As the fuel is irradiated in the reactor its isotopic composition changes. The effect is illustrated in Figure 1.17 which shows what would hap­pen, in theory, to 1 kg of 238U if it could remain in a reactor until it was entirely consumed by fission (something that is impossible in practice because the buildup of fission products would completely disrupt the fuel material). The quantity of 239Pu would increase, followed by 240Pu, then 241Pu and lastly by 242Pu, all in successively smaller amounts. On the linear scale of Figure 1.17 243Pu and all the americium and curium isotopes do not appear because the quantities produced are very small. This reflects the fact that, as far as any effect on the oper­ation of the reactor is concerned, they are quite unimportant. Their effect on the waste stream, which is far from unimportant, is discussed later.

The extent of irradiation is indicated in Figure 1.17 in terms of the burnup, the fraction of the “heavy atoms” (i. e. nuclei of uranium or plutonium) that have been fissioned. Since all fissions, of whatever isotope, liberate roughly the same amount of energy (about 200 MeV), burnup can also be measured in terms of the energy released. 100% burnup — i. e. complete destruction by fission — would yield about 80 TJ/kg. Another convenient way of measuring burnup is in terms

of megawatt-days per tonne (MWd/t). Complete burnup is equivalent to about 106 MWd/t.

Figure 1.18 shows how the isotopic composition of the plutonium in Figure 1.17 changes with burnup. The most notable feature is the steady increase of the 240Pu fraction. The concentrations of 241Pu and 242Pu are always small. The composition tends asymptotically towards 239:240:241:242 — 56:36:5:2. (The precise ratios depend on the spec­trum of the neutron flux.)

Figure 1.19 shows how the quantities of the various isotopes would vary with burnup in an idealised uranium-cycle reactor with a continu­ous feed of fertile 238U. The reactor is assumed to generate 2500 MW (thermal) from a core containing a total of 7.4 tonnes of fissile and fertile material (i. e. heavy atoms). The initial enrichment in 239Pu is

Figure 1.19 The evolution of fuel composition in a uranium-cycle reactor (2500 MW thermal, 7.4 tonnes of heavy atoms).

23% but this declines as the concentration of fissile 241Pu builds up. The buildup of the other plutonium isotopes can also be seen.

Figure 1.20 shows the same information for a thorium-cycle reactor that has an initial loading of 239Pu to make it critical. The uranium iso­topes build up very slowly and for a prolonged period 239Pu has to be added to maintain criticality. The fact that only very small quantities of 237U and 238U, the sources of higher actinides (see Figures 1.14 and 1.15), are produced indicates that thorium-cycle reactors pro­duce less of the hazardous higher-actinide waste than uranium-cycle reactors.

However, as stated earlier, Figures 1.19 and 1.20 are theoretical because in practice the fertile feed is not continuous but comes in batches when the core is reloaded after irradiated fuel is removed for reprocessing. The maximum burnup achievable in practice is around 20%, at which point in a uranium-cycle reactor the plutonium contains around 77% 239Pu and 21% 240Pu. If plutonium with a higher 239Pu

concentration is required the fuel has to be removed and reprocessed much sooner, after at most a few percent burnup. Plutonium rich in 239Pu is sometimes called “high-grade plutonium”.

Figure 1.21 shows how the isotopic abundances vary typically in a reactor. While it operates the quantities of both 238U and 239Pu decrease (usually they are said to “burn down”), the reactivity being maintained by withdrawing control absorbers from the core. At the end of a period of operation (usually called a “run”) some of the irradiated fuel is removed and taken for reprocessing. The plutonium is separated, some fresh plutonium is added to it to replace that con­sumed, and it is returned to the reactor. In the example of Figure 1.21 it is assumed that the plutonium in the core at startup and added at each reload is pure 239Pu. The quantities of the higher plutonium isotopes increase steadily from run to run. 242Pu is present but its abundance is indistinguishable on the scale of Figure 1.21.

2.5.1 Temperatures

In the early days of the development of fast reactors, when a high breeding ratio was thought to be of great importance, it was realised that the best fuel material from the point of view of the neutron eco­nomy would be a metal, either uranium or an alloy of uranium and plutonium. By the 1960s however it was realised that high burnup was important, and as at that time metal fuel was thought to be limited to about 3% burnup interest almost everywhere turned to oxide. The sole exception was in the USA where work continued in support of the metal-fuelled EBR-II test reactor. That work was ultimately successful in that a ternary U-Pu-Zr alloy fuel capable of up to 20% burnup was developed, and is now an alternative to oxide.

Figure 2.17 shows the thermal conductivity of solid 70U-20Pu — 10Zr (w/o), and its integral, between 500 and 900 °C. There are few data for higher temperatures. However as explained in section 2.5.2 on irradiation the metal becomes very porous, and a porosity of 30% may reduce the effective conductivity to 40% of the value for the solid material. A value of 10 Wm-1 K-1 is a reasonable conservative approximation.

The melting points of pure uranium and plutonium metals are 1135 °C and 640 °C respectively. The solidus temperatures of 20%

and 40% Pu in U are 920 °C and 780 °C respectively and the eutectic (85%Pu) is about 620 °C. The admixture of zirconium increases the solidus temperature of U-20Pu by about 13 K for each percent. Thus the solidus temperature for 70U-20Pu-10Zr is about 1050 °C.

Unlike oxide (see section 2.3.6) metal fuel is chemically compatible with sodium, so the thermal conductance between fuel and cladding can be improved by filling the gap with sodium. As a result the temper­ature difference between the coolant and the outer surface of the fuel is very small. For a linear rating of 50 kWm-1, steel cladding 0.3 mm thick and a 0.35 mm sodium-filled gap between fuel and cladding, the difference is only 53 K. At the centre of a reactor core where the power density is greatest and the coolant temperature is 500 °C the fuel surface temperature might therefore be about 550 °C. If melting is to be avoided the temperature difference between the surface and the centre of the fuel cannot be allowed to exceed 1050-550 = 500 K. Using a conservative conductivity of 10 Wm-1 K-1 the linear heat rat­ing q = 4nKf (AT/) has to be limited to ~63 kWm-1. In practice q is limited to about 50 kWm-1 to provide a margin to melting and to allow for uncertainty over the effect of porosity on the conductivity.

Thus in spite of the differences in thermal properties the linear heat rating in a metal-fuelled reactor is likely to be similar to that in one with oxide fuel. There is however a great difference in the fuel temperatures. The volumetric average fuel temperature at the centre of the reactor of the previous paragraph would be about 800 °C, whereas that for a similar oxide-fuelled reactor (with q = 50 kWm-1 and a fuel surface temperature of 1000 °C — see section 2.2.2) would be 1700 °C. This difference has a great effect on the behaviour of the fuel under irradiation.

There may be come concern about the formation of a eutectic where the fuel touches the cladding, and the possibility that the res­ulting liquid metal might damage or even penetrate it. The eutectic temperature is in the range 700-725 °C (depending on the composi­tion of the fuel). Even if the coolant temperature at the core outlet is 600 °C the maximum fuel surface temperature in an element with a peak linear rating of 50 kWm-1 (i. e. about 25 kWm-1 at the top of the core) would be around 625 °C, leaving a substantial margin to eutectic formation.

If the surface exposed to the fluctuating temperatures is smooth and free from defects — for example, a rolled steel section that has not been subject to damage during manufacture or site assembly — it may be possible to show that no cracks will be formed. Experimental data on high-cycle fatigue damage indicate that for 316 stainless steel strain fluctuations with an amplitude of less than about 0.0008 do not initi­ate surface cracks even up to 109 cycles. This corresponds to surface temperature fluctuations of 45 K. This indicates that the above-core structure is not likely to be at risk if the differences between the coolant outlet temperatures from adjacent core or breeder subassemblies do not exceed this value.

In the case of a welded structure however it is very difficult to demonstrate freedom from surface defects 0.1-0.5 mm deep and it has to be recognised that temperature fluctuations may well make such cracks grow. In most cases they start to grow quickly, but the rate of growth soon declines. This is because high-frequency temperature fluctuations at the surface are attenuated rapidly as they penetrate into the material, and a growing crack soon reaches a depth at which it is too small to cause further growth. The crack growth is said to “arrest” at this depth.

It is usually the case that shallow cracks have no significant effect on the strength of reactor structures. Thus damage due to high-cycle fatigue can be taken to be acceptable if the crack arrest depth is 1 mm or less or, equivalently, if a crack of this depth will not grow. A crack grows if the variation of the stress intensity factor at its tip AK exceeds a critical value AKth, the growth threshold. AKth depends on the stress ratio R of the fluctuations. R is the ratio of maximum stress to minimum in the cycle, so that if the mean stress is zero R = -1,

whereas R = 0 if the stress is zero at one extreme of the cycle. For 316 stainless steel at 550 °C AKth is about 12 MPam1/2 for R = -1 and 8 MPam1/2 for R = 0.

A sinusoidal temperature fluctuation attenuates with depth x below the surface as exp(—x(nf/X)1/2) where X is the thermal diffusivity and f is the frequency, so at the tip of a crack of depth h the strain range Ає is given by

Ae(h) = aAT0 exp(—hy/n f/X). (4.2)

The condition for crack arrest is then h = hc, where

ЕАє. )yfnhc/(1 — v) = AKth. (4.3)

Here E is Young’s modulus (= 2 x 1011 Pa) and v is Poisson’s ratio (= 0.3). Figure 4.5 shows the variation of hc with AT0 for f = 1 Hz, a = 18 x 10—6 K-1 and X = 6 x 10—5 m2 s-1. For surface temperature fluctuations of AT0 = 50 K the crack arrest depth hc is about 1.4 mm.

In the last quarter of the 20th century the development of fast reactors declined. Nuclear power in general was set back, partly because of the Chernobyl accident, so that the fear that supplies of uranium would run out receded and with it the perception that breeding was neces­sary, at least for many decades. In addition, in the West in particular the public mood turned away from nuclear power and also in many countries from large government-funded development projects. The world’s largest fast reactor power station, Super-Phenix, was built in France but suffered a series of setbacks so that it lost political sup­port and was shut down prematurely. In the UK PFR struggled with a series of technical problems, and there was a sodium fire at Monju in Japan. A European collaboration succeeded in designing a “next — generation” fast reactor EFR (the European Fast Reactor) but there was no interest in constructing it. In the United States the development of oxide-fuelled reactors came to an almost complete halt. Only BN — 600 in the Soviet Union and then Russia was conspicuously successful as a reliable power station.

Amid these setbacks, however, there were several signs of poten­tial for the future. A widespread concern about the disposal of nuclear waste gave rise to interest in the use of fast reactors to consume, or “incinerate”, hazardous radionuclides. A concern about safety led to the suggestion that subcritical reactors driven by particle accelerat­ors would be less prone to damaging reactivity accidents. Experience of sodium fires led to reexamination of alternative coolants such as helium or lead. The latter was given impetus by the release of inform­ation about the Soviet submarines powered by small lead-cooled fast reactors that had been developed, unknown to the rest of the world, in the 1970s. In the United States development of metal fuel contin­ued in the 1980s and early 1990s. EBR-II was used to demonstrate burnup of nearly 20%, and this, coupled with work on pyro-chemical reprocessing of the fuel, led to a proposal for an “integral fast reactor” (IFR) system.

Throughout this period information was exchanged under the aegis of the International Atomic Energy Agency. The IWGFR (Interna­tional Working Group on Fast Reactors) was established in 1967, held regular technical discussion meetings and issued several reports including a series of “Status Reports” on fast reactor development worldwide.

1.7.1 Neutron Economy

To ensure the safety of a reactor it is essential to control the reactivity in such a way that it does not become supercritical and generate excessive amounts of heat. This may be easier if the reactor is designed to remain subcritical, so that criticality is not possible at least in normal operation. The advantages of this approach are discussed in Chapter 5.

A subcritical reactor is a multiplying assembly with ke < 1 that is driven by a neutron source. The relationship between power P, source-strength S and ke is of the form

P a S/(1 — ke).

The neutrons might come from spontaneous fission of curium isotopes (see section 1.4.1), or the 9Be(a, n)12C reactions in a radium-beryllium assembly, but for a power reactor a controllable source is required, such as can be provided by a particle accelerator. Such a system is known as an “accelerator-driven reactor” (ADR) or “accelerator — driven system” (ADS). In most cases it involves an accelerator (a linear accelerator for example or a cyclotron) that delivers a beam of high-energy protons to a spallation target consisting of material with high atomic weight located in the subcritical core. The target produces a cascade of high-energy neutrons that drive the reactor. An ADR can be seen as a device for producing neutrons that can be used for a variety of purposes — breeding fissile material such as 233U from thorium, transmuting radioactive nuclear waste (either fis­sion products or higher actinides) to reduce its hazard, or generating power.

The subcritical assembly acts to multiply the neutron output of the spallation source, and the multiplying factor depends on its ke. Figure 1.29 shows the neutron economy of an ADR. It is greatly simplified but illustrates the important aspects.

This simplified analysis shows that n + S = 1 + L + C, where, for each fissile nucleus destroyed, n = v/(1 + a), where a = af /(af + ac) is the number of fission neutrons generated; S is the number of source neutrons injected into the assembly; L is the number of neutrons lost by being captured in structure, coolant, shielding, etc.; and C is the number of neutrons available for use. In addition since the chain reaction produces n new neutrons from n + S neutrons, ke = n(n + S), so, after rearranging the terms,

S

C=it-m -1 — L (149)

For a critical reactor S = 0 and ke = 1, and

C = n — 1 — L.

If the ADR is operated as a breeder, C is the breeding ratio. If it is operated as a consumer of higher actinides account must be taken of the capture events in the fissile fuel, each of which may lead to the production of a new higher actinide nucleus, so the net reduction in the number of higher actinide nuclei is C — ac/(ac + af) = Ca(1 + a) per fuel atom destroyed.

As explained in the Introduction for a critical reactor L is in practice around 0.2, mainly because neutrons are captured in control absorbers. However it may be possible to control an ADR by means of varying the neutron source strength, in which case control rods may be unne­cessary. This might allow L to be reduced to around 0.1.

The primary economic pressure is to maximise the power output from a reactor, because this gives the best return on the capital invested in the reactor plant and the inventory of fuel committed to the reactor and the reprocessing cycle, and also maximises the breeding of fissile material or the consumption of waste products, whichever is required. Whatever the purpose of the reactor the heat generated has to be removed from the reactor core, and the power is limited by heat — transfer considerations. The crucial limits are set by conduction of heat within the fuel elements and by the flow of coolant through the core.

As explained in Chapter 2 in power reactors the fuel elements are in the form of long tubes of cladding, usually steel, containing the fuel in the form of ceramic or metal pellets or powder. If the power density in the fuel material due to fission is Q Wm-3, then q, the linear rating of the fuel element, is given by q = n RfQ, and if ATf is the temperature difference between the centre and the surface of a cylindrical fuel pellet, in the case of constant thermal conductivity, q is given by

q = 4n Kf ATf. (3.1)

As we have seen in Chapter 2 for most fuel materials the maximum acceptable value of q is about 50 kWm-1 .If q is fixed the power density Q = q/пR2f can in principle be increased indefinitely by reducing the radius of the fuel, but a practical limit is set by the cost of manufacture which rises rapidly for very small fuel elements. For this reason the fuel radius cannot be less than about 2.5 mm, which limits the maximum power density in the fuel to about 2.55 GWm-3.

1.1 INTRODUCTION

1.1.1 Safety and Design

The designer of a fast reactor, just like the designer of any other engineering enterprise, has to take into account what might happen if something goes wrong. He or she has to make sure that whatever happens the risk of injury — either to the operating staff or the general public — or of damage to property, is very slight.

There are basically two ways of making a reactor safe. First the overall design concept is chosen so that it is inherently safe. That is to say that for a number of possible accidents the design is such that the reactor behaves safely and damage does not spread even if no protective action, automatic or deliberate, is taken. But it is not possible to guard against all accidents in this way, however well the overall design is chosen. The second way to make the reactor safe is to incorporate protective systems. These are devices designed specifically to prevent the damaging consequences of accidents. A protective system can be active, such as an automatic shutdown system, or passive, such as a containment barrier.

The design aim is to make sure that the risk to the public is suf­ficiently small to meet the criteria of acceptability. To ascertain that the aim has been met the designer has to determine the response of

the reactor, with its protective systems, to a range of accidents. To test the systems thoroughly it is often necessary to assume that certain accidents happen, even though no way is known by which they could actually take place. These are known as “hypothetical accidents”. The final step is to analyse the accidents, whether hypothetical or not, and to ensure that the risks meet the criteria imposed by the authorit­ies that regulate nuclear activities. These criteria vary of course from country to country.

The main concern in reactor safety is to make sure that the radio­active materials — fuel, fission products and activation products — are contained adequately and do not escape to the environment. This is the main subject of this chapter, which is confined to consideration of the safety of the reactor alone. Questions of the safety of fuel man­ufacture and transport and of waste disposal are not addressed here, nor are other risks associated with the steam and electrical plant, for example.

The safety of nuclear reactors in general is discussed by Lewis (1977) and Farmer (1977). Detailed accounts of some of the subjects touched on briefly here are given by Graham (1971) and Waltar and Reynolds (1981).

The cross-sections of many nuclei exhibit sharp resonances over part of the energy range. Heavy nuclei such as uranium and plutonium have resonances in the range from about 1 eV up to 500 eV or more. Lighter elements have resonances mostly at higher energies of 100 keV or more, although there is an isolated resonance of 23Na at 3 keV. It would be impossible to do a fundamental mode calculation for all these resonances even if they had been resolved experimentally because there would have to be far too many fine groups. Fortunately it is possible to calculate the reaction rate in a resonance directly, but in doing this it is important to allow for the effect of temperature. In outline the method is as follows.

In the vicinity of an isolated resonance the microscopic cross­section for a certain reaction, neutron capture say, is given by

(1.32)

Here ac0 is the capture cross-section at E0, the energy of the resonance peak, and Г is the “width” of the resonance (the full width in energy at half the maximum cross-section). Ec is the kinetic energy of the neutron and nucleus relative to the centre of mass of the neutron — nucleus system. If the nucleus is stationary Ec = E/(l + 11 A) where A is the ratio of the mass of the nucleus to that of the neutron and E is the neutron energy.

Unless the reactor is at absolute zero temperature, however, the nucleus is unlikely to be stationary. It moves at random due to thermal agitation and this affects Ec, which is increased if the nucleus hap­pens to be moving towards the approaching neutron or decreased if it is moving away. The effect on the apparent cross-section can be calculated if the probability distribution of the velocity of the nucleus is known. It is usually satisfactory to assume it to have a Maxwell — Boltzmann distribution. The resulting distribution of the component of velocity parallel to a certain direction (which we can take as the direction of the neutron) is shown in Figure 1.1 for an atom of 238 U at various temperatures.

From this the probability distribution of Ec can be deduced, and hence the mean cross-section for a neutron of energy E. It is given by

1

ac (E, T) « Oc0 EE f (z, x), (1.33)

where

Z 2 = 4E0bT /AY2, (1.35)

and

x = 2(E — E0)/Y. (1.36)

T is the absolute temperature and b is Boltzmann’s constant. The approximations used in reaching equation 1.33 introduce negligible errors in most fast reactor applications.

Figure 1.2 indicates how the effective cross-section depends on temperature. The parameters f, Z and x are proportional to the cross­section, the absolute temperature and energy respectively.

Corrosion of the cladding by the fuel is discussed in section 2.4.7. It is strongly affected by the oxygen potential in the fuel and therefore by the stoichiometry. Figure 2.2 shows the variation of the oxygen potential of (U1-aPua)O2+x with x at constant temperature for various values of a. As expected the oxygen potential rises with x, but also it is higher for PuO2 (a = 1) than for UO2 (a = 0) because uranium adopts higher valency states than plutonium. The steep rise in the oxygen potential of UO2+x as x increases through zero is important.

The variation of oxygen potential with temperature is shown in Figure 2.3. Oxygen tends to migrate to the cooler parts of the fuel if x < 0, but if x > 0 the tendency is considerably reduced.

The effect of burnup is very complicated because of the wide range of elements formed as fission products. Each fission releases two

oxygen atoms, some of which go to oxidise the fission products, such as zirconium, strontium, barium and the rare earths, which have a strong affinity for oxygen. The number of oxygen atoms taken up by this oxidisation process depends on the yields of the various fission

products, and the yields differ for fission of different nuclides. Fis­sion of uranium yields more zirconium and strontium (which form oxides) and less ruthenium and palladium (which do not) than fission of plutonium. It so happens that as a result the average requirement to oxidise the fission products is for slightly more than two oxygen atoms per uranium fission and for slightly less than two per plutonium fission. The effect is shown in Figure 2.4.

In a typical reactor core fuel, far more fissions occur in 239Pu than in 238U, so oxygen is steadily released and the oxygen potential of the mixture of fuel and fission products rises. Just as in Figure 2.2 there is a particularly sharp rise at the point in burnup where the oxygen

content becomes stoichiometric, but the oxygen potential does not rise very high. An effective upper limit is set by molybdenum. The Mo/MoO2 system has an oxygen potential very similar to that of the fuel, and because the yield of molybdenum is high (about 0.06 atoms for each fast fission of either 239Pu or 238U) it forms a buffer. When the stoichiometric ratio is reached, oxygen released by further fissions is taken up by oxidising molybdenum.

To minimise oxidative corrosion of the cladding the fuel is usually manufactured a few percent sub-stoichiometric, with x = -0.02 or -0.03, but as explained in section 2.4.7 this does not prevent some corrosion taking place.

The subassembly wrappers become distorted due to the effects of thermal expansion, irradiation swelling and irradiation creep. The resulting movements have to be checked; otherwise they may cause

Flow restrictor

Coolant inlet

Figure 3.20 A typical fuel subassembly for a breeder reactor.

unwanted reactivity changes, interfere with movement of the control rods, and make withdrawal of irradiated subassemblies difficult.

As explained in section 3.2.5 there may be a considerable temper­ature difference across a subassembly at the side of the core due to the radial variation of power density. The side of the wrapper nearer the core centre is hotter and expands more, causing the subassembly to become curved or “bowed” with the convex side facing the core centre. The effect on reactivity of the resulting displacement, if it were unconstrained, is explained in section 1.6.3. A similar effect can arise from radiation-induced swelling of the wrapper, which is greater on the side nearer the core centre where the neutron flux is higher.

The effect of temperature bowing in an unconstrained core would in fact be small. Temperature differences of 10 K across subassemblies would cause radial displacements at the core centre plane of the order of 0.2 mm and reactivity changes of the order of 10-4, which are of
minor importance. The effect of irradiation swelling could be much greater. A rough estimate can be made as follows.

If the difference in linear expansion between the two sides of the subassembly is As its radius of curvature is w/Ає and its outward dis­placement at the core centre plane is d & H2As/8w if As is uniform along its length, where H is the height of the core and w is the width of the subassembly. As actually varies along the subassembly in a com­plicated way because it depends on temperature as well as fluence, but a mean value of 0.003, corresponding to a 1% difference in volumetric strain, is typical. For a subassembly 0.15 m wide this would cause a displacement of about 3 mm at the level of the core centre and about 10 mm at the top of the core, and the displacement of the top of the subassembly could be 20-40 mm, depending on how long it is. This would create many problems, and in particular it would make it dif­ficult to maintain the alignment of control rods with their operating mechanisms.

In most reactors radial movement is prevented by some sort of restraining or clamping system. Figure 3.21 shows such a system, where radial movement of the outer periphery of the radial breeder is pre­vented at two restraint planes, both above the core. According to where the restraints are placed small movements of the fuel due both to thermal expansion and to irradiation swelling still occur, but because the subassemblies are in contact with each other across the core any tendency to positive reactivity feedback can be eliminated.

A restraint system may be “active”, meaning that after the sub­assemblies have been assembled the restraints are tightened so that the whole array is clamped together, or “passive”, meaning that the restraints are fixed and prevent outward movements only after clear­ances between subassemblies have been taken up as the wrappers swell. The disadvantage of an active system is that the clamping mech­anism has to be operated remotely and reliably under sodium.

To avoid self-welding between the wrappers they can be provided with hard pads at the points where they are in contact. This is one

of the few places where neutronics affects the choice of materials: the cobalt alloys that are usually used for hard-faced surfaces are not acceptable in a reactor core because the radioactive 60Co that would be generated would create severe problems in handling the irradiated fuel and disposing of radioactive waste.

The radial loads between the restrained subassemblies vary with time and depend on the design of the restraint system, and predicting them is a very complex task. The order of magnitude can be estimated fairly simply, however. If a simple cantilever of length L is subjected to a transverse force F at its free end, the displacement d is given by d = FL3/3EI, where I is the second moment of area of the cross­section and E is Young’s modulus. For a hexagonal wrapper 0.14 m across flats made of sheet 3 mm thick, I ~ 4 x 10-6 m4. If the length of the subassembly, L, is 3 m and the displacement d is 0.01 m, typ­ical of bowing due to irradiation swelling, then with E = 2 x 1011 Pa

we obtain F и 900 N. If the restraint system is passive and the coeffi­cient of friction between subassemblies is about 1, similar forces, of the order of 1 kN, may be needed to overcome friction as a subassembly is withdrawn from the core.