A disadvantage of liquid metal coolants, as compared with water or gas, is that because of the high thermal conductivity temperature changes in the fluid are transferred readily to the structure, giving rise to thermal stresses. There are two areas of concern: thermal shock and high-cycle fatigue.

Thermal shocks arise from the sudden changes in plant operating conditions that happen when emergency action is taken, such as trip­ping the reactor or the steam plant. If the reactor is tripped the power falls very rapidly, more quickly than the primary pump speed can be reduced, causing the coolant temperature at the core outlet to fall rapidly. This may impose a severe thermal shock on the above-core structure, but in a pool reactor further effects are mild in compar­ison because mixing in the hot pool delays and smoothes out the temperature change so that the effect on the intermediate heat exchangers for example is attenuated. In a loop reactor, in contrast, sig­nificant thermal stresses may be induced in the coolant outlet nozzles from the primary vessel and in the intermediate heat exchangers.

The intermediate heat exchangers may be more at risk from a trip initiated in the steam plant. If for example the turbine stop valve is tripped shut and the steam system is blown down through the safety valves, heat transfer from the secondary sodium in the steam generat­ors is reduced very quickly. The secondary sodium pumps have to be slowed down, ideally in step with the declining heat transfer, to keep the sodium temperature at the steam generator outlet constant. This is clearly very difficult, and any mismatch changes the temperature at inlet to the intermediate heat exchangers. It is important that the resulting transient stresses do not threaten their integrity.

As explained in section 5.3.3 the secondary circuits are likely to be equipped with fast-acting isolation valves to protect the heat exchangers from damage by the caustic reaction products from a steam generator leak. Operation of these valves is however likely to cause a rapid temperature increase in the heat exchangers because, especially in the case of a pool reactor, hot primary sodium continues to flow.

The reactor plant components, and in particular the intermediate heat exchangers, have to be designed to tolerate these thermal shocks. This can be done by using the methods of fracture mechanics. It can be assumed that there are crack-like defects of the maximum size that would escape detection during manufacture. The growth of these hypothetical defects in thermal shock incidents can then be predicted and shown to be negligible or to be so small that integrity is not threatened. However it may also be necessary to keep a record of the thermal shocks actually experienced throughout the life of the reactor to ascertain that the growth of the hypothetical defects is within the limits assumed in the design. If it is not — if for example there were to be an unexpectedly large number of reactor trips — it might be necessary to inspect the components at greatest risk such as the intermediate heat exchanger tube-to-tubeplate welds to assure that they have not been damaged.

Around 1960 it became clear that there is more to a profitable fast reactor than a high breeding ratio. The fuel itself is expensive because of the original cost of the fissile material and the cost of fabricating it into fuel elements and reprocessing it after it has been irradiated in the reactor.

Fuel cannot remain in the reactor core indefinitely for a number of reasons. As irradiation proceeds the fissile material is used up. This is offset to some extent by the breeding of new fissile material but as most breeding takes place in the breeder rather than the core there is a net loss of fissile material from the core and the reactivity declines. At the same time fission products are formed. These have a small effect on reactivity in a fast reactor (unlike a thermal reactor in which they absorb the low-energy neutrons), but they disrupt the crystal structure of the fuel material and cause it to swell, and they corrode the cladding material. In addition, the cladding is weakened by the fast neutrons so that in the end it loses its integrity and allows radioactive material to escape into the coolant.

When the fuel has been irradiated in the reactor for as long as it can stand it has to be removed and stored for a period to allow the most intense fission-product radioactivity to decay. It is then reprocessed chemically to remove the fission products and replace the fissile material, refashioned into fresh fuel elements, and returned to the reactor to be used again. The more frequently this has to be done the greater the cost, both because more reprocessing has to be paid for and also because more of the expensive fuel is lying unused waiting for reprocessing or being reprocessed.

The amount of irradiation the fuel can stand before it has to be removed and reprocessed is known as the “burnup”. It can be meas­ured by determining either the fraction of the total number of atoms of uranium and plutonium (or thorium and uranium if that cycle is being used) that are fissioned, or by determining the total amount of heat transferred from the fuel. The two are equivalent because one fission releases approximately the same amount of energy whatever isotope is fissioned, and because whatever its chemical form the mass of the fuel material is almost entirely made up by the mass of the uranium, plutonium or thorium atoms. It so happens that fission of all the uranium and plutonium (i. e. all the “heavy atoms”) would, if it were possible, release about 106 MW days per tonne of fuel.

Experience with the early reactors showed that metal fuel can stand no more than about 1% burnup, or 10,000 MWd/tonne, whereas fuel in the form of dioxides (either UO2, PuO2 or a mixture of the two) can stand much higher burnup, up to 10% or more. It became obvious that the reprocessing and inventory costs of fuel that could stand only 1% burnup would be prohibitively high. Metal fuel has another disad­vantage in that it cannot tolerate operation at high temperature. Phase changes in the crystal structure of the metal itself, together with the difficulty of finding a cladding material compatible with both fuel and coolant, limit temperatures to about 250 °C. This severely limits the thermodynamic efficiency in converting heat to work and so restricts the electrical power output.

For these reasons, in most quarters, metal fuel was rejected in favour of oxide fuel. The first power demonstration reactors in France (Rapsodie) and the USSR (BOR-60), both built towards the end of the 1960s, were oxide-fuelled.

As explained in Chapter 5 the behaviour of the reactor in a serious accident may be strongly dependent on both the Doppler effect and the reactivity change due to loss of coolant. The consequences of accidents are likely to be less severe the more negative these are. It is important therefore to know how design changes affect them.

An important factor is the “enrichment”, the ratio of fissile to fertile material in the core fuel. Figure 1.9 illustrates this. For the small highly-enriched core the increase of ф* with neutron energy is much lower than for the larger core because of the reduced probability of 238U fission and because high energy neutrons are more likely to leak out of the core. As a result, in a sodium-cooled breeder, the moderating component of the sodium coefficient becomes less positive as the enrichment is increased, and at the same time the Doppler coefficient is made less negative by the reduced amount of 238U.

It is not necessary to make the core smaller to increase the enrich­ment. The height of the core can be reduced or regions or layers of breeder can be incorporated within the core. Changes of this type make the sodium coefficient more negative, the Doppler coefficient less negative, the breeding ratio higher and the critical mass larger. The change in sodium coefficient is probably more important than the reduction in the Doppler coefficient from the point of view of safety and reduced-height cores may be attractive as a result. The increase in critical mass outweighs the improved breeding, however, and together with the increased mechanical complexity there is an economic dis­advantage. Figure 1.28 shows the effect of changing the height of the cylindrical core of a sodium-cooled breeder while keeping the volume constant.

Another way to reduce the sodium coefficient is to make the spec­trum softer by incorporating more moderating material in the core, so that the effect of losing the moderation by the sodium is less import­ant. Solid moderators such as beryllium oxide, BeO, or boron carbide depleted in 10B (i. e. UB4C) have been proposed. If some 10% of the core volume were to be occupied by BeO the sodium coefficient could be made negative and in addition the Doppler coefficient would be more negative. This is in fact the only practical way that both

Doppler and sodium coefficients can be made more negative at the same time, but there is a disadvantage in that the critical mass is increased.

Increasing the fraction of 241Pu in the fuel also makes both Doppler and sodium coefficients more negative, but this is not really a useful design option because the effects are small and it is likely to be difficult to alter the composition of the plutonium in the fuel without a severe cost penalty. The effect on the sodium coefficient arises because the fission cross-section of 24lPu increases more rapidly with decreasing energy than that of 239Pu, so the importance of low-energy neutrons is increased. The higher fission cross-section of 241Pu in general means that more fertile material (238U + 240Pu) is present and the Doppler coefficient is more negative.

Replacing oxide fuel by carbide makes the spectrum harder and reduces the enrichment so the sodium coefficient becomes more pos­itive and the Doppler coefficient more negative.

Since neither lead-bismuth nor gas has significant moderating effects the coolant temperature coefficients for both lack the positive

component of the sodium coefficient. The overall coolant temperature coefficient for gas coolant is very small, while for lead-bismuth there is a small negative leakage effect.

Figure 1.12 shows that the effect of a change in the sodium density is very different for a thorium-cycle breeder. There is little variation of Ф* with energy so the moderating component of the sodium coefficient is much smaller. At the same time the Doppler coefficient is strongly negative because of the high importance of neutrons in the 1 keV energy range.

As explained in section 2.5.6 one of the advantages of the IFR system is that the higher actinides do not appear as waste products but are “automatically” recycled and consumed along with the plutonium. Irradiation testing has shown that the performance of metal fuel is not significantly affected by the presence of higher actinides. Figure 2.25 shows the radial redistribution of the alloy constituents. Neptunium does not migrate whereas americium tends to follow the zirconium and to be precipitated in pores.

Higher actinides produced in thermal reactors could be consumed in this way if, in the reprocessing plant, they were not separated from the plutonium but used with it as a feed for a metal-fuelled IFR reactor. However if existing higher actinide waste inventories were to be con­sumed fuel with much higher concentrations of americium and curium would be needed.

REFERENCES FOR CHAPTER 2

Carmac, W. J., D. L. Porter, Y. I Chang, S. L. Hayes, M. K. Mayer, D. E. Burkes, C. B. Lee, T. Mizuno, F. Delage and J. Somers (2009) Metallic Fuels for Advanced Reactors, Journal of Nuclear Materials, 392,139-150 Chamberlain, A., H. A Taylor, R. H. Allardice and J. A. Gatley (1978) The Optimisation of Fuel Design in relation to Reactor Performance and the Conflicting Demands of other parts of the Fuel Cycle, Optimisation of Sodium-Cooled Fast Reactors, pp 133-136, British Nuclear Energy Society, London

Chang, Y. I. and C. E. Till (2011) Plentiful Energy: The Story of the Integral Fast Reactor, CreateSpace online publishing Cox, C. M. and F. J. Homan (1970) Performance Analysis of a Mixed-Oxide LMFBR Fuel Pin, Nuclear Applications and Technology, 9, 317-325 Crawford, D. C., D. L. Porter and S. L. Hayes (2007) Fuels for Sodium-Cooled Fast Reactors: US Perspective, Journal of Nuclear Materials, 371, 202-213 Findlay, J. R. (1974) The Composition and Chemical State of Irradiated Oxide Reactor Fuel Material, pp 31-39 in Behaviour and Chemical State of Irradi­ated Ceramic Fuels, IAEA, Vienna

Hofman, G. L., L. C. Waters and T. H. Bauer (1996) Metallic Fast Reactor Fuels, Progress in Nuclear Energy, 31, 83-110 International Atomic Energy Agency (2009) Status of Minor Actinide Fuel Development Technical Report NF-T-4.6, IAEA, Vienna

International Atomic Energy Agency (2011) Status and Trends of Nuclear Fuels Technology for Sodium-Cooled Fast Reactors Technical Report NF — T-4.1, IAEA, Vienna

Kim, Y. S. and G. L. Hofman (2003) AAA Fuels Handbook, Argonne National Laboratory, Argonne, Illinois, USA

Kittel, J. H., B. R. T. Frost, J. P. Mustelier, K. Q. Bagley, G. C. Crittenden and J. Van Deivoet (1993) History of Fast Reactor Fuel Development, Journal of Nuclear Materials, 204, 1-13

Meyer, R. O., D. R. O’Boyle and E. M. Butler (1973) Effect of Oxygen-to — Metal Ratio on Plutonium Redistribution in Irradiated Mixed-Oxide Fuels, Journal of Nuclear Materials, 47, 265-267

Olander, D. R. (1976) Fundamental Aspects of Nuclear Reactor Fuel Elements, Energy Research and Development Administration, Washington, DC

Pahl, R. G. and R. S. Wisner (1990) Steady-State Irradiation Testing of U-Pu — Zr Fuel to >18 at% Burnup, Proceedings of the International Conference on Fast Reactor Safety IV, American Nuclear Society, Hinsdale, Illinois, USA

Perrin, J. S. (1972) Effect of Irradiation on Creep of UO2-PuO2, Journal of Nuclear Materials, 42,101-104

Powell, H. J. (1974) Fission Product Distribution in Fast Reactor Oxide Fuels, pp 379-392 in Behaviour and Chemical State of Irradiated Ceramic Fuels, IAEA, Vienna

Rodriguez, P. (1999) Mixed Plutonium-Uranium Carbide Fuel in Fast Breeder Test Reactor, Bulletin of Materials Science, 22, 215-220

Zegler, S. T. (1962) The Uranium-Rich End of the Uranium-Zirconium System Report ANL-6055, Argonne Nuclear Laboratory, Argonne, Illinois, USA

There are two main strategies for controlling a power plant of any sort, which are chosen according to whether it is required to generate constant power or to respond to a varying demand. The former is adopted for a base-load power plant, and because of their low marginal fuel cost nuclear power stations are often used in this way. If the nuclear generating capacity exceeds the minimum load demanded from the system however some nuclear power stations have to be operated in the latter “load-following” manner.

The appropriate control system for base-load operation is shown in outline in Figure 4.17 A. The “heat source” in the case of a fast reactor power station consists of the reactor together with the primary and secondary sodium circuits. Deviations of the power generated by the alternator from the preset required value are used to control the reactor heat output. The turbine control valve is then adjusted to keep the steam pressure at a preset level. If for some reason the reactor power should rise it causes an increase in the steam pressure. The turbine control valve opens to reduce it and so increases the power generated by the alternator, and this in turn causes the reactor power to be reduced.

Figure 4.17 B shows the arrangement for load-following. The tur­bine control valve is adjusted to keep the alternator frequency equal to the required preset level. Deviation of the steam pressure from a preset level is then used to control the reactor power. If the demanded load increases the alternator is very slightly and briefly retarded. The reduction in alternator frequency is used to open the control valve to admit more steam and return the alternator to its correct frequency and phase. This reduces the steam pressure, and the control system acts to increase the reactor power and restore the pressure to its pre­set value. The principles of these control systems are described by Knowles (1976).

і t pressure

В Load-Following

Figure 4.17 Plant control systems for base-load and load-following operation.

Figure 4.18 shows the control of the “heat source” in more detail. One way to adjust the heat output to give the required power output (for base-load) or steam pressure (for load-following) is to use the con­trol variable to control the primary and secondary pump speeds. The reactor control rods are then moved to keep the core outlet temper­ature at a preset level. If more power is required the primary and sec­ondary pump speeds are increased in step. The increased flow through the core decreases the outlet temperature, and the control rods are

adjusted to increase the reactor power. A typical fast reactor control system is described by Evans and colleagues (1967).

The various control system elements shown as boxes in Figures 4.17 and 4.18 are not just simple proportional controllers. Derivative or integral terms have to be included in the control function to make the system stable, and the overall gain has to be chosen to keep the main operating parameters within acceptably narrow limits. This is particularly true of the coolant temperatures because fluctuations of the sodium temperature are transmitted so readily to the structure (see section 4.2.4).

In normal operation it is not very difficult to keep temperatures constant. Because of the large mass of sodium in the primary circuit, especially in a pool reactor, power or coolant flow-rate fluctuations cause only very slow temperature changes in most of the structure. The exception may be any structural members, such as control rod guides or mechanisms, exposed to the coolant immediately on leaving the core. Similarly the mass of water in the steam generators, particularly in the steam drums of a recirculating steam generator, and the mass of metal in the drums and heat exchangers, tend to smooth out variations in steam demand so that the steam pressure responds quite slowly to changes in the turbine control valve opening.

There is an important difference, however, between the steam plant of a sodium-cooled fast reactor and that of a fossil-fuelled power sta­tion. Because of the lower heat transfer coefficients in a fossil-fuelled station where the heat is transferred to the boiler tubes by convection and radiation from a gas, the boilers are larger than the sodium-heated steam generators of a fast reactor power station. This is not important in normal operation but under “upset” conditions, especially when the steam plant is operating abnormally, the rapid response of the steam generators to pressure changes can create difficulties in control.

The difficulty of estimating how the flux varies within each group before the equations 1.9 are solved is overcome by making a very simple assumption about the spatial variation. When this assumption is made it is possible to estimate the detailed variation of the flux with energy (the “energy spectrum”) and to use it to calculate group con­stants for a proper calculation of the spatial variation. In equations 1.9 the spatial variation is contained in the first term. The simplification is made by assuming that V2фg can be replaced by —B2фg where B2 is the “buckling”, a constant that is the same for all energies.

The energy range is then divided into a large number of fine groups so that the variation of the cross-sections within each group is small. These fine groups can be denoted by the suffix n to distinguish them from the broad groups used in the spatial calculation, which are denoted by the suffix g. If B2 is chosen suitably, corresponding to the system being critical, we can write k = 1.

Because we are dealing with only one point in space the fine group fluxes can be normalised so that

N

fnФп = 1. (1.11)

n=1

The equation for Фп then becomes

In this set of linear equations фп depends only on the фп for П < n so they can be solved one after another starting with фі. It is then necessary to iterate, changing the value of B2 until equation 1.11 is satisfied. This is the procedure of a “fundamental mode” or “normal
mode” calculation. It can be carried out easily and quickly for a very large number of fine groups, typically 1000 or more, even though iteration is involved.

If the reactor consists of several regions with different compositions a separate fundamental mode calculation has to be done for each, obtaining different neutron spectra. For regions that are net absorbers of neutrons it is necessary to make B2 < 0.

Once fine group spectra have been found for each region the broad group constants can be found. Thus, for example, the group fission cross-sections are given by

V£fg Vn £ fn<Pn £>• (1.13)

neg ‘ neg

Similarly the diffusion coefficient is given by

Dg =J2 Dn<Pn/j2 Фп. (1.14)

neg ‘ neg

This is based on the assumption that V2ф varies with energy in the same way as ф. This assumption is basic to a fundamental mode calculation.

The group transfer cross-sections include contributions from both inelastic and elastic scattering. The inelastic scattering component is given by

£isg^g = пФп’ ІФі, (1.15)

neg n’eg

but the elastic scattering has to be treated differently because if the broad groups are wide compared with f Eg, where f is the mean log­arithmic energy change, elastic scattering transfers neutrons from the lower end of the group only. Thus

£esg^g ^ £esnфn|фg—1, (1.16)

net(g-1)

where the summation is over the fine groups roughly within f Eg-1 of the group boundary.

As an alternative to doing a fundamental mode calculation it is possible to make a rough estimate of the group constants as follows. In a medium with no absorption and a constant scattering cross-section Ф (E) would vary as 1 / E. Though the actual spectrum departs from this variation over wide energy ranges, over the width of a single group it is sometimes reasonably accurate to assume ф a 1/E, giving

Eg-1

ug£ fg = ё£ fdE/EUg (1.17)

Eg

where

Ug = ln (Eg-1/Eg). (1.18)

Using this assumption the elastic scattering transfer cross-section is given by

^es(g-1)^g — 4 ve4(Eg_1 )/Ug

In most cases the fuel is in the form of sintered pellets that are made from a mixture of UO2 and PuO2 powders in the correct proportion. It is important that the powders are mixed homogeneously because if they are not there is a risk of hot spots due to high local plutonium concentration. There is also the danger that if the power increases very rapidly in an accident the effect of the negative Doppler coefficient of reactivity from the 238U (see section 1.6.5) may be reduced if there is a significant delay in transferring heat from the plutonium-rich regions, where most of the fissions occur.

The oxide power is mixed with a binder or plasticiser, usually an organic compound, which allows the powder to be pressed into the required shape. The pellets are then sintered to turn them into the required ceramic form. During the sintering process the binder is broken down and driven off, and care has to be taken to remove any traces of hydrogen and carbon, which can have deleterious effects on the cladding. The porosity of the finished pellets can be controlled by careful choice of the nature and quantity of the binder and of the sintering time and temperature, and it can be made as low as 2% if required. Finally the pellets may have to be ground to the correct size. This is expensive because it produces plutonium-bearing dust which is hazardous and therefore has to be controlled carefully. Precise control of the sintering process to produce pellets of the required dimensions within a sufficiently close tolerance is preferable.

The oxygen content of the fuel can be controlled at the sintering stage. If the sintering is carried out in a reducing atmosphere, con­taining hydrogen for example, the oxygen can be reduced to a sub­stoichiometric level (i. e. x < 0).

An alternative manufacturing technique uses the “sol-gel” method, in which plutonium and uranium nitrate solutions are mixed in the cor­rect proportions. This aqueous mixture is sprayed through a vibrating nozzle to produce small gel droplets that are then dried to produce oxide microspheres in which the plutonium is in solid solution within the (U, Pu)O2 crystals. These microspheres can then be sintered into pellets.

Instead of being made into pellets the sol-gel microspheres can be used to make “vibro-compacted” or “vipac” fuel. In this technique microspheres of at least two different sizes are loaded directly into the cladding tubes, which are vibrated until they are compacted to the required density and then sintered. A disadvantage of vipac fuel is that even if the porosity of the individual particles is as low as 3 % the overall porosity of a 6-mm diameter fuel element made with 800 and 80 pm microspheres cannot be reduced below about 18%. To achieve a higher smear density a third, even smaller, particle size is required, which increases the cost of manufacture significantly. Another disadvantage is that if the small particles, or “fines” as they are called, contain plutonium they are hazardous in manufacture because of the risk of inhalation. If the plutonium is confined to the larger particles the hazard is reduced but the disadvantages of possible hot-spots and a delay in the Doppler effect are incurred.

The advantages and disadvantages of the structural materials that can be used in the core can be summarised. There are three main groups: austenitic steels, nickel alloys and ferritic steels.

Austenitic steels of the AISI 304,316 or 321 types are most widely used. They have relatively low yield strength but high ductility (which is particularly important for the fuel cladding). The creep rate can be reduced if the carbon content is reduced (as in the low-carbon 316 stainless steel) or if a stabilising additive such as niobium or titanium is included. In sodium systems these steels resist corrosion adequately provided the oxygen content is controlled. They suffer, however, from three disadvantages: irradiation embrittlement, susceptibility to

damage by thermal shock, and, most important, irradiation swelling. Cold working to produce about 20% reduction of area reduces but does not eliminate the incidence of swelling (and also increases the yield stress), and irradiation creep mitigates the effects to some extent. Nev­ertheless the necessity to accommodate volume increases of 5-10% creates many difficulties in design.

High nickel alloys are considerably stronger and are much more resistant to irradiation swelling. They have the disadvantage that the neutron capture cross-section in nickel is higher than that in iron, but this is balanced by the higher strength, which allows a smaller volume of the material to be used. However alloys containing very high nickel levels (75% or so) corrode unacceptably fast in sodium. The high solubility of nickel rules nickel alloys out completely for lead or lead-bismuth systems.

Ferritic-martensitic steels suffer a loss of strength because of decar­burization. This can be allowed for in design, and the effect is reduced if the carbon is stabilized by the addition of niobium or titanium. Ferritic steels have the significant advantages of a higher thermal conductivity and lower thermal expansion coefficient than austenitic steels, both of which reduce thermal stresses, and greater resistance to crack propaga­tion. High chromium content such as in 9Cr 1Mo gives better resistance to corrosion in lead systems.

Ferritic steels lack creep strength at high temperatures and for higher temperature applications ODS steels may be preferable. Such steels are made by alloying the metal with fine oxide powders that after consolidation by hot extrusion form minute oxide crystals within the metal crystals. The particles consist of complex oxides of yttrium, titanium and aluminium, depending on the composition of the steel, and are typically 5 nm in diameter. They act to trap and immobilise dislocations, thus inhibiting creep, and also to attract vacancies, pre­venting them from coalescing to form voids and thus reducing swell­ing. ODS steels appear to be attractive as cladding and structural

materials but they are difficult to weld and need extensive experi­mental validation before they can be used with confidence.

Table 3.1 gives typical compositions of some of these materials.

5.4.1 Accident Sequences

In the previous sections various inherent features of a fast reactor and various optional protective systems have been identified. Between them these determine what would happen when an accident occurs. To ascertain whether the reactor with its protective systems is acceptably safe we have to follow the development of a series of accidents to find out what would actually happen and what the consequences to the reactor plant, the reactor operating staff and the general public would be. In this way we can determine whether the protection system is adequate. The method of doing this is appropriate to reactors of all types, fast or thermal.

It is important to recognise that discussion of accidents has to be conducted in terms of probabilities. There are two reasons for this. Firstly we have to take account of the possibility that a protective system might not work correctly when required. Aitken (1977) shows how this can be done and how estimates can be made of the probability that a given system will work correctly on demand. Secondly we have to take account of the random nature of some of the physical processes involved. The turbulent flow of fluids, for example, or the distribution of defects in a solid body contain random elements, ultimately at the quantum level. For these reasons we have to assign probabilities to the possible outcomes of events such as the subjection of a certain structural member to a certain load.

Probabilities can best be incorporated in the determination of the outcome of an accident by expressing its development in the form of an “event tree”. The method is described by Lewis (1977), pp. 82-84. An event tree is a line that traces the development of the accident. At each point where the development can proceed in either of two ways the line branches and probabilities are attached to each branch. In this way all the possible final outcomes can be identified and the frequency of each determined.

To make a complete assessment of the safety of a reactor in prin­ciple we have to construct an event tree for all the possible events that might initiate an accident. This would be impossibly complicated, but in practice it is not necessary to go into so much detail because it quickly becomes clear that the risks to the plant and the public are dominated by a small number of accidents to which attention can be confined.

All accidents are in some sense unpredictable, because if both the nature of the initiating event and the time of its occurrence were known in advance protective measures would be taken and there would be no accident. Many accident-initiating events are quite predictable in nature, however, and unpredictable only in that it is not known when they will happen. Events such as electrical power failure or fuel ele­ment cladding failure fall into this category. The resulting accidents can be analysed quite straightforwardly by event trees.

But it is also necessary to guard against initiating events that are unpredictable in nature as well as in timing: to guard against the acci­dent that has not even been thought of. In principle this is very difficult, but in practice it is possible to make sure that all eventualities have been covered. The method is to make pessimistic assumptions in the event trees. For example we can guard against unforeseen failures of a trip mechanism by assuming arbitrarily that it does not work when required, even though we know of no way this could happen. As explained earlier in section 5.1.1 this is called a “hypothetical accident”. In the end a judgement has to be made about how much pessimism of this type should be included in the analysis.

Accident sequences for two types of initiating events, those con­cerning a single subassembly and those involving the whole core, are discussed here. They are representative of the range of hypothetical accidents that have to be analysed to demonstrate the safety of a given design.

G measures the gain in reactivity assuming the fuel is to be used in a new reactor. Breeding also has an effect on the reactivity of the reactor in which it takes place, but this is not related at all closely to the value of G because much of the new fissile material is generated in the breeder where its effect on reactivity is very small. The fissile material gen­erated within the core does have a significant effect, however, which is very important. It can be characterised by the “internal breeding gain”, GI, which is defined in exactly the same way as G except that the integral in equation 1.42 runs over the core of the reactor alone, not over the whole reactor including the breeder. GI is negative for most reactors, implying that there is a net loss of fissile material from the core, but it can be positive for metal-fuelled or gas-cooled fast reactors.

GI does not measure the reactivity change directly. In the same way as G it represents the effect on reactivity that would result if the changes in composition of the fuel in the core were distributed uniformly throughout the core, whereas in fact the changes are greatest at the centre of the core where the flux is highest. In spite of this it is a useful guide to reactivity changes and when GI is greater (i. e. less negative) the loss of reactivity with burnup is less.

It is important that the rate of change of reactivity with burnup should be as small as possible. The fuel is changed in batches when the reactor is shut down, and it is desirable to make the interval between changes as long as possible to minimise interruption to oper­ation. Between changes the reactivity of the fuel declines and has to be compensated for by withdrawing control rods containing neutron absorbers from the core. When the fuel is fresh, therefore, neutrons that could have been used for breeding are absorbed in the control rods. The higher the internal breeding the smaller the reactivity loss with burnup, the smaller the quantity of neutron-absorbing material in the core and the better the overall breeding or, alternatively, the longer the period between fuel changes.

If a reactor core is designed to consume fissile material rather than breed Gj is substantially negative and the loss of reactivity with burnup is large. This can be a major economic and operational disadvantage for a consumer reactor.