## Computation — Transport and Diffusion Theory

The information required to calculate the group fluxes and import­ances by solving equations 1.27 and 1.30 consists of the specification of the reactor and the nuclear cross-sections. The latter are available in the form of data from thousands of measurements stored in data libraries such as the USA Evaluated Nuclear Data File (ENDF), the OECD Joint Evaluated Fission File (JEFF), the Japanese Evaluated Nuclear Data Library (JENDL), the Chinese Evaluated Nuclear Data Library (CENDL) and the Russian Evaluated Nuclear Data Library (BROND). Microscopic cross-section data from these files are then used, together with data about the specification, to calculate fine-group macroscopic cross-sections for each region. Fundamental-mode calcu­lations in about 1000 fine groups are then performed to give group macroscopic cross-sections for spatial calculations, usually in 30 or 40 groups.

Equations 1.27 are solved by a double iterative method such as that described by Greenspan, Kelber and Okrent (1968). There are “inner” iterations to find the flux distribution and “outer” iterations to determine the eigenvalue, because the multigroup equations have no solution for ф until the correct value of к has been found. This outer iteration can be done in either of two ways. The composition and dimension of the reactor may be kept constant while the value of к is altered until the equations are solved. This is equivalent to finding the reactivity of a reactor that may not be exactly critical. Alternatively the composition (for example the concentration of plutonium in the core) or the dimensions (say the radius of the core) may be altered to make к = 1.

In the initial stages of design when the broad features of perform­ance are being determined the three-dimensional reactor can often be represented adequately by a two-dimensional model in (r, z) cyl­indrical polar coordinates, but for the purposes of detailed design and for calculations in support of an operating reactor a three-dimensional model is required, usually in (hex, z) or (tri, z) geometry (i. e. with the transverse planes covered by a hexagonal or triangular mesh).

Again, in the initial stages of design, diffusion theory is adequate but when it comes to the details transport theory is necessary. A typical transport theory code would use a nodal formulation of the transport equation with hexagonal nodes, each node corresponding to an indi­vidual core position occupied by a fuel subassembly, a control rod or an incineration target, etc. The code would calculate the average flux in each node and then determine the fine structure within the node in terms of spherical harmonics in angle and polynomials in space. The average flux would enable properties such as the power generated in the subassembly to be predicted, and the fine structure would give the power of individual fuel elements within the subassembly.

A typical approach to operational calculations is given by Wardle- worth and Wheeler (1974).

## Fuel Element Design

An important choice facing the designer of sealed fuel elements is whether to place the gas storage volume, or plenum as it is usually called, above or below the core. If it is below, surrounded by cooler inlet coolant, it can be smaller than if it is above, where it is immersed in the hotter outlet coolant. But if for some reason the plenum should burst or leak the gas would be released and pass upwards, displacing coolant from the core and possibly causing a positive reactivity transi­ent (see Figure 1.26).

For a breeder reactor there is usually an axial breeder region con­taining natural or depleted UO2 between the core fuel and the plenum. Provision has to be made to allow the gas from the core to pass through the breeder to the plenum. The axial breeder on the other side of the core (i. e. above the core if the plenum is below) can be incorporated in the same fuel elements with the core. Alternatively it can be made in the form of separate fuel elements that, because of the low power density in the breeder, can have a larger diameter than the core elements. The advantage of the latter arrangement is that the resistance to coolant flow is reduced, but it increases the complexity.

Figure 2.6 shows a typical core fuel element that incorporates both axial breeders, has the fuel in the form of pellets, and has the plenum below the core. The retainers are necessary only to keep the fuel pellets in position during manufacture, transport and loading into the reactor.

Retainer Upper Breeder

Figure 2.6 A typical fuel element.

Almost as soon as the power is raised the pellets swell to press against the cladding (see section 2.4.4) and become jammed.

The diameter of the fuel element is determined by heat transfer and manufacturing cost considerations (section 3.2.1). The thickness of the cladding has to be sufficient after allowing for corrosion both on the outside (sections 3.3.4 and 3.3.5) and the inside (section 2.4.7) to withstand the stresses due to fuel swelling and fission-product gas. Its thickness is usually about 0.3 or 0.4 mm.

Radial breeder fuel elements are usually similar in form to those of the core but with larger diameter. Even at the end of several years of irradiation the power density in the breeder adjacent to the core is only 20% or so of that at the core centre. The breeder elements can therefore have more than twice the diameter of the core elements before the limiting linear heat rating is reached.

## Configuration of the Reactor Core

A reactor is made up of an array of subassemblies of various types. The core subassemblies may contain fuel of several different enrichments arranged to give annular enrichment zones, as explained in section 1.3.3. The core may be surrounded by a radial breeder consisting of two or three rows of subassemblies consisting of fat fuel elements con­taining fertile material. Around this there may be a neutron reflector consisting of subassemblies similar to those of the core and breeder but containing mainly steel. Around this there may be additional sub­assemblies containing neutron-shielding material, or the shield may be a separate structure as indicated in Figure 3.23. Control rods occupy subassembly positions in the core region and are usually inserted into the core from above. They are operated by mechanisms that are situated on top of the reactor vessel so that they are available for maintenance.

Figure 3.24 shows a core pattern for a 3000 MW(heat) sodium — cooled breeder reactor. The core has two fuel enrichment zones and is surrounded by a radial breeder, which in turn is surrounded by a reflector. The neutron shielding is not shown. The effective diameter of the core is 3.6 m and it is 1 m high. Figure 3.25 shows a much smaller 600 MW(heat) sodium-cooled core that is 1.5 m in diameter and 0.9 m high. As explained in section 3.2.3 the height of the core of a sodium — cooled core is constrained by coolant flow considerations to be about 1 m, and the core diameter is adjusted to accommodate the required power output.

The configuration is different if the reactor is intended to consume rather than breed fissile material. Figure 3.26 shows how the core shown in Figure 3.24 could be modified for this purpose. There is no
breeder, and in addition some of the 238U is removed from the core (by increasing the fuel enrichment). This would make the core excessively reactive so some of the fuel subassemblies have to be removed and replaced by diluent subassemblies containing inert material.

Inner

Core

Outer

Core

Breeder

Reflector

Control

Rods

REFERENCES FOR CHAPTER 3

Allen, T. R. and D. C. Crawford (2007) Lead-Cooled Fast Reactor Systems and the Fuels and Materials Challenges, Science and Technology of Nuclear Installations, article ID 97486

Bagley, K. Q., J. W. Barnaby and A. S. Fraser (1973) Irradiation Embrittle­ment of Austenitic Stainless Steels, pp 143-153 in Irradiation Embrittlement and Creep in Fuel Cladding and Core Components, British Nuclear Energy Society, London

Bramman, J. I., C. Brown, J. S. Watkin, C. Cawthorne, E. J. Fulton, P. J. Burton and E. A. Little (1978) Void Swelling and Microstructural Changes in Fuel Pin Cladding and Unstressed Specimens irradiated in DFR, pp 479-508 in Radiation Effects in Breeder Reactor Structural Materials, American Society of Mining Engineers, New York

Dwyer, O. E. (1968) Heat Transfer to Liquid Metals flowing In-line through Unbaffled Rod Bundles, pp 139-168 in Heat Transfer in Rod Bundles, Amer­ican Society of Mechanical Engineers, New York

Etherington, E. W., J. I. Bramman, R. S. Nelson and M. J. Norgett (1975) A UKAEA Evaluation of Displacement Damage Models for Iron, Nuclear Engineering and Design, 33 82-90

Friedland, A. J. and C. F. Bonilla (1961) Analytical Study of Heat Transfer Rates for Parallel Flow of Liquid Metals through Tube Bundles, Journal of the American Institute of Chemical Engineering, 7, 107-112

Hoffman, H. and D. Weinberg (1978) Thermodynamic and Fluiddynamic Aspects in Optimizing the Design of Fast Reactor Subassemblies, pp 133­139 in Optimisation of Sodium-Cooled Fast Reactors, British Nuclear Energy Society, London

Hsiung, L., M. Fluss and A. Kimura (2010) Structure of Oxide Nanoparticles in Fe-16Cr MA/ODS Ferritic Steel Lawrence Livermore National Laboratory report LLNL-JRNL-427350

Mosedale, D. and G. W. Lewthwaite (1974) Irradiation Creep in Some Aus­tenitic Stainless Steels, Nimonic PE16 Alloy, and Nickel, pp 169-188 in Creep Strength in Steel and High-Temperature Alloys, London, The Metals Society, London

Nettley, P. T., I. P. Bell, K. Q. Bagley, D. R. Harries, A. W. Thorley and C. Tyzack (1967) Problems in the Selection and Utilization of Materials in Sodium Cooled Fast Reactors, pp 825-849 in Fast Breeder Reactors (BNES Conference proceedings), Pergamon, Oxford

Subbotin, V. I., A. K. Papovyants, P. L. Kirillov and N. N. Ivanovskii (1963) A Study of Heat Transfer to Molten Sodium in Tubes, Soviet Journal of Atomic Energy, 13, 991-994

Tang, Y. S., R. D. Coffield and R. A. Markley (1978) Thermal Analysis of Liquid-Metal Fast Reactors, American Nuclear Society, Hinsdale, Illinois, USA

Thorley, A. W. and C. Tyzack (1973) Corrosion and Mass Transport of Steel and Nickel Alloys in Sodium Systems, pp 257-273 in Liquid Alkali Metals, British Nuclear Energy Society, London

Zhang, J. and N. Li (2007) Review of the Studies on Fundamental Issues in LBE corrosion, Journal of Nuclear Materials, 373, 351-377

## Core-Disruptive Accidents — Passive Protection

It may be possible to make the consequences of a core-disruptive accident less severe by incorporating “passive” protective devices in the design. By “passive” is meant a mechanism that takes protective action without external actuation, either by the automatic trip system or by human intervention. There are two main classes: devices to reduce reactivity and devices to prevent recriticality.

Reduction of Reactivity. The reactor trip system works by inserting the control and shut-off rods into the core on receipt of a trip signal (see section 5.2.1). The reduction of reactivity can be made passive by designing the control-rod mechanisms so that the absorbers enter the core in direct response to overheating. This can be done for example by making the core of the electromagnets that attach the absorbers to their actuators of a material with a Curie point above but close to the normal core outlet temperature. In a Slow LOF or Slow TOP accident the outlet temperature rises, the magnets become ineffect­ive and the absorbers fall under gravity into the core. An alternative is to incorporate a component with a high thermal expansion coef­ficient, which responds to the overheating by pushing the absorbers away from the magnets or disengaging mechanical latches, so that they fall.

If the accident has distorted the core the absorbers might not be able to fall freely in their guide tubes. Articulated absorbers, with joints that enable them to negotiate bends, may have a higher probability of entering the core. It may also be possible to increase the chance of insertion by means of spring mechanisms that propels the absorbers downwards when they have been disconnected from the actuators.

Another approach to reducing reactivity automatically when the core is overheated is to increase the neutron leakage. As explained in section 1.6.4, in the case of liquid coolants, loss of coolant from the periphery of the core reduces reactivity because it increases the leakage. The effect can be enhanced in a number of ways. If the neut­ron reflector above the core or, in the case of a breeder reactor, the upper axial breeder is replaced by coolant (sometimes called a coolant “plenum”), when the outlet temperature rises the density of the coolant falls, leakage is increased and reactivity falls. For a sodium- cooled reactor the effect is much greater in a more severe accident in which the coolant boils and the plenum is filled with vapour.

Radial leakage can be increased by “gas expansion modules”, or GEMs as they are often known. These are subassemblies at the periphery of the core that normally contain coolant, but also have reservoirs of trapped gas arranged so that when the gas expands on overheating it expels the coolant. GEMs are attractively simple and reliable, but suffer from the disadvantage that, unless there are very many of them, the amount of reactivity reduction is small. They also have a deleterious effect on the performance of the reactor because they reduce the reactivity in normal operation so that for example the enrichment has to be higher than would otherwise be necessary.

Relocation of Material. The risk of recriticality arises when the fuel becomes free to move, and particularly if it melts. It may be possible to design the structure in such a way that molten fuel is led safely out of the core. One approach is to incorporate in some or all of the subassemblies central ducts that are normally empty except for coolant. The walls of these ducts are made of a material that has a lower melting point than the subassembly wrappers. During the transition phase the molten fuel melts the wall, enters the duct and flows out of the core, either under the influence of gravity or more likely propelled by boiling and vaporising coolant.

A variant of this is to use the control rod and shut-off rod guide tubes, which are already present as ducts through the core. The guide tubes themselves would be made of low-melting-point material and molten fuel could flow out through them. The control rod guide tubes would not be so effective at the beginning of the life of a new core, however, when they would be occupied by the fully inserted control absorbers, but the shut-off rod guide tubes would always be available when the reactor was critical.

The main drawback of any passive mechanism to control the move­ment of molten fuel is that it would be difficult to demonstrate that it worked correctly. Extensive testing would be required. And it should be noted that such testing of the behaviour of molten fuel as has been done indicates that its “natural” tendency is to disperse, without the provision of any special dispersal path or duct.

## AN INTRODUCTION. TO THE ENGINEERING. OF FAST NUCLEAR REACTORS

Anthony M. Judd

It is intended for the newcomer to the study of fast reactors, either as a student or at a later stage of his or her career. It will probably be most useful to someone who already has some knowledge of nuclear reactors. There are many excellent introductory texts for the beginner in nuclear engineering but they all concentrate on thermal reactors. The purpose of this book is to provide an up-to-date account of fast reactors for those who want to take the next step.

Fast reactor technology has become a wide field, so wide that it is not possible to cover all of it in depth in a single book of reason­able length. What I have attempted is to cover the whole in sufficient detail to allow the reader to understand the important features, and to provide suitable references for further study. I have gone into detail on the neutron physics because any fast reactor engineer, whether he or she is a designer, an operator or a researcher, needs to understand how the machinery works at a basic level. I have also attempted to include the results of experience, often hard-won, of operating a fast reactor power station.

I have divided the subject matter up in chapters according to dis­cipline. Chapter 1 about the physics of fast reactors is the most detailed and mathematical. This is to give those who have to use the numbers produced by the complex computer codes that predict reactor per­formance some idea of where they come from. Chapter 2 is mainly about the chemistry of fast reactor fuel. Chapters 3 and 4 are about the application of mainly conventional engineering disciplines to fast reactors so they contain less theoretical detail. In Chapter 5 I have tried to show how safety can be attained by careful attention to detail in design. The Introduction includes an explanation of the difference between fast reactors and thermal reactors and a brief summary of the history of fast reactor development.

I wish to thank Argonne National Laboratory for permission to reproduce Figures 2.19, 2.22 and 2.25.

Many of my colleagues in the atomic energy industry have been very generous in helping me to write this book and its predecessor. They are for too numerous to mention by name. By way of thanks I wish to dedicate this account of the technology to the hundreds of engineers, scientists and technicians whose achievements made pos­sible the success of the British Fast Reactor project, started in 1946 and abandoned prematurely in 1993.

Tony Judd

## Reactivity Requirements

In general the reactivity of a reactor core decreases with increasing temperature (as explained in the following section) and with burnup. Thus a new, cold reactor core is in its most reactive state and a core at power at the end of its refuelling cycle is least reactive. The control rods, fully inserted in the new core, have to have enough negative reactivity to compensate for these changes so that, when they are fully withdrawn at the end of the cycle, the reactor remains critical. Table 1.3 gives typical values of the reactivity requirements for a breeder reactor.

The “shutdown margin” is a safety allowance to make sure that the reactor remains subcritical during refuelling even if errors are made and excessive fuel is added. It also has to allow for one or more control rods themselves being removed and replaced. The safety rods are there so that the reactor can be shut down from any operating condition even if some of the control rod mechanisms fail to work, including the possibility of a rod being accidentally withdrawn. These points are discussed in more detail in Chapter 5.

In principle there is no difference between the control, shut-off and safety rods: they could be identical items distinguished only by differ­ent names to denote their different functions. However as explained in Chapter 5 the reliability of the shutdown system, which is crucial for the safety of the reactor, is enhanced by diversity. Thus the shut-off rods might utilise a different absorber material from the control rods or different operating mechanisms.

It is important to note that Table 1.3 applies to a typical breeder reactor in which the loss of reactivity by burnup of fissile nuclides is reduced substantially by internal breeding of new fissile material in the core (see section 1.4.3). In the core of a reactor designed to con­sume fissile material the internal breeding is much reduced or possibly eliminated entirely, so that the loss of reactivity with burnup is much greater, possibly three times as much as indicated in Table 1.3. In a typ­ical breeder reactor core some 7-10% of the space is occupied by con­trol rods (including shutdown and safety rods), but in a consumer core the proportion is likely to be greater. Loss of reactivity with burnup may in fact limit the length of the refuelling cycles for such a reactor.

## Reprocessing and Fabrication

The development of metal fuel has taken place in conjunction with that of the “integral fast reactor” (IFR) concept, which is based on close integration of a reactor with a reprocessing and fuel fabrication facility. It is not appropriate to give a full description of the IFR here, but it is necessary to describe it in outline if the nature of the fuel it uses is to be understood.

Central to the IFR system is the reprocessing of the irradiated fuel at high temperature in the molten state, a process called “pyropro — cessing”. The earliest version involved “melt-refining”. After a brief cooling period the irradiated fuel was melted in a zirconia crucible. Some of the fission products were driven off by evaporation and oth­ers formed a residue in the crucible. The fuel, containing the remainder of the fission products and with the addition of new fissile or fertile material as required, was then cast into new fuel elements and sent back to the reactor. The main disadvantage of this simple process was the buildup of fission products after multiple recycling, which reduced the reactivity significantly making it hard to reach high burnup. In addition there were unacceptable losses of uranium and plutonium in the crucible residues.

To eliminate these disadvantages the separation efficiency was increased by replacing the melt-refining process by electro-refining, which involves electrolysis after dissolution in a mixture of molten

Table 2.4 Energy of formation of chlorides at 500 °C

 Compound -AG (kJ/g) Compound -AG (kJ/g) Compound -AG (kJ/g) BaCl2 367 CmCl3 268 ZrCls 195 CsCl 367 PuCl3 261 CdCl2 148 RbCl 364 NpCl3 243 FeCl2 122 KCl 362 UCls 231 NbCl5 112 SrCl2 354 MoCl4 70 LiCl 345 TcCl4 46 NaCl 339 RhCl3 42 CaCl2 337 PdCl2 38 LaCl3 293 RuCl4 25 PrCl3 288 CeCl3 287 NdCl3 284 YCl3 272

salts. The fuel elements are chopped into short lengths and placed in a steel basket that is immersed in a steel vessel containing a molten mixture of lithium and potassium chlorides at 500 °C. At the bottom of the vessel is a layer of molten cadmium. Cadmium chloride is added, and this oxidises the actinides so that they produce a sufficient ion concentration to allow the salt mixture to conduct electricity.

Table 2.4 shows the free energies of formation of the chlorides of the various metals. They fall into three groups: the chlorides of the alkaline earths and most of the rare earths (Ba to Y) are stable and tend to remain in the salt phase; those of the transition metals (Cd to Ru) are unstable so the metals are precipitated in the molten cadmium; whereas the actinides and zirconium form chlorides of intermediate stability that can be separated by electrolysis.

A potential of about 1 volt is applied between the basket of fuel element fragments, which becomes the anode, and two cathodes are used in sequence. The first is a steel rod, on which uranium is deposited as the metal. Plutonium, being more stable, cannot be precipitated until its concentration in the molten salt is high, but when the uranium concentration has been reduced sufficiently it can be precipitated at a second cathode which consists of a crucible containing liquid cadmium. At this cathode, plutonium and the higher actinides form inter-metallic compounds such as PuCd6. After electrolysis the deposits from the cathodes are taken to a furnace where the remaining salts and the cadmium are removed by evaporation. They are then blended to obtain the required fuel composition, melted and cast into moulds to form new fuel pellets.

The decontamination factors are low, by design, and as a result the new fuel, containing significant amounts of fission products, particu­larly the rare earths, is highly radioactive. For this reason the entire process has to be conducted remotely, but it confers the advantage of protecting the new fuel, and the plutonium it contains, from illicit diversion.

The main advantages of pyroprocessing with electro-refining are that it is cheap and the out-of-reactor fuel inventory is minimised. Another advantage is that the minor actinides are recycled and do not appear in the waste stream (see section 2.7.4). There is evidence that small additions of americium and neptunium to the U-Pu-Zr fuel alloy do not affect its performance adversely, although the high volatility of americium makes for difficulty in the high-temperature fabrication process.

## Refuelling

A power reactor is usually designed to operate continuously for up to a year between refuelling shutdowns, at each of which up to half the core fuel, which has reached the end of its irradiation life, is removed and replaced by new.

New Fuel. New ceramic fuel subassemblies are usually delivered from the manufacturing plant in an atmosphere of air and can be kept in an air-filled store until required. Radioactive heating of new ceramic fuel is normally very slight so there is little requirement for cooling the store, but it has to be configured to prevent criticality. Before the fuel is committed to the reactor the store has to be purged with an appropriate gas. In the case of a gas-cooled reactor this would be the cooling gas, carbon dioxide or helium. For a metal-cooled reactor it would be the primary circuit cover gas — usually argon in the case of sodium coolant. The subassembly can then be transferred from the store to its required location in the reactor vessel where it is immersed in the primary coolant.

In the case of sodium coolant this is an irrevocable step, because once it has been wetted the subassembly cannot be withdrawn into an air environment until it has been thoroughly cleaned. This is because any residual sodium would react with atmospheric moisture to form caustic sodium hydroxide that might damage the cladding. If a new subassembly had for some reason to be withdrawn before it had been

irradiated it would have to be inspected and requalified before it could be returned to use.

Recycled metal fuel in the IFR system (see section 2.5.6) contains fission products, the radioactive decay of which generates a signific­ant amount of heat. New IFR fuel subassemblies have to be cooled continuously from manufacture until loaded into the reactor.

Irradiated Fuel. The route for withdrawing irradiated fuel from the reactor and dispatching it either for reprocessing or disposal as waste has to provide cooling to remove the decay heat produced by the fission products. It is important to prevent overheating which might cause failure of the cladding and release of radioactive fission products, fuel material or higher actinides to the environment.

The decay heat from a typical irradiated subassembly is shown in Figure 4.8. It depends slightly on the irradiation history, the fuel com­position and the burnup. The high initial decay heat rating implies that an irradiated core subassembly has to be kept under forced-convection cooling for a period of around a day. In practice this means that the movement of irradiated fuel cannot start for a day after the reactor has been shut down. During the refuelling period the primary coolant is circulated, usually at around 10% of the full-power rate.

After this initial period the decay heat is low enough for the sub­assembly from a liquid-cooled reactor to be cooled by natural con­vection of the primary coolant. It can be removed from its position in the reactor core and placed in a storage position, but throughout the move it has to be kept immersed in the coolant. Only after a period of several months can it be withdrawn into a gas atmosphere.

The Fuel Transfer Route. The irradiated fuel store has to have the capacity to hold some 200 subassemblies. It can be located either within the primary vessel or in a separate vessel. In some older pool reactors it took the form of a rotating carousel in the primary vessel outside the neutron shield, but a more compact arrangement, which allows the main vessel to be smaller and therefore less costly, is to store the irradiated fuel in a ring around the core outside the neutron shield (see Figure 4.2). The alternative, which allows the main vessel to be even more compact, is to place the store in a separate vessel. The disadvantage of this is that it requires complex transfer equipment to lift the subassemblies out of the main vessel and lower them into the storage vessel while keeping them immersed in the coolant.

The transfer procedure for a sodium-cooled reactor is as follows. Fuel-handling machines are mounted on the eccentric rotating shields in the reactor roof (see Figure 4.3). The shields are manoeuvred to bring a handling machine over the subassembly to be moved. An arm is lowered from the machine and attached to the lifting ring at the top of the subassembly (see Figure 3.20). It then lifts the subassembly out of the core, keeping it below the surface of the sodium. The shields are then rotated to bring the subassembly over a transfer position into which it is lowered. A second move involving a second handling machine may be required to bring it to a position from which it can be removed from the reactor vessel.

At the removal position it is received into a cylindrical container, sometimes called a “bucket”. The bucket full of sodium, with the subassembly in it, is then lifted up out of the reactor vessel and lowered down into the separate fuel storage vessel, where it is retained until it has cooled sufficiently to be removed from sodium. It is then lifted into an inert gas atmosphere, taken to a cleaning facility where the residual sodium is removed, and despatched to reprocessing or long­term storage.

## Comparison with Thermal Reactors

The physics of fast reactors differs considerably from that of thermal reactors. The most important difference is that the composition of the fuel is different. In a fast power reactor the fraction of fissile material in the fuel is about 20-30% compared with 0.7-3% in a thermal reactor. In a reactor designed to consume fissile or waste materials it may be higher. This and the lack of a moderator means that fast reactor cores are much smaller, with dimensions of the order of 1 m compared with 3 m for light-water reactors and 10 m for graphite or heavy-water reactors, and the power density is much higher.

In a fast reactor thermal neutrons are almost absent so the mater­ials with high thermal neutron absorption cross-sections, which are so important in thermal reactors, do not affect the performance of a fast reactor nearly as much. Fission products such as 135Xe and 147Sm and impurities such as boron are relatively unimportant. There is no xenon poisoning problem for a fast reactor and the decrease of reactivity with burnup of the fuel due to the accumulation of fission products is much slower than in a thermal reactor. Because most materials have similar cross-sections for fast neutrons nuclear considerations place much less severe limits on the choice of materials for a fast reactor core.

The mean free path of fast neutrons is longer than that of thermal neutrons so the core of a fast reactor is more closely coupled than that of a thermal reactor. There is no question of zonal instability and there is less depression of the neutron flux in the fuel elements.

The temperature coefficients of reactivity come from entirely dif­ferent sources — the Doppler effect and coolant expansion in fast react­ors rather than moderator expansion and change in thermal energy in thermal reactors — but the magnitudes are similar so the dynamics of fast and thermal reactors are very similar in normal operation. Only in very rapid transients is there any difference because the prompt neutron lifetime is of the order of 10-7 s in a fast reactor, compared with about 10-3 s in a thermal reactor.

In spite of the simplicity of a fast reactor neutron flux calculations are much more complex because the simplifying assumptions valid for a thermal reactor cannot be made. In a thermal reactor most of the neutrons have energies in a narrow range and one-group or few-group calculations are useful. In a fast reactor the neutrons have a wide range of energies and multigroup calculations are essential. There is no fast reactor equivalent to the “four-factor formula”.

## Power Density

The neutron flux distribution in an ADR is affected by the degree of subcriticality. Figure 1.30 shows the radial distribution of the total flux in ADRs with ke = 0.995 and 0.95 compared with that in a critical reactor. The core is cylindrical, 1 m high and 2 m in diameter, with properties similar to those of the standard sodium-cooled oxide-fuelled core described in Table 1.1, but with a neutron source located on the axis. It will be seen that the source has little effect on the flux in the outer part of the core, but is higher close to the source and more so the greater the subcriticality. As in a critical reactor the effect on the power distribution can be reduced by varying the composition of the fuel in different radial zones (see section 1.3.2), but the peak close

to the source may necessitate specific design measures to avoid local overheating.

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