [Case and Zweifel 1963] [Casper and Carver 1958] [Celiktas 2011] [Chapman 1966] [Chapman and Storrs 1955] [Chappell 1958] [Chen et al. 2015] [Chen et al. 2021] [Chen et al. 2024a] [Chen et al. 2026] [Chilton 1961] [Chilton 1967] [Chilton 1979] [Chong and Sagara 2025] [Claiborne and Fowler 1956] [Clark 1969a] [Clemons et al. 1970] [Clifford et al. 1971] [Conner et al. 1970] [Cramer and Dodds 1980] [Cucinotta and Benton 2006] [Das 1996] [Das et al. 2023] [Dawn and Palmtag 2023] [de Beer 1975] [Deliormanli et al. 2023] [Deparis et al] [deSaussure 1958] [Desdin and Ceballos 2000] [Desdin and García 2000] [Determination of Scattered Gamma 1992] [Dod’ and Yudin 1977] [Dong et al. 2026] [Dunn et al. 1992] [Eamon 1976] [Eggen et al. 1961] [Eisenhauer and Simmons 1973] [Eisenhauer and Simmons 1975] [Eisenman et al. 1964] [El-Faramawy et al. 2015] [El-Khayatt 2010] [El-Khayatt 2017b] [El-Khayatt and Akkurt 2013] [El-Khayatt and El-Sayed Abdo 2009] [El-Khayatt et al. 2025] [El-Megrab 2013] [El-Zaidia and Darwish 2026] [Elias et al. 1975] [Elkady 2014] [Elsafi et al. 2024] [Ermis and Celiktas 2021] [Fasso et al] [Fathy et al. 2021] [Fero 2001] [Fieno and Peoples 1969] [Fillmore and Doyas 1958] [Firas M. Fathi 2006] [Fitzgerald and Silverman 1968] [Fournie and Chilton 1980] [Fu and Ingersoll 1987a] [Furuta et al. 1961] [Gage 1957] [Gamma Spectrum Measurements SNAP 1965] [Gardner and Mettler 1965] [Gardner et al. 1965] [Gasser and Kazimi 1977] [Gaylord 2004] [George 1988] [Golshani et al. 1996] [Gomaa and El-Tayebany 2026] [Gopal and Sanjeevaiah 1973] [Guo et al. 2026] [Guyonvarh et al. 1967] [Güngör et al. 2018] [GÜNoĞLu 2025] [Halley 2026] [Hanfi et al. 2026] [Harima 1983b] [Harima 1983a] [Harima and Nishiwaki 1972] [Harima et al. 1986] [Harima et al. 1987] [Harries et al. 1963] [Hasan et al. 2019] [Hashim et al. 2026] [Hayes 2004] [Hertel et al. 2005] [Hill 1951] [Hirayama 1987] [Hirayama 1996] [Hirayama 2000] [Hirayama 2001] [Hirayama and Trubey 1988] [Hiremath et al. 2026] [Huang 2026] [Hışıroğlu et al. 2025] [Ibrahim 2000] [Iida et al. 1998] [Iliyasu et al. 2026] [Impact of the Structural 2022] [Ingersoll 1986] [Islam 2023] [Jacob et al. 1984] [Jalali 2006] [Jalali and Mohammadi 2008] [Jenkins 1971] [Jiang 1980] [Jingru et al. 2017] [Jordan and Wohl 1969] [Jordanova et al. 1985] [Jyothi and Vijayakumar 2025] [Kam and Clark 1967] [Kamaruddin et al. 2024] [Kang and Zu 2026] [Kara et al. 2025] [Kaundal 2022] [Kaundal 2024] [Kavaz and Yorgun 2018] [Kavaz et al. 2022] [kaya 2024] [Kazanskii et al. 1966] [Khabaz 2022] [Khan et al. 2025a] [Kim et al. 2012] [Kim et al. 2014] [Kitazume 1965] [Kitazume and Ogushi 1967] [Kitsos et al. 1994] [Kitsos et al. 1996b] [Kitsos et al. 1996a] [Kiyani et al. 2013] [Kloosterman 1992] [Kloosterman and Hoogenboom 1990] [Klupak et al. 2011] [Korkut and Korkut 2025] [Kouzes et al. 2008] [Kouzes et al. 2009] [Kovalev and Osanov 1959] [Kozlovska et al. 2015] [Kozlovska et al. 2019] [Kraishan 2026] [Ku and Kolibal 1983] [Kucuk 2008] [Kucuk 2010] [Kuluöztürk 2023] [Kumar et al. 2018] [Kurudirek et al. 2014] [Kuspa and Tsoulfanidis 1973] [Kyncl 1994] [Körpınar and Akat 2026] [Lagutina et al. 1989] [Lahti 1968] [Lahti and Mueller 1973] [Laletin 1967] [LaRue et al. 1951] [Lebedev et al. 1974] [LeDoux and Chilton 1961] [Lee 2014] [Lee et al. 1995] [Lee et al. 2020c] [Li et al. 2020] [Lin et al. 1996] [Livengood et al. 1973] [Lois] [Lois 1969] [Mahmoud and Marashdeh 2023] [Mahmoud et al. 2019] [Maienschein 1967] [Maki 2002] [Mann and Korkut 2013] [Marashdeh and Saleh 2019] [Mater et al. 2024] [Matijević et al. 2025b] [Matijević et al. 2025a] [Meem and Johnson 1951] [Meenakshisundaram et al. 1979] [Meier 1964] [Merz et al. 2011] [Metghalchi 1978] [Metghalchi 1979b] [Metghalchi 1979a] [Michieli 1994] [Miller et al. 1954] [Miura et al. 2000] [Mohsen et al. 2022] [Monzen et al. 2026] [Morris 1973] [Morris and Chilton 1970] [Morris et al. 1975] [Mukherjee 2023] [Nagaya 2014] [Nagaya 2015] [Najam et al. 2016] [Namito et al. 1995] [Natarajan et al. 1983] [Nava and Mazzini 1977] [Neely and Schmittroth 1982] [Nemoto et al. 2000] [Ngoc and Ha 2010] [Obaid et al. 2018] [Ohgushi and Kitazume 1968] [Oka et al. 1976] [Oka et al. 1998] [Oto et al. 2015] [Otoo et al. 2022] [Otoo et al. 2023] [Park et al. 2009] [Parkin and Goland 1976] [Peng 1986] [Pond and Matos 1996] [Pond and Matos 2000] [Ponnunni et al. 1966] [Profio et al. 1971] [Putra et al. 2026b] [Qadr 2019] [Qadr 2022] [Rabi’ee and Hosseini 2019] [Radev and Hall 2000] [Rahimi et al. 2009] [Rammah et al. 2021] [Rashid 2018] [Reiss 1977] [Remetti et al. 2012] [Research Committee on Shielding of 1988] [Rexroad et al. 1964] [Rezaul Karim et al. 2024] [Ristić and Ninković 1976] [Rossin 1963] [Roy 1959] [Rzepecki 1985] [Sabri et al. 2022] [Sabry et al. 2021] [Sabry et al. 2022] [Sakamoto et al. 1988] [Sani et al. 2025] [Sardari et al. 2011] [Saudi and Gomaa 2018] [Sayyed et al. 2017] [Sayyed et al. 2024b] [Sayyed et al. 2024a] [Scarinci et al. 2023] [Schreiber 1961] [Setiawan et al. 2022] [Sharaf and Saleh 2015] [Shaikh et al. 2023] [Sharma and Jindal 2026] [Sheu et al. 2003] [Shin and Hirayama 1994] [Shin and Hirayama 1995] [Shure 1979b] [Shure 1979a] [Shure and Wallace 1977] [Shure and Wallace 1988] [Simanullang et al. 2022] [Simpson et al. 2016] [Singh and Badiger 2013] [Singh et al. 2006a] [Singh et al. 2008] [Singh et al. 2013] [Singh et al. 2014b] [Sm et al. 2017] [Smith and Wagner 2005] [Soliman 2025] [Song et al. 1969] [Spiegler 1960] [Stedry et al. 1996] [Stevens and Trubey 1968] [Stevens and Trubey 1972] [Stewart et al. 2024c] [Su and Jiang 1989] [Subbaiah and Sarangapani 2008] [Sun et al. 2025b] [Sun et al. 2025a] [Sunshine and Skyshine 2026] [Suteau et al. 2004] [Suzuki et al. 2011] [Swarup 1980] [Tahir et al. 2027] [Takeuchi and Tanaka 1984] [Tanaka and Takeuchi 1986] [Tashlykov and Mahmoud 2025] [Tasnim et al. 2021] [Tayama et al. 2000] [Terry 2005] [Thabit et al. 2024] [Atomics International, Canoga Park, Calif. and Thiele 1967] [Thiele et al. 1966b] [Thiele et al. 1966a] [Tobbala 2019] [Toshimas and Nobuo 1983] [Trubey 1966] [Trubey 1970a] [Trubey 1988] [Trubey 1991] [Tsubosaka et al. 2000] [Uematsu and Kurosawa 2005] [Vaidyanathan et al. 1977] [Van Tuyl 1970] [Varvayanni et al. 2008] [Velimirovic et al. 2023] [Vetter and Chilton 1971b] [Vetter and Chilton 1971a] [Vitali] [Vrubel’ et al. 1973] [Waly et al. 2016] [Wang et al. 2025c] [Wang et al. 2025a] [Wang et al. 2026c] [Wang et al. 2026b] [Wheeler 1950] [Wincel and Tsoulfanidis 1982] [Wogulis and Rooney 1964] [Wood 1982b] [Wood 1982a] [Wood 1982c] [Xu et al. 2023b] [Yadav et al. 2024] [Yamakoshi 1971] [Yamamoto 2014] [Yang 2026] [Yang et al. 2025b] [Yang et al. 2026b] [Yastrebinskii et al. 2023] [Yavuzkanat and ŞAhmaran 2024] [Yener and Mersinoĝlu 1989] [Yermakov and Zolotukhin 1967] [Yi et al. 2024] [Young 1980] [Yu et al. 2026b] [Yıldırım 2024] [Yıldız Yorgun et al. 2019] [Zadeh et al. 2025] [Zerby 1957] [Zharkov et al. 1973a] [Zharkov et al. 1973b] [Zhukovsky 2024] [Çağlar et al. 2026] [Çelebi et al. 2027] [Özdemir et al. 2018] [Şirin et al. 2026]

Decay heat, kinetics and reactor safety

The heat that does not stop. Fission-product decay heat measurement and standards, decay heat removal, reactor kinetics and accident analysis. 291 of its 400 records name decay heat, afterheat or decay heating, almost all of it for reactors that stay where they are built, which is taken up under Thin Subjects.

400 records. [A Fortran Code 1963] [Adams et al. 2016] [Ade and Gauld 2011] [Akiyama and An 1983] [Akiyama et al. 1998] [Akutsu et al. 1992] [Albright 1984] [Alfonsi et al. 2018] [Algora et al. 2010b] [Algora et al. 2010a] [Algora et al. 2011] [Algora et al. 2014] [Algora et al. 2025] [Alramady 2022] [American National Standard 1979] [Andrews et al. 2001] [Andritsos et al. 1994] [Antonello et al. 2022] [Antonello et al. 2023] [Apperson 1981] [Apperson 1982b] [Apperson 1982a] [Aqrawal and Guppy 1981] [Author 1960a] [Bali and Mayer 2024] [Bali and Mayer 2025] [Barclay and Dormuth 1974a] [Barclay and Dormuth 1974b] [Beasley et al. 1981] [Beaver et al. 1982] [Benoit et al. 2012] [Berkoe 1995] [Berry 1980] [Berry and Sanders 1981b] [Berry and Sanders 1981a] [Berry and Sanders 1982] [Berry and Sanders 1983] [Birney et al. 1988] [Bittermann and Wehling 1977] [Biwalkar et al. 2020] [Bloomfield and Bennet 1959] [Bopche and Sridharan 2010] [Bostelmann et al. 2024] [Boyack 1986] [Boyack et al. 1983] [Boyack et al. 1986] [Brady Raap et al. 2006] [Branco-Katcher et al. 2025] [Buchanan 1978] [Bunch and O’Dell 1969b] [Bunch and O’Dell 1969a] [Burns et al. 2022a] [Cadoff and Newby 1963] [Cardoni 2014] [Carter and Cillan 1985] [Cave and Kastenberg 1987] [Chakraborty et al. 1986] [Chang et al. 1985] [Chatham 1975] [Chen 2022b] [Chen and Yeh 1983] [Chen et al. 2025b] [Cheng and Ludewig 2007] [Cheng and Wei 2009] [Cheng et al. 2006] [Chesnut 1991] [Chiang 2013] [Chung and Welsh 1958] [Chunis et al. 1979] [Cillan and Carter 1985] [Clarity et al. 2021] [Clarity et al. 2022] [Coffield et al. 1980] [Corngold 1956] [Couchell et al. 1994] [Craig 1964] [Cramond et al. 1987a] [Cramond et al. 1987b] [Crum 1969] [Daugherty et al. 1970] [De Bear 1959] [Decay Heat Fractions 1997] [Decay Heat Power 1980] [Decay Heat Removal System 1956] [DECAY HEAT REMOVAL SYSTEM. 1959] [Dickens 1979] [Dickens 1981] [Dickens 1983] [Dickens 1986] [Dickens 1987b] [Dickens 1987a] [Dickens 1989] [Dickens 1990b] [Dickens 1990a] [Dickens 1991] [Dickens et al. 1976] [Dickens et al. 1991] [Dickey 1978] [Ding et al. 2025] [Doda et al. 2011] [Domanus and Sha 1988] [Dopchie et al. 1958] [Dueweke et al. 1989] [Dunn 1989] [Elgawhary et al. 1980] [Elkhawas et al. 2025] [Emrich 2016c] [Emrich 2023c] [England and Maynard 1972] [England et al. 1978] [Erbacher et al. 1995] [Ericson et al. 1989] [Estienne and Sonzogni 2018] [Experiment Design Manual 1964] [Westinghouse Electric Corp., Pittsburgh, Pa. (USA). Astronuclear Lab. 1964] [Feiye et al. 2017] [Feldman and Wei 2002] [Fijałkowska et al. 2017] [Fischer et al. 1997] [Fission Product Release 2003] [Foley et al. 1985] [Forsberg 2006a] [Forsberg 2007a] [Freitag] [Friesenhahn et al. 1976] [Fukuda et al. 2020] [Gao et al. 2023] [Garelis 1959] [Gasser 1960] [Gauld 2001] [Gauld 2006] [Gauld and Ryman 2000] [Gauld et al. 2010] [Geng et al. 2025] [Glasstone and Sesonske 1994a] [Graham and Godfrey 2023] [Graham et al. 2023] [Graham et al. 2024] [Grimble and LeTourneau 1958] [Gross and Strain 1980] [Grossman and Stein 1978] [Grzywacz 2013] [Gupta et al. 2010] [Gyorey et al. 1992] [Hahn 1958] [Haried 1982] [Harrington 1983] [Hartung 1978] [Hassan and Raja 1993] [Hatch et al. 1987b] [Hatch et al. 1987a] [Haugh et al] [Hawila 2019] [Hermann et al. 1994] [Hishida and Takeda 1991] [Hoffmann et al. 1989] [Hoffmann et al. 1993] [Holm et al. 1975] [Hong et al. 2016] [Honig and Mercado 1970] [Hopkins 1966] [Hottel et al. 1977] [Huaqi et al. 2022] [Hummel and Sen 2017] [Hung 1989] [Hwang and Kim 2022] [Ilas and Burns 2021b] [Ilas and Burns 2021a] [Ilas and Gauld 2014] [Ilas and Liljenfeldt 2017] [Illies 1971] [Iyori 1965] [Jaboulay and Bourganel 2012] [Jaquith et al. 1984] [Jeon and Wieselquist 2024] [Jiao et al. 2024] [Jin and Bang 2025] [Jin and Bang 2026a] [Jin and Bang 2026c] [Jin and Bang 2026b] [Jin and Bang 2026d] [Kamide et al. 1997] [Kang et al. 2012] [Karol et al. 1984] [Kasinathan et al. 1995] [Katakura 1992] [Keepin 1957] [Kelly and Erdmann 1978] [Kemmish et al. 1982] [Kiang et al. 1982] [Kiang et al. 1984] [Kim et al. 1961] [Kim et al. 2002] [Knebel and Mueller 1996] [Knebel et al. 1997] [Kolar 1968] [Kucinski et al. 2022] [LaBauve and England 1978] [LaBauve et al. 1979] [Lahaye et al. 2016] [Langerman 1994] [Laubie 1971] [Lee and Bang 2023] [Lee and McClanahan 2024] [Lee et al. 2006] [Lee et al. 2017] [Lewis 1971] [Lewis 2008] [Liao and Wright 2019] [Lisowski et al. 2021] [Litwin and Delgado 1989] [Liu et al. 2024b] [Loomis and Cozzuol 1988] [Lu et al. 2018] [Lu et al. 2019] [Ma et al. 2020] [Ma et al. 2021b] [Madni et al. 1979] [Magee and Hunsbedt 1989] [Magruder 2011] [Malinovic and Kazimi 1986] [Marr and Bunch 1971a] [Marr and Bunch 1971b] [Marshall et al. 1992] [Matulis et al. 2025] [Mayer and Guba 2023] [McMurry and Jones 1974] [Menegus and Ring 1958] [Mercier 2025] [Miltenberger and Henry 1992] [Minato et al. 2005] [Mo et al. 2020] [Mochizuki 2022] [Mochizuki 2026] [Mocquard 1971] [Moisseytsev and Sienicki 2015] [Morrison et al. 1975b] [Morrison et al. 1975a] [Mudali et al. 1993] [Namekawa et al. 1983] [Nellis et al. 2026] [Nelson et al. 1978] [Newby et al. 1963] [Ngoc Son 2014] [Nichols et al. 2023] [Niemczyk et al. 1983] [Nuclear Reactor Kinetics 2020] [Nuclear Reactor Kinetics 2024] [Nutt et al. 1979] [Obot et al. 1988] [Oka 2012] [Okuyama et al. 2024] [Orlov 1972] [Ostmeyer 1985] [Parker et al. 1971] [Parks 1988] [Parks and O’Kula 1985] [Patterson et al. 2026] [Pawlikiewicz 1961] [Peelle and Dickens 1982] [Perkins and Bari 1979] [Perkins et al. 1977] [Petrik and Turney 1970] [Pettus and Snioow 1972] [Pieczynski and Stewart 1968] [Plys and Paik 1989] [Polishchuk and Brezhniev 2026] [Porta et al. 2016] [Prosek et al. 1994] [Rahayu et al. 2025] [Raja et al. 1992] [Rasco et al. 2017] [Regulatory and Backfit Analysis 1988] [Reich 1987] [Roblyer 1988] [Rochman et al. 2026] [Roglans et al. 1992] [Roy et al. 1990] [Rudstam 1980] [Ruggles 1990a] [Ruggles and Morris 1989] [Pratt and Whitney Aircraft, Middletown, Conn. (USA). Connecticut Advanced Nuclear Engineering Lab. 1963c] [Saito 1973] [Sanders et al. 1987] [Sanokawa and Ouchi 1963] [Sasamoto and Tasaka 1970] [Savic 1959] [Sawan et al. 1978] [Sawyer 1993] [Schenter and Schmittroth 1975] [Schenter and Schmittroth 1979] [Schenter et al. 1990] [Schier and Couchell 1993] [Schier and Couchell 1994] [Schier and Couchell 1996] [Schier and Couchell 1997] [Schmittroth 1976] [Schmittroth 1978] [Schmittroth and Schenter 1975] [Schmittroth and Schenter 1976] [Schmittroth and Schenter 1977] [Schmittroth and Schenter 1979a] [Schmittroth and Schenter 1979b] [Schnitzler 1981] [Schriener and El-Genk 2014b] [Schrock 1978] [Schrock 1979a] [Schrock 1979b] [Schrock et al. 1978] [Schubert 1984] [Schwarz et al. 1991] [Serkiz and Lusk 1971] [Shaver et al. 1967] [Shen and Tian 2023] [Sherba and Sherman 1955] [Shure 1974] [Shure 1981] [Shure 1982] [Sieh and Bindra 2024] [Sienicki et al. 2006] [Singer et al. 1975] [Singer et al. 1979] [Singer et al. 1985] [Skoda et al. 2008] [Small Modular Reactor Digital 2026] [Smets 1961] [Smith et al. 1962] [Son and Hai 2016] [Sonzogni et al. 2023] [Soucy and Amar 1990] [Sporrer and Christenson 1975] [Sridharan 1990] [Stamatelatos and England 1975] [Storrer 1994] [Strupczewski 2020] [Suddath 1959] [Sun et al. 2025d] [Takeda 2008] [Talaat and Chen 2024] [Tasaka 1979] [Telleschi et al. 1971] [Thompson 1959] [Tiphine and Vallet 2022] [Todreas et al. 1996] [Trapp 1978] [Tumelero et al. 2022] [Turney and Petrick 1970] [Turney et al. 1972] [Tyror and Vaughan 1970] [Tzanos 1997] [Tzanos 1999] [Tzanos 2004] [Tzanos and Pedersen 1991] [Tzanos et al. 1982] [Tzoref and Saphier 1990] [Udy 1982] [Los Alamos Scientific Lab., N. Mex. and USDOE 1967] [van Dam 1998] [Vassilenko et al. 2022] [Vikram et al. 2023] [Vinck et al. 1972] [Vine 1986] [Volkov et al. 2020] [Wang and Jiang 2025] [Wang et al. 2019b] [Warkentin 1966] [Warner and Reeder 1986] [Watanabe and Hirano 1992] [Weaver et al. 2003] [Weaver et al. 2005] [Wells 1995] [Wichner et al. 1984b] [Wichner et al. 1984a] [Wieselquist et al. 2022] [Wilhelm 1997] [Williams et al. 2004] [Winegardner and Romsos 1972] [Wittekind 1994] [Wright 2001] [Wright and Lipinski 2006] [Yamamoto and Sugiyama 1978] [Yamamoto et al. 2011] [Yamoah et al. 2013] [Yarnell and Bendt 1976] [Yarnell and Bendt 1977a] [Yarnell and Bendt 1977b] [Yarnell and Bendt 1978] [Yoshida 1977] [Yoshida 2012] [Yoshida and Nakasima 1981] [Zaleski et al. 1974] [Zaytsev et al. 2013] [Zemanick and Brown 1975] [Zheng et al. 2012] [Zhengy and Shi 2008] [Zhong et al. 2025b] [Zhong et al. 2025a] [Zohuri and Abedi-Varaki 2026] [Zohuri and McDaniel 2019b] [Zohuri et al. 2025]

Shield design, optimisation and weight

The shield as an engineering problem. Shield design methods, minimum-weight and shadow shield optimisation, reactor-specific shield designs, and the Oak Ridge Tower Shielding, Lid Tank and Bulk Shielding facilities. The cluster’s median publication year is 1972, and 58 titles concern those three facilities, two of which appear in the programme’s own reports.

348 records. [Aalto et al. 1964] [Abagyan et al. 1969] [Abagyan et al. 1972] [Abbott 1953] [Adams et al. 2017] [Adams et al. 2019] [Adkins 1974] [Albert and Welton 1950] [Alharbi and Alharbi 2025] [Allen 1993a] [Army Gas-Cooled Reactor Systems 1965] [Arnold 1964] [Atwell et al. 1989] [Bagheri et al. 2024] [Bagley 1958] [Barnes et al. 1988] [Barthel and Sarigul-Klijn 2016] [Bartine and Williams 1977] [Bartine and Williams 1978] [Bartine et al. 1975b] [Bartine et al. 1975a] [Bartine et al. 1979] [Basu et al. 2022] [Beever and Rusling 1965] [Benchmark Shielding Calculations 1990] [Berzonis and Bolyatko 1989] [Billings 1972] [Billings and Langley 1965] [Blessing 1957] [Blizard 1953] [Blizard and Clifford 1950b] [Blizard and Clifford 1950a] [Blizard et al. 1953] [Bloomfield 1967] [Blosser and Clifford 1952] [Bonsall et al. 1969] [Boulette and Bunch 1971] [Boulette and Marr 1972a] [Bouquet 1962] [Brainina et al. 1967] [Bugis and Liu 2018] [Buongiorno 2004] [Burgart 1971] [Burgart 1972] [Butler 1964] [Butler 1967] [Butler and Cook 1959] [Cady 1960] [Cain 1964] [Cain et al. 1964] [Capo et al. 1957] [Carter 1983] [Cegelski 1962] [Celnik and Nakache 1964] [Celnik et al. 1964] [Champion et al. 1986] [Chapman and Flynn 1953a] [Chapman and Flynn 1953b] [Chapman et al. 1954] [Chapman et al. 1965] [Sunil 2025] [Chen and Wang 2010] [Chen and Yan 2023] [Chen et al. 2019] [Chen et al. 2023] [Clark 1969b] [Clark et al. 1971] [Clifford 1950] [Clifford and Blizard 1951] [Clifford et al. 1954] [Clifford et al. 1967] [Clifford et al. 1969] [Cochran et al. 1954] [Cochrane and Mesh 1970] [Connolley and Lahti 1971] [Courtney and Dwight 1991] [Culambourg et al. 1969] [De Angelis 2003] [Deane et al. 1992] [deGanahl et al 1954] [Diamond 1957] [Disney 1977] [Dodds et al. 1981] [Dresner 1959] [Dudziak and Battat 1967] [Dudziak and Battat 1969] [Dunford, et al 1973] [Edwards 1954] [Edwards 1957] [Edwards et al. 1958] [El-Sheikh 1974] [Enginol 1968] [Engle and Mynatt 1973] [Englesson 1962] [Fagan 1959] [Fagan 1960] [Fei et al. 2016] [Fei et al. 2019b] [Fei et al. 2021] [Fischer et al. 2004] [Foster 1965] [Foutch et al. 2024] [Freestone et al. 1970] [Friedman 1958] [Frisina 1985] [Fritz et al. 1972] [Fu and Ingersoll 1987b] [Futtermenger et al. 1975] [Gallmeier et al. 1995] [Ganapol et al. 1975] [Generozov and Sakovich 1970] [Generozov and Sakovich 1972] [Generozov et al. 1973] [Gerstl 1977] [Goddard et al. 1972b] [Goldstein and Blizard 1951] [Gonçalves et al. 2001] [Goryachev et al. 1974] [Grotenhuis and Butler 1956] [Grotenhuis et al. 1962] [Han et al. 2025c] [Hansda and Mammen 2021] [Hansen 1963] [Hanson et al. 2024] [Hardtke 1961] [Harima et al. 1989] [Harima et al. 1991] [Harris et al. 1989] [Haschke et al. 1975] [Hatefi Moadab and Kheradmand Saadi 2019] [Havranek 1971] [He et al. 2022a] [Herrmann and Lahti 1969] [Holland 1970] [Holland 1971] [Holland and Kolb 1970] [Homeyer 1964] [Horton 1958] [Howard and Jacks 1963] [Huang et al. 2024b] [Huang et al. 2025b] [Hurwitz 1957] [Ibrahim et al. 2022] [Ibrahim et al. 2023] [Ingersoll 1990a] [Ito 1972] [Ivakhin et al. 2012] [Jaeger 1970] [Jandaghian et al. 2024] [Jaske 1951] [Jiang and Sheu 1993] [Johnson 1960] [Johnson and Mason 1965] [Johnson and Mason 1966] [Jordan et al. 1965] [Kam and Schamberger 1961] [Kanai and Ito 1973] [Kansouh 1994] [Karcher 1967] [Karp et al. 1972] [Kataoka 1964] [Keshishan and Dix 1992] [Kidd 1970] [Kim 1975] [Kim and Youn 2023] [Klumpp 1971] [Klumpp 1972] [Knight and Anghaie 2002] [Kolekar et al. 2013] [Kramer et al. 2013] [Kramer et al. 2018] [Krueger 1966] [Krueger 1971] [Kwak et al. 2021] [Lahti 1969] [Lahti 1971] [Lahti 1973a] [Lahti 1973b] [Lawrence and Dorning 1980] [Lee 1958b] [Lee 1971] [Lee and Cho 2025] [Leech] [Leech and Rohach 1972] [Li et al. 2022c] [Li et al. 2023f] [Li et al. 2024] [Liu 1998] [Liu 2018] [Liu et al. 2017] [Liu et al. 2022b] [Liu et al. 2026a] [Lowen and Sowle 1966] [MacKellar 1959] [MacKellar 1961] [MacKellar et al. 1961] [Maerker and Muckenthaler 1972] [Maerker and Muckenthaler 1976] [Maerker et al. 1971] [Magnuson and Callihan 1956] [Manturov and Nikolaev 2016] [Manuilov 1967] [Marshall 1986] [Marshall and Gallup 1991] [Marshall et al. 1987] [McArthy and Kirn 1969] [McCaffrey et al. 2009] [McCool 1956] [McCool and Otis 1960] [McWherter 1953] [Meem and Fairbanks 1956] [Mesh and Cochrane 1969] [Miller et al. 1975] [Millet and Sparks 2026] [Mitchell 1954] [Mittelman 1965] [Morrison et al. 1972] [Moteff 1960] [Muckenthaler 1992] [Muckenthaler 1997] [Muckenthaler et al. 1963] [Nagel et al. 1975] [Nasrabadi and Baghban 2013] [Nealy 2003] [Norman and Oliver 1966] [Odano et al. 2000] [Ondo Meye et al. 2022] [Operating Manual 1985] [Otis 1959] [Pal Chowdhury et al. 2026] [Pautz et al. 2019] [Penny 1971] [Pepper 1969] [Peterson 1961] [Peterson 1962] [Phelps 1961] [Podgor 1951] [Ponti 1980] [Preiser et al. 1954] [Preliminary Study of Fast 1954] [Radcliff and Williams 1990] [Radiation Shielding Design 1974] [Radiation Shielding Design 1975] [Radulescu et al. 2024a] [Radulescu et al. 2024b] [Radulescu et al. 2025] [Rashed 1972] [Reactor and Shield Design 1965] [Reed 1970] [Rees and Malenfant 2002] [Removal Site Evaluation Report 1996] [Renken 1970] [Robb 2004] [Rockwell 1956] [Rodriguez and Shapiro 1972] [Roh and Choi 2004] [Roh et al. 2008] [Rohach 1967] [Rohloff and Crommen 1970] [Rooyen 1993] [Ruehle 1973] [Sahin 1973] [Sankaranarayanan et al. 1971] [Sapyta and Simmons 1973] [Sapyta and Simmons 1975] [Sarangapani et al. 2006] [Sariyer and Küçer 2018b] [Sasse 1965] [Sasse 1966] [Sato et al. 1996] [Schamberger 1961] [Schleifenheimer 1958] [Schnier 1970] [Schnier 1971] [Schultz and Vogt 1975] [Schultz et al. 1967] [Scoles and Crouch 1962] [Seifferth et al. 1978] [Shield Design for Snap 1961] [Shin 2003] [Siler 1961] [Slater and Bucholz 1995] [Slater et al. 1979] [Slater et al. 1980] [Slater et al. 1981a] [Smith 1966] [Smith et al. 1989] [Smolen 1956] [Song et al. 2020] [Atomics International, Canoga Park, Calif. and Steichen 1963] [Stevens and Claiborne 1970] [Stewart et al. 2024a] [Stoces et al. 1971] [Suarez 1967] [Subbaiah et al. 2013] [Sun et al. 2016b] [Sutondo and Syarip 2018] [Suzuoki et al. 2000] [Syarip et al. 2025] [Szilvasi 1965b] [Tanaka 1966] [Tanaka and Higashihara 1968] [Tanaka et al. 1972a] [Technical Specifications 1979] [Technical Specifications Tower Shielding 1982] [Technical Specifications Tower Shielding 1986] [Terney and Fenech 1967] [Tillotson 1961] [Tomlinson 1959] [TOWER SHIELDING FACILITY. Preliminary 1953] [Tran and Turner 1984] [Troubetzkoy 1962] [Troubetzkoy and Kalos 1961] [Troubetzkoy and Wohl 1970] [Trubey 1970b] [Tunes et al. 2017] [Ueki and Yamakoshi 1972] [Umeda 1969] [Van Thuong et al. 2024] [Vlachovsky 1968] [Wallace 1974] [Wallace 1981] [WAllace 1996] [Ward and Holland 1979] [Warman 1971] [Weber 1971] [Westover et al. 2012] [Whetstone and Kearfott 2016] [Williams 1977] [Williams and Engle 1976] [Williams and Engle 1977a] [Williams and Engle 1977b] [Willoughby 1976] [Wilson and Holland 1961] [Wohl and Spielberg 1971] [Wohl et al. 1972] [Woodsum and Rost 1957] [Wrights 1980] [Wu et al. 2021] [Yadav 2025] [Yamaji and Sako 1994] [Yang and Iotti 1975] [Yi and Qiang 2019] [Yin et al. 2013] [Zhang and Li 2021] [Zheng et al. 2024] [Zirkind 1951] [Zuo et al. 2018]

Reactor fuel, cooling and the wider nuclear literature

The residual, reported and not hidden. Reactor work that belongs to no heading above, including fuel elements and their fabrication, fission product release, liquid-metal-cooled reactors, the Plum Brook test reactor, gaseous-core and pulsed propulsion concepts, and general surveys of nuclear propulsion that span ships, aircraft and rockets at once.

301 records. [Abadie-Maumert 1960] [Abernathy 1961] [Abou Jaoude 2020] [Aithal et al. 1993] [Aithal et al. 1994] [Althaus et al. 1974] [Altomare et al. 1966] [Altseimer et al. 1974] [Ancona et al. 2025] [Anderson 1971] [Air Force Nuclear Propulsion 1959] [Baldwin and Clark 1993] [Baldwin et al. 1980] [Barkley 1969b] [Barkley 1969a] [Bass and Johnson 1978] [Battat et al. 1968] [Beall 1951] [Benedict et al. 1963] [Bengtsson and Skygge 1962] [Bennett and Miller 1991a] [Bennett and Miller 1991b] [Bhattacharyya et al. 1988] [Bhattacharyya et al. 1993] [Blevins et al. 2001] [Bloomfield et al. 1986] [Bolin et al. 1991] [Bolt et al. 1958] [Bolukbasi and Margulis 2026a] [Borbash et al. 1968] [Bowles and Arrighi 2004] [Von Braun 1966] [Bricklen and Davis 1969] [Brisbois and L’Homme 1975] [Brown 1962] [Bussard 1959] [Bussard 1963] [Bussard 1968] [Bussard 1988] [Butterfield 1956] [Butz 1959] [Cassady et al. 2007] [Cassenti 1991] [None 1967a] [None 1967b] [Chandler et al. 1957] [Chandler et al. 2025] [Chapman 1960] [Chikazawa et al. 2009] [Primachenko 2013] [Cho et al] [Ciesla et al. 1968] [Clark 1952] [Clark et al. 1992b] [Clement and Rust 1978] [Collins 1987] [Conn et al. 1957] [Connolly 1963] [Conway 1956] [Cooper 1961] [Cooper 1965a] [Cooper 1965b] [Cooper 1966] [Coppi and Casci 1962] [Corliss 1960] [D’elia 1965] [D’Elia 1973] [D’Elia 1974] [Dalcher 1969] [Dalzell and McGee 1957] [Davis 1963] [DayDay 1982] [De Santis et al. 2013] [Delson 1964] [Denisov 1974] [Pratt and Whitney Aircraft, Middletown, Conn. (USA). Connecticut Advanced Nuclear Engineering Lab. 1964a] [Pratt and Whitney Aircraft, Middletown, Conn. (USA). Connecticut Advanced Nuclear Engineering Lab. 1963a] [Pratt and Whitney Aircraft, Middletown, Conn. (USA). Connecticut Advanced Nuclear Engineering Lab. 1963b] [Pratt and Whitney Aircraft, Middletown, Conn. (USA). Connecticut Advanced Nuclear Engineering Lab. 1964b] [Design Studies of Nuclear 1962] [Atomics International, Canoga Park, Calif. and Dickenson 1967] [Dillon and Burris 1954] [Dobranich 1987] [Dolatshahi and Kaul 1983] [Doyle 1948] [Dugan and Kahook 1992] [Dugan and Kutikkad 1993] [Economic Study of Nuclear 1961] [Edwards 1959] [Effluent Containment System 1995] [Ефимов et al. 2022] [El-Genk et al. 1993b] [El-Genk et al. 1994b] [English 1982] [Farbman et al. 1960] [Fecych 1968] [Fecych 1969] [Feldman 2020] [Finger 1963] [Finger and Rom 1962] [Fox 1961] [Fox 1963] [Gaffin 1959] [Gardner 1958] [Garro et al. 1972] [Gleicher et al. 2023] [Gleicher et al. 2024] [Gluyas and Watson 1975] [Goryachenko and Sabaev 1970] [Gotsky et al. 1959] [Grey 1973] [Gronich 1964] [Hadley et al. 1965] [Haffner 1956] [Hartland 1960] [Hasse 1971] [Haubenreich and Leland 1954] [Heat-aided method for separating 1986] [Hedden 1962] [Helstrom 1956] [Henderson 1967] [Hewitt et al. 1978] [Hill et al] [Hoecker et al. 1963] [Howe 1994] [Islam and Haque 2025] [Jaffe et al. 1988a] [Jaffee et al. 1965] [Jahshan and Kammash 2005] [Jaumotte 1968] [Jiaju et al. 2025] [Jiang et al. 2026] [Johnson 1964] [Jones 1964] [Juhasz 2007] [Kadokawa 1970] [Kanareykin 2022] [Karimi and Wolf 1978] [Keller 1962] [Kerwin 1971] [Khurmi 2021b] [Kirchgessner et al. 1971] [Kish and Weinstein 1970] [Klein et al. 1988] [Koenig and Lell 1989] [Kramer and Gronich 1965] [Krasnow et al. 1959] [Kress et al. 2020] [Kuhlman and Glasgow 1957] [Kukhtevich et al. 1965] [Kukhtevtch et al. 1960] [Kwant and Boardman 1992] [Lahti et al. 1968] [Lamb 1990a] [Lamb 1990b] [Lanzo and Savino 1962] [Lanzo and Savino 1963] [Lee et al. 1976] [Lewis et al. 1990] [Li et al. 2026c] [Liquid metal cooled nuclear 1983] [Liquid metal-cooled nuclear reactor 1986] [Lowry 1977] [Lustig 1971] [Madsen 1992] [Mantle and Morss 1970] [Marcille 2006] [Marjon 1957] [Marjon 1963a] [Mather 1968] [McCauley and Brown 1972] [Atomics International Div., Canoga Park, Calif. (USA) and McClelland 1969] [McClung 1962] [McClung 1965] [McGonnagle and Perry 1959] [McGonnagle et al. 1959] [McLafferty 1968] [Medin and Clark 1956] [Author 1962a] [Merckx 1961] [Merriman and Chase 1955] [Michael 2004] [Miller et al. 1991] [Mitsuboshi and Sagara 2025] [Mohammad Jaradat et al. 2024a] [Mohler 1967] [Moisseytsev and Petroski 2023] [Moser 1958] [Murgatroud 1956] [Murray 1980] [Murray 1993] [Murray 2001] [Murray 2009] [Murray and Holbert 2015] [Murray and Holbert 2020] [Murray and Holbert 2026] [Murthy 1971] [Proceedings of Nuclear Propulsion 1962] [Nakazato 1957] [Nelms and Cooper 1959] [New Götaverken System 1962] [Nuclear Powered Tanker Design 1959] [Nuclear propulsion] [Nuclear Propulsion Technical Interchange 1993a] [Nuclear Propulsion Technical Interchange 1993b] [Nuclear Propulsion 2008] [Nuclear Reactor Sources 1984] [Olsen et al. 1993] [Westinghouse Electric Corp., Pittsburgh, Pa. (USA). Astronuclear Lab. 1967] [Parlos and Metzger 1993] [Parlos and Metzger 1994] [Partain et al. 1969] [Paul et al. 2025] [Pelaccio et al. 1993b] [Perry et al. 2014] [Pincock and Chase 1969] [Pincock and Kunze 1969] [Pitkin 1972] [Plebuch and Martinez 1969] [Division of Isotopes Development, AEC 1964] [Powell et al. 1987] [Powers 2020] [Poznanski 1967] [Present Status and Problems 1971] [Proceedings of an Advanced 1967] [Pshenichnikov 1975] [Quinteros] [reactor program, progress report 1965] [reactor program, progress report 1965] [Reitmayr et al. 2024] [Ribeiro and Pittner 2018] [Roelofs et al. 2019] [Rojas-Palma 2004] [Rom 1959] [Rom 1971a] [Rom and Finger 1962] [Rosa 1962] [Rothman 1963a] [Rothman 1963b] [Ruggles 1990b] [Salley and Burt 1959] [Samaras] [Samim Anghaie et al. 2002] [Schmitz et al. 2008] [Shen and Haas 1962] [Shobe 1963] [Shoults 1948] [Skibin 1972] [Smith and Anghaie 2004] [Smith and Doe 1963] [Pratt and Whitney Aircraft, Middletown, Conn. (USA). Connecticut Advanced Nuclear Engineering Lab. 1962] [None and Atomics International, Canoga Park, Calif. 1966] [Sondelski and Nellis 2019a] [Sondelski and Nellis 2019b] [Spinrad and Tripathi 1978] [Stark 1993] [Steinberg 1962] [Stephens 1964b] [Stone et al. 1993a] [Straker and Muckenthaler 1969] [Summary of Nuclear Propulsion 1975] [Tanner 1995] [Tasaka and USNRC 1979] [Teräsvirta and Hyvärinen 2024] [Thermal Hydraulics Aspects 2019] [Thompson 1957] [Thorpe 1965] [Thurston et al. 1963] [Tribus 1955] [Tseng and Jester 1984] [Tumm 1968] [Ullmann 1960] [Venetoklis 1994] [Venting Device for Sodium-Cooled 1973] [Kernforschungszentrum Karlsruhe (Germany). Inst. fuer Reaktorentwicklung et al. 1973] [Wakelin and James H. 1960] [Wang et al. 2023b] [Wang et al. 2024a] [Ward et al. 2020] [Ward et al. 2021] [Warren 1955] [Watanabe et al. 1991] [Waters et al. 1962] [Weisbrodt et al. 1965] [Weitzberg 2003] [Westhoven 1969] [Westmoreland et al. 1961] [Westphal 1954] [Whitmarsh 1971] [Wijker 1964] [Wilks 1959] [Williams et al. 2005b] [Witteman et al. 2023] [Woods 1954] [Woolson 1972] [Woyski 1967] [Woyski 1968] [Wyatt 1962] [Zhang 2023] [Zohuri 2016] [Zohuri 2019]

The nuclear aircraft and its programme record

The programme’s own record, and the reason this survey reaches into the Office of Scientific and Technical Information. Quarterly and semiannual progress reports, the Aircraft Reactor Experiment, the Heat Transfer Reactor Experiments, the Aircraft Shield Test Reactor, the nuclear turbojet studies and the later proposals for nuclear-powered transports. 200 of its 260 records date from 1961 or earlier, the year the programme was cancelled, so most of what was written about the aircraft was written while it was being attempted.

260 records. [A Report 1954] [Adams and Nelson 1950] [Ahrends 1955] [Aircraft Nuclear Propulsion Project 1958a] [Aircraft Nuclear Propulsion Project 1958b] [Aircraft Nuclear Propulsion Project 1960] [AIRCRAFT NUCLEAR PROPULSION PROJECT 1961] [Alvis and Chessman 1957] [Arnold 1960] [NEPA Medical Advisory Panel 1949] [Nuclear Powered Aircraft 1950] [NEPA Project Quarterly Progress 1950] [Background Information for Nuclear 1957] [Aircraft Nuclear Propulsion Project 1957b] [Aircraft Nuclear Propulsion Project 1957a] [Summary Report of HTRE 1959] [Aircraft Nuclear Propulsion Project 1959] [Papers Presented at Anp 1959] [Baker 1953] [Barnes 1960] [Baxter et al. 1960] [Bettis et al. 1957b] [Bettis et al. 1957a] [Bogart and Valerino 1953] [Brady 1958] [Brady 1960] [Breslauer 1960] [Brocklehurst 1959] [Bruner 1948] [Cain 1957b] [Cain 1957a] [Cannon et al. 1961] [Cathers and Ferguson 1953] [Cavicchi et al. 1959] [Cohen et al. 1956] [Comassar 1962] [Connolley and Weber 1958] [Cooley 1948] [Cooley 1953] [Cooper and Henderson 1960] [Cope 1957] [Cottrell 1951] [Cottrell 1952a] [Cottrell 1952b] [Cottrell 1952c] [Cottrell 1953] [Cottrell 1960] [Cottrell et al. 1955b] [Cottrell et al. 1955a] [Cottrell et al. 1958] [Coveyou and Macauley 1951] [Crabbe 1955] [Crocker 1957] [Cuneo 1956b] [Cuneo 1956a] [Cyl-Champlin and Krase 1956] [Delaney 1959a] [Delaney 1959b] [Delaney 1961a] [Delaney 1961b] [Delaney 1961c] [Deng et al. 2022] [Deng et al. 2023] [Dibble 1958] [Digital Start-up Control 1958] [Dini 1961] [Doyle 1951] [Edwards and Simpson 1962] [Elgert et al. 1959] [Ellis and Thompson 1950] [Emmert 1957] [Ergen et al. 1957] [Farris 1954] [Ferguson 1957] [Ferry 1961] [Finnegan and Rom 1968] [Finnegan et al. 1971] [Fischer 1960] [Fischer et al. 1961] [Fishbach 1969] [Fishbach and Strack 1968] [Fishback 1969] [Foster et al. 1959] [Fraas and Savolainen 1954] [Fraas and Savolainen 1956] [Fries 1958] [Gamertsfelder 1954] [Gasser 1947] [Gilbert 1955c] [Gilbert 1955b] [Gilbert 1955a] [Goodman 1948] [Gorker 1955] [Graff 1947] [Greenwood 1968] [Grey 1969] [Griffin 1959] [Gumto and Puthoff 1970a] [Gumto and Puthoff 1970b] [Haffner et al. 1958] [Haffner et al. 1959] [Hanchon and Pope 1960] [Harper and Habel 1960] [Henderson 1960] [Hobbs et al. 1948] [holmes 1951] [Holton 1972] [How ANP Turbine Lubricants 1959] [Hullings and McDaniel 1960] [Humble et al. 1950] [Hutton et al. 1952] [Hyland and Lennon 1970] [Improvements in Thermal Nuclear 1957] [Jankiewicz 1967] [Johnson and Reedy 1966] [Jones and Thompson 1974] [Jordan et al. 1957] [Joseph et al. 1954] [Kerkhoff 1957] [Ketron 1959] [Kim et al. 2025] [King et al. 1958] [Klein 1948] [Kokkinos 2005] [Koshuba 1949] [Kostigen 1960] [Krasnow et al. 1957] [Kress 1958] [Lalor and Schmill 1960] [Larson 1958c] [Larson 1958b] [Larson 1959a] [Larson 1959c] [Larson 1959b] [Larson 1959d] [Larson 1960d] [Larson 1960g] [Larson 1960b] [Larson 1960a] [Larson 1960c] [Larson 1960e] [Larson 1960f] [Layman 1962] [Level 1962] [Leverett 1959] [Levine and Ekern 1960] [Levine and Ekern 1961] [Lewis 2024] [Link and Clark 1961] [Lubarsky and Greenstreet 1953] [Manly et al. 1958] [Manned Space Flight Nuclear 1972b] [Manned Space Flight Nuclear 1972c] [Manned Space Flight Nuclear 1972d] [Manned Space Flight Nuclear 1972a] [Marjon 1958] [Martin et al. 2024] [McCusker 1989] [McLay 1961] [McLay and Campbell 1961] [Meyer 1965] [Mills and Meem 1972] [Mitrica et al. 2010] [Morand and Gehring 1961] [Muehlenkamp 1955] [Na 1957] [Nance 1956] [Nance 1957] [Nance and Perry 1958] [Nash 1980] [NERVA 1971] [Nielsen 1950] [Ntantis and Mohammed 2026] [NUCLEAR REACTOR AS 1961] [Nuclear-Powered Aircraft? 1995] [Orazio and Werle 1970] [Parker et al. 1960] [Perry 1958] [Poppendiek and Greene 1956] [Porter 1957] [Powell 1960] [Powell and Ratliff 1960] [Price 1957] [Pritzlaff 1957a] [Pritzlaff 1957b] [Propulsion of Aircraft 1950] [Pryor 1961] [Puechl 1956] [Puthoff and Silverstein 1970] [Battelle-Northwest, Richland, Wash. Pacific Northwest Lab. 1971] [Redding 1948] [Reed 1959] [Reid and Terrall 1957] [Report of the Shielding 1950] [Riley 1961] [Robson and Peters 1972] [Rodgers and Mausteller 1963] [Rom 1969] [Rom 1970] [Rom 1971b] [Rom and Masser 1971] [Ross 1960] [Rothrock 1948] [Ruffman 1952] [Russell et al. 1960] [Russell et al. 1961] [Salam and Elisabeth 2020] [Savage et al. 1958] [Savolainen 1954] [Savolainen 1955] [Savolainen 1956] [Schaeffer and French 1959] [Schaeffer and Stokes 1958] [Schludi 1963] [Schmickrath 1960] [Schwartz 1952] [Schwartz 1953] [Schwartz et al. 1950] [Selengut 1955] [Seventeenth Quarterly Progress Report 1960] [Seventh Meeting 1960] [Shoults 1958] [Silverstein 1969] [Site Survey Monitoring 1959a] [Site Survey Monitoring 1959b] [Sixth Semi-Annual ANP Shielding 1958] [Skirvin 1961] [Smith 1958] [Spry 1992] [Starling and Emmert 1955] [Stever 1948b] [Stever 1948a] [Stigall 1958] [Strack 1971] [Strong 1959] [Szawlewicz 1956a] [Szawlewicz 1956b] [Szawlewicz et al. 1957b] [Szawlewicz et al. 1957a] [Szekely 1961] [The Nuclear powered Bomber 2018] [the Nuclear-Powered Bomber 2019] [Thermal Nuclear Reactor 1956] [Thornton and Blumberg 1961] [Thornton and Rothstein 1962] [Vasiljevic 1964] [Vineberg 1960] [Wehrmann 1950] [Weinberg 1950] [Weinberg 1957] [Wells et al. 2014] [Wenstrup 1961a] [Wenstrup 1961b] [Whitmire 1975] [Whittemore 1988] [Wild 1967] [Wild 1968] [Williamson 1953] [Woodbridge 1955] [Wright 2003]

Radiation effects on materials, components and electronics

What the reactor does to the aeroplane around it. Radiation damage to lubricants, elastomers, plastics, metals and electronic components. 13 titles name the aircraft, among them studies of aircraft lubricants and fuels, tyres, transparent materials and tank sealants.

217 records. [Aguiar and Martinella 2026] [Alberman and Stoller 2009] [Alexander 1991] [Allen 1962] [Anderson 1952] [Asmus 1975] [Radiation Damage to Elastomers 1954] [HANDBOOK OF NUCLEAR RADIATION 1956] [Proceedings of the Second 1958] [Auden 2023] [Barnes 1981] [Bauerlein 1959] [Bezerra et al. 2007] [Bezerra et al. 2011] [Bobbitt and US Atomic Energy Commission (AEC) 1949] [Boehmer et al. 2003] [Bolt and Carroll 1957] [Bolt and Carroll 1958b] [Bolt and Carroll 1958a] [Bopp and Sisman 1953] [Bopp and Sisman 1956] [Born 1961] [Bosnak 1960] [Bramman et al. 1973] [Brinkman and Wiedersich 1965] [Brueck 2016] [Bräunig and Wulf 1999] [Bunch 1967] [Litton Industries INC Woodland Hills CA 1963] [Hughes Aircraft Co Fullerton Ca 1963] [Cernak 1960b] [Charlesby 1975] [Chyi-Shan et al. 1994] [Clark 2011] [Collins and Calkins 1956] [Coombe et al. 1964] [Cortissone et al. 1965] [Cosgrove et al. 1961] [Coyle et al. 1961] [Cupp 1963] [Daly 2013] [Daly and Noffke 1971] [Westinghouse Electric Corp., Pittsburgh, Pa. (USA). Astronuclear Lab. 1966a] [Decrescente et al. 1968] [Delman et al. 1960] [Delman et al. 1961] [General Dynamics Corp Pomona Ca Pomona Div 1963] [EFFECTS OF RADIATION 1957b] [EFFECTS OF RADIATION 1957a] [Effects of Radiation 2006] [English and Hyde 2012] [Factors Affecting Radiation Damage 1994] [Fink 1957] [Firle and Flanagan 1970] [Floriduz and Devine 2018] [Freas 1964a] [Freas 1964b] [Freis et al. 2008] [Fritz 1964] [Fukuoka and Cleland 1980] [Gauster 1976] [Gedam] [Gietzen et al. 1972] [Greenwood 1989] [Griesbach and Server 1999] [Griffiths 2026] [Groos 1972] [Gunst et al. 1974a] [Gunst et al. 1974b] [Gunst et al. 1975] [Ha and Kim 2025] [Haas et al. 1960] [Haley and Wyer 1966] [Haley and Wyer 1967] [Harrington 1956] [Hart et al. 1978] [Hasse and Hartley 1972] [Higgins 1953] [High-Resolution Imaging of Radiation 2000] [Hnatek 1969] [Hoagland 1965] [Hopkins et al. 1962] [Hotten and Carroll 1958] [Howe 1974] [Iida et al. 2001] [Jackson et al. 2025] [Jeong et al. 2026] [Johnson and Sicilio 1957] [Jones et al. 1963] [Junga et al. 1978] [Kalin 1982] [Kangilaski 1967] [Khan et al. 1981] [Kocherov 1991] [Kumar et al. 2025] [Laine 1962] [Lan et al. 2024] [Lee 1985] [Li and Kraner 1992] [Lidbury et al. 2005] [Lidbury et al. 2007] [Liebowitz 1992] [Lindgren 1984] [Liscka et al. 1995] [Liu et al. 2025] [Llewellyn 1964] [Louis et al. 2024] [Lu et al. 2006] [Macha et al. 2025] [Mammadov 2024] [Marwick 1975] [Massoud et al. 2010] [Matthes 1989] [Mayberry 2012] [McCormick 1963] [McKeen 2020] [Mendes and Tomal 2025] [Merkel] [Meta-Linked Polyphenyl Ethers as 1961] [Meyer et al. 1964] [Miler and Parkinson 1957] [Miller and van Lint] [Mills and Parker 2005] [Mitchell and Wilson 1965] [Moniwa and Nakamura 1966] [Monreal et al. 2019] [Moore et al. 1972] [Morgan 1961] [Moteff et al. 1969] [Mukherjee] [Mulligan et al. 2023] [Neimark 1961] [Nekrasova et al. 2019] [Nelson 1975] [Northwood and Gilbert 1974] [Obermueller et al. 2018] [Olesen 1966] [Onchi 1995] [Ondracek and Materna 2018] [Onozuka et al. 1977] [Papaioannou et al] [Pappas 1966] [Park et al. 2000] [Peng et al. 2025] [Perkins 1963] [Phillips et al. 2022] [Pirfo Barroso et al. 2010] [Platt et al. 2007] [Pooley 1975] [Proceedings of an IAEA 1987] [Properties of Reactor Materials 1962] [Properties of Reactor Materials 1963] [Radiation Damage 1994] [Radiation Damage in Materials 2020] [Radiation Damage in Reactor 1964] [Radiation Damage of Structural 1994] [Radiation Damage to Zirconium 1994] [Cai et al. 2025] [Radiation-Hardened Optoelectronic Components 1992] [Rafik and Izerrouken 2020] [Ray 2023] [Recovery from Radiation Damage 1994] [Reynolds 1963a] [Rice 1960] [Rinaudo et al] [Robertson 1970] [Rochman et al. 2023] [Rose 1989] [Scheiwe and Harrison 1963] [Schlosser et al. 1962] [Schmidt 1958] [Schmidt and Johnson 1956] [Schrimpf et al. 2010] [Seguchi and Morita 1999] [Seidel 1969] [Senn 1989] [Shimkova and Slunechko 1968] [Shure 1966] [Shure 1983] [Simulation of Neutron Irradiation] [Sisman and Bopp 1957] [Smith and Alkire 2003] [Snow et al. 1969] [Some Effects of Gamma 1957] [Some Effects of Gamma 1958] [Spencer et al. 2000] [Stephens 1964a] [Stephens 1964c] [Straalsund and Dahl 1971a] [Straalsund and Dahl 1971b] [Westinghouse Electric Corp., Pittsburgh, Pa. (USA). Astronuclear Lab. 1966b] [Tarneja et al. 1963] [Oak Ridge National Lab., Tenn. 1958] [The Effect of Nuclear 1962a] [The Effect of Nuclear 1962b] [The Effect of Nuclear 1963] [The Effects of Nuclear 1958] [The Radiation Damage Event] [Third Semi-Annual Radiation Effects 1959] [Towle 1980] [Trimmer 1982] [Truong et al. 2002] [Tucker and Wechsler 1970] [Southwest Research Inst San Antonio TX 1963] [Van de Voorde 1969] [Wall 1975] [Wattier et al. 1965] [Williamson and Beetham 2020] [Wilson et al. 1966] [Wolf 1971] [Woolley 1962] [Xiao et al. 2023] [Xiao et al. 2024] [Zhang and Platt 2011] [Ziao et al. 2022] [Übeyli 2007] [Übeyli and Übeyli 2009]

Crew dose and the human limit

The dose the crew was allowed, and a literature that measures a different one. Crew radiation exposure, radiation effects in people and primates, and the shielding of space crews. 49 of its 65 records name aircrew or cosmic radiation, and every one of them concerns the natural radiation field at altitude, so the modern literature on dose in flight is about the sky rather than about a source carried aboard.

65 records. [Abeyratne 1997] [Aircrew and Cosmic Radiation 2016] [Al Anid et al. 2013] [Allen et al. 1959] [Almeida Filho et al. 2023] [andNa 2000] [Barker et al. 1974] [Beck et al. 2009] [Bolch and Parlos 1996] [Bolch et al. 1994] [Cha et al. 2022] [Curzio et al. 2001a] [Curzio et al. 2001b] [DeWitt et al. 2009] [Dumouchel et al. 2015] [Fajić et al. 2023] [Federico et al. 2010] [Ferrari 2004] [Ferrari et al. 2001] [Ferrari et al. 2005] [Fogtman 2025] [Gaza et al. 2009] [Green et al. 2006] [Hajek et al. 2002] [Hajek et al. 2004] [Hajek et al. 2005] [In-Flight Measurements at High 1993] [Kai et al. 1992] [Kubančák et al. 2019] [Lahti 1967] [Lee et al. 2014] [Lewis 2004] [Lewis et al. 2001] [Lewis et al. 2005] [Lewis et al. 2009] [Loomis and Arnold 2005] [McAulay 1999] [McCall et al. 2009] [McDowell et al. 1959] [Meier and Matthiä 2017] [Meier and Matthiä 2019] [Nounu et al. 2012] [O’Sullivan 1995] [Pallu] [Parent 1970] [Pepin et al. 2023] [Pickering et al. 1958] [Ploc et al. 2008] [Regulla et al. 1993] [Romero et al. 2004] [Round Table Discussion 1993] [Saenger et al. 1968] [Saenger et al. 1970] [Saenger et al. 1972] [Scherpelz and Cezeaux 2014] [Singleterry et al. 2015] [Spurn 1997] [Spurny et al. 2004] [Spurný 2002] [SpurnÝ et al. 1996] [Colazzo et al. 2026] [Takada et al. 2007] [Taylor 1994] [Thierfeldt et al. 2009] [Townsend 2001]

Similarity, information and the design of experiments

The general method the article borrows. Similarity, sampling, information and the design of experiments, which The Source Base names as foundational primaries.

6 records. [Buckingham 1914] [Chaloner and Verdinelli 1995] [Lindley 1956] [Nyquist 1928] [Shannon 1948] [Drake and Williams 1958]

Where the Framing Breaks Down

The keystone framework fits an unbuilt aircraft badly in three ways, and the ways are instructive.

There was no flight, so there was no measurement of the keystone. Everything in the sizing section above is a calculation, and calculations were available in 1948. An instrument model that treats a research aircraft as reducing uncertainty has nothing to work with when the aircraft does not exist, and what the X-6 reduced was uncertainty about the programme’s cost rather than about its physics.

The programme’s most valuable output is unrelated to its keystone. A molten salt reactor is not an answer to the question of whether shielding can be carried. It is a reactor concept that happened to suit an aircraft’s requirements for high temperature at low pressure, and it survived because those requirements recur in contexts having nothing to do with aircraft. A framework scoring an effort against its own question will miss this entirely, although it is the most important thing that happened.

The cancellation was not a technical decision and the framework has no place to put that. Intercontinental ballistic missiles made the indefinitely loitering bomber strategically uninteresting, and aerial refuelling made unlimited range achievable by other means, a refuelled bomber having flown nonstop around the world in 1949. The second of those can be put beside the shield directly. A tanker delivers fuel at a cost in sorties rather than in airframe mass, so the range a refuelled conventional bomber achieves is

\[R_{\text{refuelled}} = \frac{V}{c_t} \frac{L}{D} \sum_{i} \ln \left( \frac{m_{i}}{m_{f,i}} \right) \tag{92}\]

summed over refuelling segments, and the sum has no upper bound that the aircraft itself imposes. Unlimited range was achieved by a logistics arrangement rather than by a propulsion technology, at zero cost in payload. The nuclear aircraft was competing against a solution that had already won on the metric it was optimizing. The X-6 was not defeated by its shield. It was made pointless by two unrelated technologies while it was still arguing with its shield, and engineering work ends that way far more often than by outright failure.

The Source Base

The source base for this article differs from every other in the series in one structural respect, and it is worth stating explicitly.

The primary record is not in the NASA archive. ANP was an Atomic Energy Commission and Air Force programme, so its reports went to the AEC and are held today by the Department of Energy, discoverable through the Office of Scientific and Technical Information rather than through the NASA Technical Reports Server. The consequence for anyone retracing this work is that the standard search for an X-plane returns almost nothing, and the standard conclusion, that the record is thin, is exactly wrong. The record is enormous and is in a different building.

The documentary record proper is the quarterly and semiannual progress report series, running from Cottrell 1951 through Cottrell 1952a, Cottrell 1952b, Cottrell 1953, Savolainen 1954, Savolainen 1955, Savolainen 1956, 1957, Jordan et al. 1957, 1957, Na 1957, and 1959, with Dibble 1958 and Perry 1958 giving the management view. That series alone runs to tens of thousands of pages and is the single strongest argument against calling this a thinly documented aircraft. The founding documents are Gasser 1947 on the NEPA project, the Lexington Project minutes and their companion, and the NEPA quarterly report of 1950. Late-programme summaries are the General Electric direct-air-cycle programme report, the reactor and shield physics volume, and the powerplant data compilation. Study of seaplane systems employing nuclear power shows how far the application space was searched, and the engineering proposal for nuclear turbojet development shows what was still being proposed at the end. Shielding computer program specifications, the two-component method of shield analysis, a shield specification, shield weights for a Boeing mission, the LID tank shield study, the seventh shielding information meeting papers, aircraft reactor control systems, and HTRE fuel reprocessing studies fill in the technical detail. Two-dimensional diffusion theory applied to a fuel-plate-removal experiment, tungsten-uranium dioxide fuel retention, and ceramic fibre development are NACA and NASA contributions to the surrounding materials problem. Reactor kinetics has a bibliography of its own, while the computational aids of the period run to a reactor power calculator, both of which convey how much of this work was done before the tools existed to do it easily.

The secondary literature on the aircraft itself is thin, which is the opposite of the primary situation. Miller 2001, Jenkins et al. 2003, Winchester 2005, and Peebles 2014 give the roster treatment, and Hallion 1972, Hallion 1984, Gorn 2001, and Bilstein 1989 supply institutional context, with Gunston 1992 the wider framing.

The engineering texts behind the relations are Hill and Peterson 1991 and Sutton and Biblarz 2016 for propulsion, Incropera and DeWitt, Carslaw and Jaeger 1959, and Boley and Weiner 1960 for heat transfer and thermal stress, Anderson 2001, Anderson et al. 1999, and Bertin and Cummings 2013 for aerodynamics, and Raymer et al. 2012, Nicolai et al. 2010, Torenbeek and Synthesis of subsonic airplane design 1979, and Roskam and Airplane design 1989 for design method and mass estimation. Structures are Bruhn 1973, Niu and Niu 1988, and Megson and Aircraft structures for engineering students n.d.. Error analysis is Taylor 1997 and Bevington and Robinson 2002, with design of experiments in Box et al. 2005 and Gelman et al. 2013, and information accounting in Cover and Thomas 2006. The epistemology is Vincenti 1990, Petroski 1985, and Ferguson 1992, and the organizational reading, which this article leans on more than most, is Perrow 1984, Vaughan 1996, Sagan 1993, and Reason and Human error 1990. Institutional histories are Baals and Corliss 1981, Hansen 1987, and Chambers and Chambers 2008, with Heppenheimer 2007 and Jenkins 2000 on the high-speed thread and Launius and Jenkins 2012 and Merlin 2009 on the successors.

Foundational primaries bearing on the surrounding arguments include Drake and Williams 1958 on the research airplane rationale, Buckingham 1914 on similarity, Nyquist 1928 and Shannon 1948 on sampling and channel capacity, and Lindley 1956 and Chaloner and Verdinelli 1995 on experimental design. Related work on this blog appears in History of Rocketplanes on the rocketplane lineage, Two-Stage Flying Delta Wing Vehicles for Civil and National Security Applications on large high-speed configurations, Rocket Propellant Chemistry, A Design-Tradeoff Space on propellant chemistry, Aerospace, Programming Languages, and Information Technology Co-Development: Framing and the Co-Development Mechanism and Aerospace, Programming Languages, and Information Technology Co-Development: Aerospace Simulation and Real-Time Systems on the computing and simulation infrastructure, and Introduction to Space Studies on space policy. The NASA History Office and the Armstrong Flight Research Center hold the aeronautical side of the record, with Oak Ridge and Idaho holding the nuclear side.

The survey rests on 5,653 research records drawn from Crossref, the NASA Technical Reports Server, the Defense Technical Information Center and the Office of Scientific and Technical Information, of which 3,172, being 56.1 percent, are report primaries by the identifier rule set out under The Definition of Primary. 638 of the 5,556 dated records, being 11.5 percent, were published between 1946 and 1961, the life of the programme, and 2,086, being 37.5 percent, date from 2015 or later. The median publication year is 1999, and the records fall into 13 clusters.

The Definition of Primary

Primacy is read from the identifier. A record is a report primary when its address is a NASA Technical Reports Server citation, a record of the Office of Scientific and Technical Information, or a digital object identifier under the 10.2172 prefix, which Crossref registers for the Department of Energy reports that office holds, or under the 10.21236 prefix, which it registers for Defense Technical Information Center reports. One Department of Energy report is reachable both as an office record and as a 10.2172 identifier, and the survey cites each such report once. Of the 3,172 report primaries, 2,646 are Department of Energy reports, 436 are NASA reports and 90 are Defense Technical Information Center reports.

The rule does not reach the journal papers that the programme’s own engineers published, so 56.1 percent is a lower bound on how much of the survey is first-hand. The documents that carry the argument are the progress reports and comprehensive technical reports named above, and every one of them is a report primary by this rule.

Thin Subjects

Six subjects that this article’s derivations depend on have thin literatures. Each count below is the number of research records in this survey whose title carries at least one of the listed terms, with a hyphen read as a space.

Subject	Title terms counted	Records
the reactor-to-crew separation and the divided shield	divided shield, unit shield, shadow shield, separation distance, crew compartment, crew shield	16
air activation in a direct-cycle engine	argon-41, nitrogen-16, air activation, activation of air, activated air	12
core heat-up and melting after loss of cooling	meltdown, melt-down, core melt, melting, heat-up	7
decay heat in a reactor that moves	decay heat, afterheat or decay heating, together with aircraft, mobile, transportable, ship, marine, naval, space, rocket, propulsion, microreactor or heat pipe	10
the dose to a crew from a reactor carried with it	crew, aircrew, personnel or pilot within eighty characters of reactor, nuclear powered or nuclear aircraft	2
shield mass against reactor power	shield weight, shield mass or shield thickness within sixty characters of power, megawatt or MW	2

The separation optimum is the clearest case of a subject answered elsewhere. 13 of the 16 records concern the shadow shield, which covers only the solid angle the crew occupies, and the three most recent, all from 2022, are for reactors in space. No title names the separation between a reactor and a crew inside one fuselage as the quantity to be optimised. Air activation is thin in a different way, since its records concern stack releases, research reactors, water coolants and measurement technique, and none concerns air drawn through a core to propel an aircraft, which is the direct cycle’s defining property.

Decay heat is not a thin subject, but decay heat in a reactor that moves is. The decay heat cluster holds 291 records naming it, and 10 of all the survey’s records join it to a mobile, marine, space or propulsion reactor. That a shield’s thickness grows with the logarithm of reactor power is almost never published as a finding, because it follows from the exponential attenuation law in one line, so the article’s claim stands on the relation rather than on a literature.

What the Survey Admits

A record is admitted only when a person reading its title finds it on this article’s subject, which is the nuclear aircraft, its reactor, its shield, the descendants of each, and what replaced the aircraft’s mission. Many words this subject depends on also name something else, and a record that shares only such a word is excluded. Shielding also names the self-shielding of resonance cross sections, electromagnetic and acoustic shielding, debris shields and the thermal radiation shields of cryostats and Stirling engines. Radiation also names thermal and solar radiation, a reactor is also a chemical, electrical or plasma vessel, and a microreactor is also a device for flow chemistry. Pluto is also the name of a research reactor at Harwell, the acronym of the programme is also that of atrial natriuretic peptide, and the name of its predecessor project, NEPA, is also that of the National Environmental Policy Act. Lithium hydride is also a chemical reagent, a scattered-radiation measurement is also a radiograph, and the attenuation of gamma rays also measures soil, wood, grain and ore. Fusion devices, particle accelerators, medical radiology, aircraft striking a reactor and nuclear aircraft carriers are excluded as other subjects. Correction, retraction and withdrawal notices, abstracts of other papers and the front and back matter of books are excluded as well, because a survey counts research works and those are editorial events or parts of works. Book reviews, reference, encyclopedia and dictionary entries other than authored articles of more than two pages, unsigned news items, and a second deposit of a document already held, such as a preprint of a kept article or a repository copy of a kept report, are not admitted either, because the first three are not research works and the last would count one work twice.

Some records of doubtful relevance are kept. Decay heat measurement for power reactors, aircrew exposure to cosmic radiation, shielding materials developed for medical and industrial radiation, and the high-temperature gas-cooled power reactor line each share a method or a quantity with this subject, so each is kept and a reader may weigh it accordingly. The 1948 index to the Lexington Project reports is cited in the body as evidence of how the study was organised, and since an index is not a research work it is listed under Reference and not counted in the survey. The records that sit furthest from the aircraft among those the body cites, on semiconductor radiation effects, accelerator shielding and ship propulsion, are kept because the passages citing them use them as neighbouring science.

Every research title has been read for relevance, so the off-topic share that remains is a matter of reading judgement. No sample measures it, and what remains is whatever a reader of titles alone could misjudge.

Epistemic State

Established historical fact includes the start of Project NEPA on 28 May 1946 under the Army Air Forces, its replacement by the joint AEC and Air Force ANP programme in May 1951, the assignment of the direct air cycle to General Electric and the indirect cycle to Pratt and Whitney, the MX-1589 modification of two B-36 airframes, the tornado damage to 51-5712 at Carswell on 1 September 1952, its rebuilding as the NB-36H, its carriage of the one megawatt Aircraft Shield Test Reactor, its 47 flights and 215 hours between 17 September 1955 and March 1957 with the reactor operated for 89 of those hours, the operation of the Aircraft Reactor Experiment at Oak Ridge in 1954 as the first molten salt reactor, the ground testing of a direct-cycle nuclear turbojet in the HTRE series, and the cancellation of the X-6 work at Convair in 1953, and the cancellation of the programme in March 1961 without the X-6 being built.

Established engineering analysis includes every relation in the sizing sections. The exponential attenuation law with buildup, the logarithmic dependence of shield thickness on power and on dose limit, the separation optimum, the Way-Wigner decay heat correlation, the turbojet thrust and heat addition relations, and the heat exchanger effectiveness relation are standard results.

Derived here and not taken from a source are the hundred megawatt thermal power estimate for a B-36-class cruise, the 0.44 kilogram uranium consumption over a hundred hours, the gamma source strength and the ten gray per second unshielded dose rate at ten metres, the attenuation requirement of $7.1 \times 10^{7}$ that follows from a fifty millisievert mission limit, the 25.7 centimetre lead thickness and the 222 centimetre lithium hydride thickness, the 8.7 centimetre thickness increment for a thousandfold power increase, the 10.1 metre separation optimum, the 41 tonne gamma shield mass with a 66 tonne upper bound including neutrons and their ratios to gross weight and payload, the 100 megawatt per cubic metre core power density, the 1211 kelvin indirect-cycle reactor outlet requirement, the 23 minute adiabatic melt time, and the decay heat figures. These follow by arithmetic from published dimensions and standard physical constants and can be reproduced or refuted by any reader with them.

Inference includes the central claim that the shield mass rather than any other difficulty was the binding constraint, and the subsidiary claim that the logarithmic dependence made the programme insensitive to relaxing the crew dose limit. Both are consistent with the record and with the fact that shield optimization was a named research subject throughout the programme, but neither is a statement the primary reports make in those terms.

Weakly supported are the representative values. The lift-to-drag ratio of eighteen, the cruise speed of 200 metres per second, the overall propulsive efficiency of 0.20, the shadow shield area of 14.1 square metres, the fuselage structural mass of 400 kilograms per metre, the fifty millisievert mission dose allowance from which the attenuation requirement follows, the four percent gamma energy fraction, the mean photon energy of one megaelectronvolt, the lithium hydride removal cross-section, the buildup factor of ten, the six square metre crew shield area used in the comparison with the NB-36H, and the five tonne core mass used in the melt-time estimate are all plausible figures for the class rather than values taken from the design. The shield mass estimate should be read as establishing an order of magnitude and a ratio, not a design number. The ratio is more trustworthy than the absolute value, and the qualitative conclusion that shielding consumes a payload-sized fraction of a B-36 is robust to any reasonable choice of inputs.

Contested or unresolved in the sources consulted is the total programme cost, given as about one billion dollars by the Comptroller General and seven billion in the X-6 entry, a discrepancy most plausibly explained by inflation adjustment but not stated as such by either source. NEPA’s 1947 funding of ten million dollars rests on a single secondary account. The crew shield mass is given as eleven tons in the NB-36H entry and twelve in the X-6 entry, neither saying whether short or metric tons are meant, and read as short tons the computed 11.2 and 12.7 tonnes would both lie above the reported range rather than bracket it. The window thickness is given as six inches in one account and ten to twelve in another, and the scrapping of the NB-36H is placed at Fort Worth in 1958 in one account and at Carswell in 1957 in another. None of these are load-bearing for the argument, and all are stated here as reported rather than resolved.

A note on temporal position. This article carries an editorial date of 2025-10-12 and is written from current knowledge, including contemporary literature published well after that date.

Out of Scope

This article does not treat the X-1, X-2, X-3, X-4, or X-5 beyond the comparisons drawn, all of which have their own articles. It does not derive the standard relations reused here, since the series opener does that once for all seventy-two articles, including the flight envelope, load factor, wing loading, lift and drag coefficients, lift-to-drag, Reynolds and Prandtl numbers, measurement uncertainty and its propagation, and the standard atmosphere in its tabulated form.

It does not attempt a history of the Aircraft Nuclear Propulsion programme, which is a large subject with a literature of its own and is treated here only where it bears on the aircraft. It does not treat nuclear fission or the nuclear reactor as subjects, nor nuclear fuel, enriched uranium, neutron moderators, or beryllium as materials, nor radiation protection and ionizing radiation as disciplines, nor the sievert and absorbed dose as units, nor gamma rays and neutron radiation as phenomena, nor the half-value layer and Monte Carlo method as techniques, nor nuclear accidents as a category. It does not cover the turbojet as a machine, transonic or supersonic flow, swept wings, the aspect ratio, Mach and dynamic pressure as quantities, the speed of sound, flight dynamics, longitudinal and directional stability, aeroelasticity, buffeting, shock waves and oblique shocks, wave drag, boundary layer and separation behaviour, the aerodynamic centre, moments of inertia, the wing root, wing configuration as a taxonomy, delta wings, stability augmentation, duralumin, yield, telemetry, strain gauges, accelerometers, takeoff and landing gear, the sound barrier, wind tunnels, flight testing, Edwards and the Armstrong Flight Research Center, Bell Aircraft, Chuck Yeager, the NACA and NASA as organizations, the National Museum of the United States Air Force, the list of X-planes, or experimental aircraft as a category, all of which are treated where they belong.

Conclusion

The Convair X-6 was never built, and what it would have had to carry can be computed in a page.

A B-36 at cruise needs about a hundred megawatts of thermal power, and a reactor supplying it consumes less than half a kilogram of uranium in a hundred hours against 837 tonnes of kerosene for the same energy. That factor of nearly two million is the entire attraction. Unshielded at ten metres that reactor delivers about ten grays per second, when about five grays is a median lethal dose, so one second of exposure would kill the crew. Holding them to fifty millisieverts over a hundred-hour flight demands an attenuation of seven times ten to the seventh, or twenty-six centimetres of lead, and the geometry that minimizes the total mass puts the reactor about ten metres from the crew, which a B-36 fuselage accommodates easily. The gamma shield that results weighs about 41 tonnes, twenty-two percent of the aircraft and slightly more than the whole of its bomb load, and the neutron layer takes the upper bound to about 66 tonnes. A nuclear bomber buys unlimited range by surrendering the payload that made the range worth having.

The exponential that makes shielding work also makes it stubborn. Shield thickness depends on the logarithm of reactor power, so a thousandfold increase in power costs under nine centimetres of lead. The shield is therefore a fixed overhead and not a proportional cost, and small nuclear aircraft are not merely difficult but excluded. The same logarithm means that accepting ten times the crew dose saves about two and a half percent of the aircraft. The programme could not have been rescued by being braver.

One aircraft flew and it was not the X-6. The NB-36H carried a one megawatt reactor 47 times to measure what shielding does, and it established that the shielding worked, for a source a hundred times smaller than the one that would have propelled it. A direct-cycle nuclear turbojet ran on a test stand in Idaho and produced thrust from fission. The programme reached that point and was cancelled in 1961, not because the shield defeated it but because ballistic missiles and aerial refuelling had made an indefinitely loitering bomber a solution without a problem.

What survives is a reactor. The Aircraft Reactor Experiment ran at Oak Ridge in 1954 as the world’s first molten salt reactor, built for high temperature and high power density, which a molten salt core gives at low pressure. An aircraft wants that combination and, as it turns out, so does a good deal else. Seventy years later that concept is under commercial development while the aircraft it was invented for remains unbuilt. An effort that produces no aircraft and one durable reactor technology has not failed in any sense worth the word, and the fact that it is remembered as a failure is a defect in how such work is scored, not in what this one did.

The next article takes the Lockheed X-7, a ramjet test vehicle that was launched rather than flown, and asks what changes when the aircraft is expendable.

Equations

This section collects the 92 display equations of the article in the order they appear, each under its number and reproduced exactly as it stands in the text. A title in bold names an established result, and a title in italics beginning with the word Bespoke names a construction made for this analysis. Of the 92, 57 are established and 35 are bespoke. Dose is stated in grays and sieverts, which the shield estimates treat as interchangeable, the lead attenuation coefficient appears as 0.794 per centimetre in the thickness relations and 79.4 per metre in the separation and mass relations, and $\lambda$ is a structural mass per metre in the separation optimum but the decay constant of argon-41 in the activation relation.

Equation 1, Specific Energy of Fission and of Kerosene. Complete fission of uranium-235 releases about $8.2 \times 10^{13}$ joules per kilogram against about $4.3 \times 10^{7}$ for kerosene.

\[E_{\text{fission}} \approx 8.2 \times 10^{13} \ \text{joules per kilogram}, \qquad E_{\text{chem}} \approx 4.3 \times 10^{7} \ \text{joules per kilogram} \tag{1}\]

Equation 2, Energy per Fission and Specific Energy of Uranium-235. About 200 megaelectronvolts per fission times the Avogadro constant over the molar mass gives the specific energy of fission.

\[E_f \approx 200 \ \text{MeV} = 3.20 \times 10^{-11} \ \text{joules}, \qquad E_{\text{fission}} = \frac{E_f \, N_A}{M_{235}} \tag{2}\]

Equation 3, Ratio of Fission to Chemical Specific Energy. Fission releases about two million times the energy of combustion per unit mass.

\[\frac{E_{\text{fission}}}{E_{\text{chem}}} = 1.9 \times 10^{6} \tag{3}\]

Equation 4, Fission Rate at a Given Power. The fission rate is the thermal power divided by the energy per fission.

\[\dot{N}_f = \frac{P}{E_f} \tag{4}\]

Equation 5, Fission Rate of a Hundred Megawatt Core. A hundred megawatt core fissions about $3.12 \times 10^{18}$ nuclei per second.

\[\dot{N}_f = \frac{10^{8}}{3.20 \times 10^{-11}} = 3.12 \times 10^{18} \ \text{nuclei per second} \tag{5}\]

Equation 6, Endurance from Fuel Mass and Thrust Specific Fuel Consumption. Endurance is the fuel mass divided by the thrust specific fuel consumption times the thrust.

\[t_{\text{endurance}} = \frac{m_{\text{fuel}}}{\text{TSFC} \times F} \tag{6}\]

Equation 7, Thrust Specific Fuel Consumption of a Nuclear Aircraft. Because a nuclear aircraft burns almost no fuel mass, its thrust specific fuel consumption tends to zero and endurance is bounded by something other than fuel.

\[\text{TSFC} = \frac{\dot{m}_{\text{fuel}}}{F} \longrightarrow 0 \quad \Longrightarrow \quad t_{\text{endurance}} \longrightarrow \text{limited by something else} \tag{7}\]

Equation 8, Criticality Condition. A reactor is critical when neutron production equals absorption plus leakage, so that the effective multiplication factor is one.

\[k_{\text{eff}} = \frac{\text{production}}{\text{absorption} + \text{leakage}} = 1 \tag{8}\]

Equation 9, Non-Leakage Probability of a Bare Spherical Core. In diffusion theory the non-leakage probability falls with the geometric buckling times the migration area, and the buckling of a sphere grows as its radius shrinks.

\[P_{\text{NL}} \approx \frac{1}{1 + B^{2} M^{2}}, \qquad B^{2} = \left( \frac{\pi}{R} \right)^{2} \ \text{for a sphere} \tag{9}\]

Equation 10, Wing Loading of the B-36. A gross mass of about 186,000 kilograms on 443 square metres gives a wing loading of about 4.12 kilonewtons per square metre. B-36

\[\frac{W}{S} = \frac{186{,}000 \times 9.80665}{443} = 4.12 \times 10^{3} \ \text{newtons per square metre} \tag{10}\]

Equation 11, Aspect Ratio of the B-36. The span of 70.1 metres and the wing area give an aspect ratio of 11.1. B-36

\[A = \frac{b^{2}}{S} = \frac{70.1^{2}}{443} = 11.1 \tag{11}\]

Equation 12, Bespoke Cruise Thrust at Maximum Takeoff Weight. Taking the maximum takeoff weight as an upper bound on cruise weight and a lift-to-drag ratio near eighteen gives a required thrust of 101 kilonewtons.

\[F = \frac{W}{L/D} = \frac{186{,}000 \times 9.80665}{18} = 1.01 \times 10^{5} \ \text{newtons} \tag{12}\]

Equation 13, Bespoke Propulsive Power at an Assumed Cruise Speed. At an assumed cruise speed of 200 metres per second, about twice the listed cruising speed, the propulsive power is 20.3 megawatts.

\[P_{\text{prop}} = F V = 1.01 \times 10^{5} \times 200 = 20.3 \ \text{megawatts} \tag{13}\]

Equation 14, Thermal Power and Overall Propulsive Efficiency. The reactor thermal power is the propulsive power divided by the overall efficiency, the product of thermal and propulsive efficiencies.

\[P_{\text{thermal}} = \frac{P_{\text{prop}}}{\eta_{\text{overall}}}, \qquad \eta_{\text{overall}} = \eta_{\text{thermal}} \, \eta_{\text{propulsive}} \tag{14}\]

Equation 15, Bespoke Reactor Thermal Power. An assumed overall efficiency of 0.20 for a turbojet of the period gives a thermal power of about 101 megawatts.

\[P_{\text{thermal}} = \frac{20.3}{0.20} = 101 \ \text{megawatts} \tag{15}\]

Equation 16, Uranium-235 Consumed on a Hundred-Hour Mission. A hundred megawatts for a hundred hours fissions about 0.44 kilograms of uranium-235.

\[m_{\text{U-235}} = \frac{P \, t}{E_{\text{fission}}} = \frac{10^{8} \times 3.6 \times 10^{5}}{8.2 \times 10^{13}} = 0.44 \ \text{kilograms} \tag{16}\]

Equation 17, Bespoke Escaping Gamma Power. The article takes about eight of the two hundred megaelectronvolts per fission as escaping gamma energy, so the gamma power is four percent of the thermal power.

\[P_\gamma \approx 0.04 \, P = 4.0 \ \text{megawatts} \tag{17}\]

Equation 18, Bespoke Gamma Source Strength. Dividing the gamma power by an assumed mean photon energy of one megaelectronvolt gives $2.50 \times 10^{19}$ photons per second.

\[S_\gamma = \frac{P_\gamma}{\bar{E}_\gamma} = \frac{4.0 \times 10^{6}}{1.60 \times 10^{-13}} = 2.50 \times 10^{19} \ \text{photons per second} \tag{18}\]

Equation 19, Fast Neutron Source Strength. The neutron source is the mean number of neutrons per fission times the fission rate, about $7.49 \times 10^{18}$ neutrons per second.

\[S_n = \nu \, \dot{N}_f = 2.4 \times 3.12 \times 10^{18} = 7.49 \times 10^{18} \ \text{neutrons per second} \tag{19}\]

Equation 20, Point-Kernel Dose Rate with Buildup. The dose rate behind a shield of thickness $x$ is the inverse-square source term attenuated exponentially and multiplied by the buildup factor for scattered photons. Auslender 1957

\[\dot{D}(r, x) = \frac{k \, P}{4 \pi r^{2}} \, B(\mu x) \, e^{-\mu x} \tag{20}\]

Equation 21, Bespoke Unshielded Photon Fluence Rate at Ten Metres. The assumed gamma source spread over a sphere of ten metres radius gives a fluence rate of $1.99 \times 10^{16}$ per square metre per second.

\[\varphi = \frac{S_\gamma}{4 \pi r^{2}} = \frac{2.50 \times 10^{19}}{4 \pi \times 100} = 1.99 \times 10^{16} \ \text{per square metre per second} \tag{21}\]

Equation 22, Bespoke Unshielded Tissue Dose Rate at Ten Metres. The fluence rate times the mean photon energy times the mass energy-absorption coefficient of tissue gives the dose rate from the assumed source.

\[\dot{D} = \varphi \, \bar{E}_\gamma \left( \frac{\mu_{en}}{\rho} \right)_{\text{tissue}} = 1.99 \times 10^{16} \times 1.60 \times 10^{-13} \times 3.09 \times 10^{-3} \tag{22}\]

Equation 23, Bespoke Unshielded Dose Rate Value. The assumed hundred megawatt source unshielded at ten metres delivers about 9.8 grays per second.

\[\dot{D} = 9.8 \ \text{grays per second} \tag{23}\]

Equation 24, Shield Thickness for a Dose Limit. Inverting the point-kernel relation with the buildup factor held fixed gives the thickness that holds the dose at the limit.

\[x = \frac{1}{\mu} \ln \left( \frac{k \, P \, B}{4 \pi r^{2} \dot{D}_0} \right) \tag{24}\]

Equation 25, Linear Attenuation Coefficient of Lead Near One Megaelectronvolt. A mass attenuation coefficient of about 0.070 square centimetres per gram times the density of lead gives 0.794 per centimetre. attenuation coefficient lead

\[\mu = 0.070 \times 11.34 = 0.794 \ \text{per centimetre} \tag{25}\]

Equation 26, Tenth-Value Layer of Lead. The tenth-value layer is the natural logarithm of ten over the attenuation coefficient, 2.90 centimetres of lead.

\[x_{1/10} = \frac{\ln 10}{\mu} = \frac{2.303}{0.794} = 2.90 \ \text{centimetres} \tag{26}\]

Equation 27, Bespoke Crew Dose Rate Limit for a Hundred-Hour Mission. An allowance the article chooses of fifty millisieverts over a hundred hours sets a rate limit of $5 \times 10^{-4}$ grays per hour.

\[\dot{D}_0 = \frac{0.05}{100} = 5 \times 10^{-4} \ \text{grays per hour} \tag{27}\]

Equation 28, Bespoke Attenuation Demanded of the Gamma Shield. The ratio of the unshielded rate to the chosen limit is $7.1 \times 10^{7}$.

\[\mathcal{A} = \frac{\dot{D}_{\text{unshielded}}}{\dot{D}_0} = \frac{3.54 \times 10^{4}}{5 \times 10^{-4}} = 7.1 \times 10^{7} \tag{28}\]

Equation 29, Bespoke Gamma Shield Thickness. With the chosen limit and an assumed buildup factor of ten the lead thickness is 25.7 centimetres.

\[x = \frac{\ln \left( \mathcal{A} B \right)}{\mu} = \frac{\ln \left( 7.1 \times 10^{8} \right)}{0.794} = \frac{20.4}{0.794} = 25.7 \ \text{centimetres} \tag{29}\]

Equation 30, Fast Neutron Attenuation by a Removal Cross-Section. The fast neutron flux falls exponentially with thickness at a rate set by the macroscopic removal cross-section. Chapman and Storrs 1955

\[\varphi_n(x) = \varphi_n(0) \, e^{-\Sigma_R x} \tag{30}\]

Equation 31, Bespoke Lithium Hydride Neutron Shield Thickness. A removal cross-section near 0.095 per centimetre and a required attenuation of $1.5 \times 10^{9}$ give 222 centimetres of lithium hydride.

\[x_n = \frac{\ln \left( 1.5 \times 10^{9} \right)}{0.095} = 222 \ \text{centimetres} \tag{31}\]

Equation 32, Logarithmic Growth of Shield Thickness with Power. Because thickness depends on the logarithm of the source strength, a change in power adds only the logarithm of the power ratio over the attenuation coefficient.

\[\Delta x = \frac{1}{\mu} \ln \left( \frac{P_2}{P_1} \right) \tag{32}\]

Equation 33, Added Lead for a Thousandfold Power Increase. A thousandfold increase in power adds 8.7 centimetres of lead.

\[\Delta x = \frac{\ln 1000}{0.794} = 8.7 \ \text{centimetres} \tag{33}\]

Equation 34, Shield Thickness as a Function of Separation. Holding the crew dose fixed, the point-kernel thickness falls by twice the logarithm of the separation over the attenuation coefficient.

\[x(r) = \frac{1}{\mu} \left[ \ln \left( \frac{k P B}{4 \pi \dot{D}_0} \right) - 2 \ln r \right] \tag{34}\]

Equation 35, Bespoke Shadow Shield Mass Against Separation. A shadow shield of fixed area $A$ whose thickness follows the separation relation has a mass that falls logarithmically with distance.

\[m_{\text{shield}}(r) = \rho_s A \, x(r) = C - \frac{2 \rho_s A}{\mu} \ln r \tag{35}\]

Equation 36, Bespoke Linear Structural Mass of the Separation. The article takes the structure spanning the separation to add a fixed $\lambda$ kilograms per metre.

\[m_{\text{struct}}(r) = \lambda r \tag{36}\]

Equation 37, Bespoke Optimum Separation. Setting the derivative of total shield and structure mass to zero gives an optimum separation proportional to shield areal density over attenuation coefficient and structural mass per metre.

\[\frac{d m_{\text{total}}}{d r} = -\frac{2 \rho_s A}{\mu r} + \lambda = 0 \quad \Longrightarrow \quad r^{*} = \frac{2 \rho_s A}{\mu \lambda} \tag{37}\]

Equation 38, Bespoke Optimum Separation Value. Lead on a forward hemisphere of 1.5 metre radius with an assumed 400 kilograms per metre of fuselage structure gives an optimum near ten metres.

\[r^{*} = \frac{2 \times 11{,}340 \times 14.1}{79.4 \times 400} = 10.1 \ \text{metres} \tag{38}\]

Equation 39, Bespoke Gamma Shield Mass. The chosen area and the 25.7 centimetre thickness give about 41 tonnes of lead.

\[m_{\text{shield}} = \rho_s A x = 11{,}340 \times 14.1 \times 0.257 = 4.11 \times 10^{4} \ \text{kilograms} \tag{39}\]

Equation 40, Bespoke Gamma Shield Fraction of Gross Mass. The estimated lead shield is 22 percent of the gross mass.

\[\frac{m_{\text{shield}}}{m_{\text{gross}}} = \frac{41{,}100}{186{,}000} = 0.221 \tag{40}\]

Equation 41, Bespoke Upper Bound on Total Shield Fraction. Adding the lithium hydride layer as a separate mass gives an upper bound of 35 percent of the gross mass.

\[\frac{m_{\text{Pb}} + m_{\text{LiH}}}{m_{\text{gross}}} = \frac{41{,}100 + 24{,}500}{186{,}000} = 0.353 \tag{41}\]

Equation 42, Bespoke Gamma Shield Mass Against Bomb Load. The estimated lead shield weighs 1.05 times the maximum bomb load of about 39,000 kilograms.

\[\frac{m_{\text{shield}}}{m_{\text{payload}}} = \frac{41{,}100}{39{,}000} = 1.05 \tag{42}\]

Equation 43, Mass of a Divided Shield. The total mass of a divided shield is the sum of the areal masses of the reactor and crew shields. Shield optimization

\[m_{\text{total}} = \rho_s A_r x_r + \rho_c A_c x_c \tag{43}\]

Equation 44, Dose Constraint on a Divided Shield. The direct dose, which depends on the reactor shield, and the scattered dose, which depends on both, must together meet the limit. Shield optimization

\[\dot{D}_{\text{direct}} \left( x_r \right) + \dot{D}_{\text{scatter}} \left( x_r, x_c \right) \le \dot{D}_0 \tag{44}\]

Equation 45, Equal Marginal Dose Reduction per Unit Mass. At the constrained optimum the dose reduction bought by a unit of mass must be equal in the reactor and crew shields. Shield optimization

\[\frac{1}{\rho_s A_r} \frac{\partial \dot{D}}{\partial x_r} = \frac{1}{\rho_c A_c} \frac{\partial \dot{D}}{\partial x_c} \tag{45}\]

Equation 46, Bespoke Thickness Relation for the Optimum Division. Taking each shield to attenuate its own exponential term of equal strength reduces the optimum condition to a relation between the two optical thicknesses and the areal masses.

\[\mu_r x_r - \mu_c x_c = \ln \left( \frac{\rho_c A_c \, \mu_r}{\rho_s A_r \, \mu_c} \right) \tag{46}\]

Equation 47, Bespoke Air-Scattered Dose Scaling. The article writes the scattered dose as proportional to the air density along the path times the source fluence and a geometric factor.

\[\dot{D}_{\text{scatter}} \propto \rho_{\text{air}}(h) \, \frac{S_\gamma}{4 \pi r^{2}} \, f_{\text{geom}} \tag{47}\]

Equation 48, Exponential Atmosphere. Air density falls exponentially with altitude with a scale height near 8.4 kilometres.

\[\rho_{\text{air}}(h) = \rho_0 \, e^{-h / H}, \qquad H \approx 8.4 \ \text{kilometres} \tag{48}\]

Equation 49, Density Ratio at Twelve Kilometres. At twelve kilometres the exponential atmosphere gives a quarter of sea-level density.

\[\frac{\rho(12{,}000)}{\rho_0} = e^{-12/8.4} = 0.24 \tag{49}\]

Equation 50, Turbojet Thrust and Ideal Exhaust Velocity. Thrust is the mass flow times the velocity increase, and the ideal exhaust velocity follows from isentropic expansion from turbine inlet conditions.

\[F = \dot{m} \left( V_e - V_0 \right), \qquad V_e = \sqrt{2 c_p T_4 \left[ 1 - \left( \frac{p_0}{p_4} \right)^{\frac{\gamma - 1}{\gamma}} \right]} \tag{50}\]

Equation 51, Heat Added Across the Core. The thermal power is the mass flow times the specific heat times the temperature rise from compressor discharge to turbine inlet.

\[P_{\text{thermal}} = \dot{m} \, c_p \left( T_4 - T_3 \right) \tag{51}\]

Equation 52, Ideal Brayton Cycle Efficiency. The ideal Brayton thermal efficiency depends only on the compressor pressure ratio, which also fixes the compressor discharge temperature.

\[\eta_{\text{th}} = 1 - \left( \frac{1}{\pi_c} \right)^{\frac{\gamma - 1}{\gamma}}, \qquad T_3 = T_2 \, \pi_c^{\frac{\gamma - 1}{\gamma}} \tag{52}\]

Equation 53, Convective Heat Flux and the Dittus-Boelter Correlation. The surface heat flux is the heat transfer coefficient times the wall-to-air temperature difference, with the Nusselt number given by the Dittus-Boelter correlation.

\[q'' = h \left( T_w - T_{\text{air}} \right), \qquad \mathrm{Nu} = \frac{h D_h}{k} = 0.023 \, \mathrm{Re}^{0.8} \mathrm{Pr}^{0.4} \tag{53}\]

Equation 54, Heated Surface Required. The fuel element surface is the thermal power divided by the achievable heat flux.

\[A_{\text{fuel}} = \frac{P_{\text{thermal}}}{q''} \tag{54}\]

Equation 55, Bespoke Core Power Density. A hundred square metres at a megawatt per square metre packed into an assumed cubic metre gives about a hundred megawatts per cubic metre.

\[\frac{P}{V} \approx 100 \ \text{megawatts per cubic metre} \tag{55}\]

Equation 56, Duct Friction Pressure Loss. The fractional pressure loss through the core is the friction factor times the length over hydraulic diameter times the dynamic pressure over static pressure.

\[\frac{\Delta p}{p} = f \frac{L}{D_h} \frac{\rho V^{2}}{2 p} \tag{56}\]

Equation 57, Activation of Argon-40. The argon-41 activity produced is the capture cross-section times the flux times the number of target nuclei times the saturation factor for the residence time.

\[A_{41} = \sigma_c \, \phi \, N_{40} \left( 1 - e^{-\lambda t_{\text{res}}} \right) \tag{57}\]

Equation 58, Heat Exchanger Outlet Temperature from Effectiveness. An exchanger of effectiveness $\varepsilon$ raises the air from compressor discharge temperature by that fraction of the available temperature difference.

\[T_{4} = T_3 + \varepsilon \left( T_{\text{reactor}} - T_3 \right) \tag{58}\]

Equation 59, Reactor Temperature Excess over Turbine Inlet. The reactor must run hotter than the turbine inlet by one less the effectiveness times the available difference.

\[T_{\text{reactor}} - T_4 = \left( 1 - \varepsilon \right) \left( T_{\text{reactor}} - T_3 \right) \tag{59}\]

Equation 60, Number of Transfer Units and Effectiveness. The number of transfer units is the conductance-area product over the smaller capacity rate, and for a large capacity ratio the effectiveness is one less the exponential of its negative.

\[\mathrm{NTU} = \frac{U A_{\text{HX}}}{\left( \dot{m} c_p \right)_{\min}}, \qquad \varepsilon = 1 - e^{-\mathrm{NTU}} \ \text{for a large capacity ratio} \tag{60}\]

Equation 61, Transfer Units for Effectiveness of 0.9 and 0.95. Raising effectiveness from 0.9 to 0.95 raises the number of transfer units from 2.30 to 3.00.

\[\mathrm{NTU} = -\ln \left( 1 - \varepsilon \right) : \quad 2.30 \longrightarrow 3.00 \tag{61}\]

Equation 62, Bespoke Reactor Outlet Temperature for the Indirect Cycle. With an assumed compressor discharge of 600 kelvin, a turbine inlet of 1150 kelvin and an effectiveness of 0.9 the reactor outlet must be about 1211 kelvin.

\[T_{\text{reactor}} = T_3 + \frac{T_4 - T_3}{\varepsilon} = 600 + \frac{550}{0.9} = 1211 \ \text{kelvin} \tag{62}\]

Equation 63, Heat Exchanger Mass Scaling. Exchanger size and hence mass scale with the heat transferred over the overall coefficient and the log-mean temperature difference.

\[m_{\text{HX}} \propto \frac{P_{\text{thermal}}}{U \, \Delta T_{\text{lm}}} \tag{63}\]

Equation 64, Coolant Pumping Power. Pumping power is the mass flow times the loop pressure drop over the coolant density and the pump efficiency.

\[P_{\text{pump}} = \frac{\dot{m}_{\text{coolant}} \, \Delta p_{\text{loop}}}{\rho_{\text{coolant}} \, \eta_{\text{pump}}} \tag{64}\]

Equation 65, Way-Wigner Decay Heat Law. After shutdown the decay heat falls as a power law of time with an exponent of minus 0.2.

\[\frac{P_{\text{decay}}(t)}{P_0} \approx 0.066 \, t^{-0.2} \tag{65}\]

Equation 66, Decay Heat of a Hundred Megawatt Core. The decay law gives 6.6 megawatts at one second, 1.28 at one hour and 0.68 at one day.

\[P_{\text{decay}}(1 \ \text{s}) = 6.6 \ \text{MW}, \qquad P_{\text{decay}}(1 \ \text{h}) = 1.28 \ \text{MW}, \qquad P_{\text{decay}}(1 \ \text{day}) = 0.68 \ \text{MW} \tag{66}\]

Equation 67, Adiabatic Heating Rate of an Uncooled Core. Without heat removal the core temperature rises at the decay power over the core heat capacity.

\[\frac{dT}{dt} = \frac{P_{\text{decay}}(t)}{m_{\text{core}} \, c_{p,\text{core}}} \tag{67}\]

Equation 68, Bespoke Heating Rate of a Five Tonne Core. An assumed five tonne core of specific heat 500 joules per kilogram kelvin heats at 0.51 kelvin per second at the one-hour decay power.

\[\frac{dT}{dt} = \frac{1.28 \times 10^{6}}{5000 \times 500} = 0.51 \ \text{kelvin per second} \tag{68}\]

Equation 69, Bespoke Time to Core Melting. Holding the one-hour decay power constant, a 700 kelvin margin to melting is consumed in about 23 minutes.

\[t_{\text{melt}} \approx \frac{700}{0.51} = 1.4 \times 10^{3} \ \text{seconds} = 23 \ \text{minutes} \tag{69}\]

Equation 70, Integrated Decay Energy. Integrating the decay law from shutdown gives the energy released, which grows as the 0.8 power of time.

\[E_{\text{decay}} = \int_0^{T} 0.066 \, P_0 \, t^{-0.2} \, dt = \frac{0.066 \, P_0}{0.8} T^{0.8} \tag{70}\]

Equation 71, Accumulated Component Dose. The dose a component accumulates is the integral of the local dose rate over the mission.

\[D_{\text{component}} = \int_0^{t_{\text{mission}}} \dot{D}(\mathbf{r}, t) \, dt \tag{71}\]

Equation 72, Displacements per Atom. Displacement damage is the displacement cross-section times the fast neutron fluence.

\[\text{dpa} = \sigma_d \int_0^{t} \varphi_n \, dt = \sigma_d \, \Phi_n \tag{72}\]

Equation 73, Component Life from a Fluence Limit. A component’s life is its fluence limit divided by the local fast neutron flux.

\[t_{\text{life}} = \frac{\Phi_{n,\text{limit}}}{\varphi_n} \tag{73}\]

Equation 74, Mission Dose. Mission dose is the dose rate times the mission duration.

\[D_{\text{mission}} = \dot{D} \, t_{\text{mission}} \tag{74}\]

Equation 75, Bespoke Shield Mass Against the Dose Limit. For a shadow shield of fixed area the mass grows with the logarithm of the reciprocal dose limit.

\[m_{\text{shield}} \propto \ln \left( \frac{1}{\dot{D}_0} \right) \tag{75}\]

Equation 76, Bespoke Shield Mass per E-Fold of Permitted Dose. The areal density of lead over its attenuation coefficient on the chosen area gives about two tonnes per factor of $e$ in the dose limit.

\[\frac{\partial m_{\text{shield}}}{\partial \ln \left( 1 / \dot{D}_0 \right)} = \frac{\rho_s A}{\mu} = \frac{11{,}340 \times 14.1}{79.4} = 2.01 \times 10^{3} \ \text{kilograms per e-fold} \tag{76}\]

Equation 77, Crew Dose from Reactor Operating Time. The crew dose is the shielded dose rate times the 89 hours of reactor operation. one account

\[D_{\text{crew}} = \dot{D}_{\text{shielded}} \, t_{\text{reactor}} = \dot{D}_{\text{shielded}} \times 89 \ \text{hours} \tag{77}\]

Equation 78, Bespoke Shielded Dose Rate of the NB-36H. An allowance the article chooses of fifty millisieverts across the 89 hours sets the shielded rate at $5.6 \times 10^{-4}$ sieverts per hour.

\[\dot{D}_{\text{shielded}} = \frac{0.05}{89} = 5.6 \times 10^{-4} \ \text{sieverts per hour} \tag{78}\]

Equation 79, Bespoke Unshielded Dose Rate at the NB-36H Crew Station. Scaling the hundred megawatt estimate linearly to one megawatt and by the inverse square from ten to an assumed fifteen metres gives the rate at the crew station.

\[\dot{D}_{\text{ASTR}} = \dot{D}_{100} \left( \frac{P_{\text{ASTR}}}{P_{100}} \right) \left( \frac{r_{100}}{r_{\text{ASTR}}} \right)^{2} = 9.84 \times \frac{1}{100} \times \left( \frac{10}{15} \right)^{2} \tag{79}\]

Equation 80, Bespoke Unshielded Dose Rate Value for the Shield Test Reactor. The scaling gives 0.044 grays per second, or 157 grays per hour.

\[\dot{D}_{\text{ASTR}} = 0.044 \ \text{grays per second} = 157 \ \text{grays per hour} \tag{80}\]

Equation 81, Bespoke Attenuation and Lead Thickness for the Shield Test Reactor. The required attenuation of $2.8 \times 10^{5}$ with a buildup factor of ten gives 18.7 centimetres of lead.

\[\mathcal{A} = \frac{157}{5.6 \times 10^{-4}} = 2.8 \times 10^{5}, \qquad x = \frac{\ln \left( 2.8 \times 10^{6} \right)}{0.794} = 18.7 \ \text{centimetres} \tag{81}\]

Equation 82, Bespoke Crew Shield Mass of the NB-36H. Taking an assumed six square metres of compartment cross-section gives 12.7 tonnes, against a reported eleven to twelve tons.

\[m = \rho_s A x = 11{,}340 \times 6.0 \times 0.187 = 1.27 \times 10^{4} \ \text{kilograms} \tag{82}\]

Equation 83, Clausius-Clapeyron Saturation Pressure. The integrated Clausius-Clapeyron relation gives the saturation pressure as an exponential in the reciprocal temperature.

\[p_{\text{sat}}(T) \approx p_c \exp \left[ \frac{\Delta H_{\text{vap}}}{R} \left( \frac{1}{T_c} - \frac{1}{T} \right) \right] \tag{83}\]

Equation 84, Ratio of Water Reactor to Molten Salt Pressure. A pressurised water reactor near 15.5 megapascals against a fluoride salt vapour pressure below a kilopascal is a ratio of at least $1.5 \times 10^{4}$. molten salt reactor

\[\frac{p_{\text{PWR}}}{p_{\text{salt}}} \approx 1.5 \times 10^{4} \tag{84}\]

Equation 85, Thin Spherical Pressure Vessel. The wall thickness of a thin sphere is the pressure times the radius over twice the allowable stress, so the vessel mass is proportional to the pressure.

\[t = \frac{p R}{2 \sigma} \quad \Longrightarrow \quad m_{\text{vessel}} = 4 \pi R^{2} \rho t = \frac{2 \pi \rho \, p R^{3}}{\sigma} \tag{85}\]

Equation 86, Temperature Coefficient of Reactivity. The temperature coefficient is the derivative of the multiplication factor with temperature, which is negative for a circulating fuel salt.

\[\alpha_T = \frac{\partial k_{\text{eff}}}{\partial T} < 0, \qquad \delta k = \alpha_T \, \delta T \tag{86}\]

Equation 87, Minimum-Mass Layered Shield. The modern problem minimises the total areal mass of the layers subject to the dose limit and non-negative thicknesses.

\[\min_{\mathbf{x}} \ \sum_{j} \rho_j A_j x_j \quad \text{subject to} \quad \dot{D}\left( \mathbf{x} \right) \le \dot{D}_0, \quad x_j \ge 0 \tag{87}\]

Equation 88, Bespoke Two-Radiation Dose of a Layered Shield. The article writes the dose as a gamma term attenuated and built up layer by layer as a product plus a neutron term attenuated by each layer’s removal cross-section.

\[\dot{D} \left( \mathbf{x} \right) = \dot{D}_\gamma \prod_j B_j e^{-\mu_j x_j} + \dot{D}_n \prod_j e^{-\Sigma_{R,j} x_j} \tag{88}\]

Equation 89, Payload Mass Budget. Payload is gross mass less empty mass, fixed installation and consumed mass.

\[m_{\text{payload}} = m_{\text{gross}} - m_{\text{empty}} - m_{\text{fix}} - m_{\text{consumed}} \tag{89}\]

Equation 90, Bespoke Viability Condition for a Fixed Installation. The article states that a configuration is viable only while the fixed installation fraction leaves at least a minimum payload fraction.

\[\frac{m_{\text{fix}}}{m_{\text{gross}}} < 1 - \frac{m_{\text{empty}}}{m_{\text{gross}}} - \frac{m_{\text{payload,min}}}{m_{\text{gross}}} \tag{90}\]

Equation 91, Gravimetric Index of a Hydrogen Tank. The gravimetric index is the hydrogen mass over the hydrogen and tank mass, which fixes the tank mass per kilogram of fuel.

\[\eta_g = \frac{m_{\text{H}_2}}{m_{\text{H}_2} + m_{\text{tank}}} \quad \Longrightarrow \quad \frac{m_{\text{tank}}}{m_{\text{H}_2}} = \frac{1 - \eta_g}{\eta_g} \tag{91}\]

Equation 92, Breguet Range Summed over Refuelling Segments. Summing the Breguet range of each segment between refuellings gives a total with no limit imposed by the aircraft itself.

\[R_{\text{refuelled}} = \frac{V}{c_t} \frac{L}{D} \sum_{i} \ln \left( \frac{m_{i}}{m_{f,i}} \right) \tag{92}\]

Notation

• $E_f$, the energy released per fission
• $E_{\text{fission}}$, the energy released per kilogram of uranium-235 fissioned
• $\dot{N}_f$, the fission rate
• $P$, the reactor thermal power
• $F$, the thrust
• $\text{TSFC}$, the thrust specific fuel consumption
• $k_{\text{eff}}$, the effective neutron multiplication factor
• $P_{\text{NL}}$, the neutron non-leakage probability
• $B^{2}$, the geometric buckling of the core
• $M^{2}$, the neutron migration area
• $W$, the aircraft weight
• $S$, the wing reference area
• $\eta_{\text{overall}}$, the overall efficiency of the propulsion system
• $S_\gamma$, the gamma source strength in photons per second
• $S_n$, the fast neutron source strength in neutrons per second
• $\nu$, the mean number of neutrons released per fission
• $\dot{D}$, the dose rate
• $\dot{D}_0$, the permitted crew dose rate
• $\mu$, the linear attenuation coefficient of the gamma shield
• $B$, the photon buildup factor
• $x$, the shield thickness
• $r$, the distance from reactor to crew
• $\varphi$, the photon fluence rate
• $\mathcal{A}$, the attenuation the shield must supply
• $\Sigma_R$, the macroscopic fast neutron removal cross-section
• $\varphi_n$, the fast neutron flux
• $\rho_s$, the density of the reactor shield material
• $\lambda$, the structural mass per metre of separation, and in the activation relation the decay constant of argon-41
• $r^{*}$, the optimum separation between reactor and crew
• $T_3$, the compressor discharge temperature
• $T_4$, the turbine inlet temperature
• $\pi_c$, the compressor pressure ratio
• $\gamma$, the ratio of specific heats, taken as 1.4 for air
• $A_{\text{fuel}}$, the heated fuel element surface area
• $q’’$, the heat flux from a fuel element surface into the air
• $\varepsilon$, the heat exchanger effectiveness
• $\mathrm{NTU}$, the number of transfer units
• $P_{\text{decay}}$, the decay heat power after shutdown
• $\Phi_n$, the fast neutron fluence
• $\alpha_T$, the temperature coefficient of reactivity
• $\eta_g$, the gravimetric index of a hydrogen tank
• $m_{\text{fix}}$, the mass of a fixed installation that performs no work during the mission

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