# Improving Nuclear Safety of Fast Reactors by Slowing Down Fission Chain Reaction

Authors: G. G. Kulikov; A. N. Shmelev; V. A. Apse
Journal: International Journal of Nuclear Energy
 (2014)

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## Abstract

Light materials with small atomic mass (light or heavy water, graphite, and so on) are usually used as a neutron reflector and moderator. The present paper proposes using a new, heavy element as neutron moderator and reflector, namely, “radiogenic lead” with dominant content of isotope208Pb. Radiogenic lead is a stable natural lead. This isotope is characterized by extremely low micro cross-section of radiative neutron capture (~0.23 mb) for thermal neutrons, which is smaller than graphite and deuterium cross-sections. The reflector-converter for a fast reactor core is the structure capable of transforming some part of prompt neutrons leaked from the core into the reflected neutrons with properties similar to those of delayed neutrons, that is, sufficiently large contribution to reactivity at the level of effective fraction of delayed neutrons and relatively long lifetime, comparable with lifetimes of radionuclides-emitters of delayed neutrons. It is evaluated that the use of radiogenic lead makes it possible to slow down the chain fission reaction on prompt neutrons in the fast reactor. This can improve the fast reactor safety and reduce some requirements to the technologies used to fabricate fuel for the fast reactor.


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## Body

## 1. Introduction

Importance of such physical characteristic as prompt neutron lifetime for nuclear reactor safety is well known for a long time and was reflected in numerous publications, for example, in one of such fundamental works as [1]. The longer prompt neutron lifetime could produce the most favorable effects on nuclear reactor safety under conditions of the reactivity-induced accidents.The positive role to be played by the radiogenic lead, that is, lead with a dominant content of isotope208Pb, as a coolant for fast reactor safety was first noted in works [2, 3], where a possibility for significant improvement of the coolant temperature reactivity coefficient was shown. Later, some possibilities for improving other neutron-physical and thermal-hydraulic parameters of power fast reactors were considered at usage of the radiogenic lead as a coolant [4]. This direction of researches has been developed in work [5], where, in addition to the aforementioned possibilities, the prospects of the radiogenic lead applications for developing high-flux accelerator-driven systems capable to transmute radioactive wastes and for upgrading proliferation resistance of advanced Pu-based fuel compositions were investigated too.Extension of prompt neutron lifetime in fast reactors with the radiogenic lead as a neutron reflector was first proposed in works [6, 7]. This paper presents the results of further studies carried out in this direction.


## 2. Prompt Neutron Lifetime of Different Reactors

The longer prompt neutron lifetimes can substantially improve kinetic response of the fast reactor to a jump-like insertion of relatively large (~1 $ or even more) positive reactivity. For simplicity, let effective fractionβ of delayed neutrons be the same for all the fast reactor models under consideration here, β(235U) = 0.0065.The curves presented in Figure1 demonstrate dependencies of the reactivity jump required to provide the power excursion with asymptotic time period T (without any feedback effects) in the fourth-generation lead-cooled, fast BREST-type [8] reactor (neutron reflector—50 cm thick natural lead), in thermal VVER-type and CANDU-type reactors as well as in two hypothetical reactors whose prompt neutron lifetimes are equal to 0.01 s and 0.1 s, respectively.Figure 1
Dependencies of the reactivity jump required to provide the power excursion with asymptotic time periodT (one-point model, no feedback effects).These curves demonstrate that the shorter lifetime of prompt neutrons results in the faster power excursion at the same reactivity jump. It seems helpful to reformulate the statement as follows. If prompt neutron lifetime became longer, then the power excursion with a certain asymptotic time periodT would require the larger reactivity jump. Otherwise, the power excursion will be slower. Consequently, the reactor safety can be enhanced by making lifetime of prompt neutrons longer.For example, based on one-point model of neutron kinetics, it may be concluded that application of thick208Pb reflector in the fast reactor BREST allowed us to reach prompt neutron lifetime of ~1 ms. If 1-$ reactivity jump (!) occurs in the fast reactor, then its power increases with the excursion period nearly 1 s instead of 14 ms in the fast reactor reflected by natural lead. If prompt neutron lifetime in the fast reactor BREST reflected by thick 208Pb layer is prolonged up to 10 ms, then the power excursion period will be longer than 1 s even at the reactivity jumps up to 2$. So long the power excursion periods give sufficient time for coolant to remove the heat from fuel rods. This means that feedbacks on coolant temperature and coolant density could be apparently actuated.


## 3. One-Point Model

The dependencies shown in Figure1 were calculated with the application of one-point kinetic model with six groups of delayed neutrons. No feedback effects were taken into consideration. The one-point model is based on the following set of equations:
(1)dn(t)dt=ρ-βΛ-prt·n(t)+∑i=16λi·Ci(t),dCi(t)dt=βiΛ-prt·n(t)-λi·Ci(t);(i=1,2,…,6),
where n is neutron population in the reactor core; Ci is quantity of nuclei-emitters for ith group of delayed neutrons in the reactor core; ρ=(kef-1)/kef, reactivity, where kef is the effective neutron multiplication factor in the reactor including neutron reflector; β is effective fraction of delayed neutrons; βi is effective fraction of delayed neutrons in ith group; Λ-prt mean prompt neutron lifetime (according to the terminology applied by Bell and Glasstone [1]) in the reactor including neutron reflector; λi is decay constant of nuclei-emitters in ith group of delayed neutrons. Prompt neutron lifetime Λ-prt and generation time τ are linked by the relationship: τ=Λ-prt/kef. Since only critical and nearly critical (within some dollars from criticality) states are analyzed here, lifetime and generation time differ insignificantly. These terms are regarded below as being equivalent.Within the frames of one-point kinetic model (1), the inverse-hour equation that links the asymptotic period of the power excursion T with the inserted positive reactivity ρ may be written in the following form:
(2)ρ=Λ-prtT+∑i=16βi1+λi·T.


## 4. Two-Point Model

As has been noted in [9], one-point model is not completely applicable for analysis of neutron kinetics in the reactor cores surrounded by neutron reflector. The associated problems were analyzed in [9–15] with application of multipoint models or with introduction of some additional (fictive) groups of delayed neutrons. The latter case takes into account the following new parameters: time of neutron staying in the reactor core before leakage, time for neutron transport from the reactor core to neutron reflector, time of neutron staying in the reflector, time for neutron transport from the reflector into the reactor core, and time from neutron arrival into the reactor core to initiation of fission reaction by this neutron. In the case under consideration here, neutron reflector is placed in the immediate vicinity to the reactor core, and the reflector is thick from physical point of view. This means that time of neutron staying in the reflector plays a dominant role in competition with all other times. If one additional group of delayed neutrons, namely, slow neutrons coming back from the reflector into the reactor core, is introduced to study the reflector-induced effects on neutron kinetics; then, the following set of equations may be written:
(3)dn(t)dt=ρ-β-ρRΛ-C·n(t)+∑i=16λi·Ci(t)+λR·CR(t),dCi(t)dt=βiΛ-C·n(t)-λi·Ci(t);(i=1,2,…,6),dCR(t)dt=ρRΛ-C·n(t)-λR·CR(t);λR=1Λ-R,
where, in addition to the aforementioned designations, CR is quantity of fictive nuclei-emitters for additional group of delayed neutrons, that is, for neutrons coming back from the reflector into the reactor core, where they can initiate fission reactions (for brevity, CR may be called a quantity of fictive nuclei-emitters in the reflector); ρR=(kef-kefC)/kef is reactivity gain caused by the reflector, that is, increase of reactivity caused by neutrons coming back from the reflector into the reactor core and subsequent initiation of additional fission reactions (for brevity, ρR may be called as a reactivity gain caused by the reflector);   kef is effective neutron multiplication factor in the reactor, including neutron reflector (like in one-point model); kefC is effective neutron multiplication factor in the reactor without neutron reflector; Λ-C is prompt neutron lifetime in the reactor without neutron reflector; Λ-R is prompt neutron lifetime caused by the reflector-induced effects; that is, Λ-R is a sum of neutron lifetime in the reactor core, time of neutron staying in the reflector and neutron lifetime in the reactor core after coming back from the reflector (for brevity, Λ-R may be called as a prompt neutron lifetime in the reflector).According to the set of equations (3), additional group of delayed neutrons, which simulates neutron diffusion in the reflector, can be characterized by its effective fraction, that is, by contribution of the reflector into reactivity and by its decay constant, that is, inverse value of prompt neutron lifetime in the reflector. The inverse-hour equation that links the asymptotic period T with the inserted positive reactivity ρ can be written in the following form for the reactor core surrounded by neutron reflector:
(4)ρ=Λ-CT+ρR1+T/Λ-R+∑i=16βi1+λi·T.
The equation differs from similar inverse-hour equation (2) in one-point model (1) by the second summand that describes the role of neutron reflector. Besides, the first summand of the inverse-hour in one-point model contains mean prompt neutron lifetime in the reactor as a whole, including neutron reflector, while the first summand of the inverse-hour equation in the model with additional group of delayed neutrons (two-point model) contains prompt neutron lifetime Λ-C in the reactor core without neutron reflector, and the second summand contains prompt neutron lifetime in the reflector Λ-R. Prompt neutron lifetime in the reflector Λ-R can be calculated from the following balance relationship (see derivation of it in Appendix C):
(5)Λ-prt=(1-ρR)·Λ-C+ρR·Λ-R,
where Λ-prt (like in one-point model) is a mean prompt neutron lifetime in the reactor with neutron reflector.The balance relationship defines prompt neutron lifetime in a system as a sum of prompt neutron lifetimes in all system components (in the reactor core plus in the reflector, for instance) with the weighing coefficients that characterize contributions of these components to total criticality.It may be concluded from (4) that ρR plays here a role of additional fraction of delayed neutrons that is characterized by Λ-R, prompt neutron lifetime in the reflector. This means, in its turn, that application of such a thick neutron reflector gives a new quality to the reactor—the larger fraction of delayed neutrons and, as a consequence, slowing down of chain fission reaction.One else important circumstance consists in the following fact. The larger fraction of delayed neutrons depends mainly on neutron leakage from the reactor core and, thus, may be chosen as a developer wills, while fraction of nuclei-emitters of delayed neutrons may be chosen only within very stringent constraints. Evidently, generation rate of these “delayed” neutrons substantially depends on leakage rate of fast and resonance neutrons from the reactor core. That is why application of thick neutron reflector is a reasonable option not only for fast reactors but also for the reactors with resonance and even thermal spectra, with small sizes of the reactor core, that is, for the reactors with significant leakage of fast and resonance neutrons from the reactor core.The inverse-hour equation (4) for the reactor core surrounded by neutron reflector with additional group of delayed neutrons coincides with the inverse-hour equation in two-point model [9]. For brevity, hereafter, the term “n-point” will be used in designation of kinetic models, changing only the number of “points.”


## 5. Multipoint Model

This model of neutron kinetics can be used by considering a neutron reflector as a whole (as one zone in two-point model) or by considering a neutron reflector as a set of annular (nonintersecting) layers (multipoint model depending on the number of these layers):(6)dn(t)dt=ρ-β-∑j=1JρRjΛ-C·n(t)+∑i=16λi·Ci(t)+∑j=1JλRj·CRj(t),dCi(t)dt=βiΛ-C·n(t)-λi·Ci(t);1(i=1,2,…,6;j=1,2,…,J);dCRj(t)dt=ρRjΛ-C·n(t)-λRj·CRj(t);λRj=1ΛRj.
Within the frames of multipoint model the inverse-hour equation (4) and the balance relationship (5) for determination of prompt neutron lifetime in a neutron reflector can be rewritten as follows:
(7)ρ=Λ-CT+∑j=1JρRj1+T/ΛRj+∑i=16βi1+λi·T,Λprtj+1=(1-ρRj+1)·Λprtj+ρRj+1·ΛRj+1,
where J is the number of annular layers in neutron reflector; ρRj is contribution of jth layer to total reactivity gain; ΛRj is prompt neutron lifetime in jth layer, that is, sum of prompt neutrons lifetime in the reactor core before they go to the reflector, time for neutron transport from the reactor core to jth layer of the reflector, time of neutron staying in jth layer, time for neutron transport from jth layer of the reflector to the reactor core, and lifetime of neutrons after they came back from the reflector; CRj is quantity of nuclei-emitters for additional group of delayed neutrons in jth layer of the reflector; Λprtj is prompt neutron lifetime in the reactor with neutron reflector consisting of the first j layers, adjacent to the reactor core.The further results were obtained for six-layer reflector (thickness of the first layer is 50 cm, thicknesses of the next layers are equal to 1 m each). Kinetics parameters such asΛ-C and spatial dependences of  Λ-R and ρR were evaluated on the base of numerical analysis using diffusion neutron transport model with an evaluated nuclear data library (RUSFOND-2010) in frames of one-dimension spherical geometry. Contributions of the reflector into the reactivity gain and prompt neutron lifetime are presented in Table 1 for two-point and multipoint models of neutron kinetics in the fast BREST-type reactor with the reactor core surrounded by neutron reflector of different thickness (from 1 m to 6 m). Multipoint model for the case of 1 m-thick reflector is, in essence, two-point model: the first point for the reactor core with 0.5 m-thick reflector, the second point for annular layer (from 0.5 m to 1 m) in the reflector. If thickness of the reflector increases up to 2 m, then the third point arises for annular layer from 1 m to 2 m. Three-point model is used in this case. Correspondingly, neutron kinetics in 6 m thick reflector is defined by seven-point model.Table 1
Dependence of reactivity gain and prompt neutron lifetime on thickness of208Pb reflector in the fast BREST-type reactor for various models of neutron kinetics.
Two-point model
Thickness of208Pb reflector, m
1
2
3
4
5
6
Reactivity gain caused by the reflector, $
3.01
5.30
6.51
7.21
7.58
7.78
Prompt neutron lifetime in the reflector, s
2.90 · 10−5
1.04 · 10−3
5.71 · 10−3
1.21 · 10−2
1.82 · 10−2
2.33 · 10−2
Multipoint models
The number of points
2
3
4
5
6
7
Annular layer in208Pb reflector, m
0.5÷ 1
1÷ 2
2÷ 3
3÷ 4
4÷ 5
5÷ 6
Increase of the reactivity gain caused by thicker reflector, $
3.01
2.29
1.21
0.69
0.37
0.20
Prompt neutron lifetime in the reflector layer, s
2.90 · 10−5
2.36 · 10−3
2.62 · 10−2
7.25 · 10−2
1.36 · 10−1
2.16 · 10−1It can be seen that, in the case of 6 m reflector (seven-point model), prompt neutron lifetime in the last 1 m thick reflector layer is considerably longer (about one order of magnitude) than that for two-point model (one point for the reflector as a whole). This means that more correct mathematical models must be used to provide proper accounting for neutron transport effects in the fast reactors surrounded by physically thick and weakly absorbing neutron reflectors.


## 6. Spherically Symmetrical Continuous Model of Neutron Kinetics in Reactor Surrounded by Physically Thick Neutron Reflector

In order to simplify explanation of continuous neutron kinetics model, it seems reasonable to consider a spherically symmetrical reactor with a physically thick neutron reflector. The reactor core is described by one point in the continuous model. When the number of the reflector layers becomes infinite, multipoint model naturally converts into the continuous model where summing operation should be replaced by integration:(8)dn(t)dt=ρ-β-ρR(rout)Λ-C·n(t)+∑i=16λi·Ci(t)+∫rinroutλR(r′)·CR(r′,t)·dr′,dCi(t)dt=βiΛ-C·n(t)-λi·Ci(t);(i=1,2,…,6),dCR(r,t)dt=dρR(r)/drΛ-C·n(t)-λR(r)·CR(r,t);λR(r)=1ΛR(r),
where rin and rout are inner and outer radii of the reflector; ρR(r) is reactivity gain caused by the reflector with outer radius r(rin≤r≤rout); dρR(r)/dr is differential reactivity gain, that is, accretion of the reactivity gain caused by adding spherical reflector layer of unitary thickness to the reflector with outer radius r; CR(r,t) is quantity of fictive nuclei-emitters for additional group of delayed neutrons in spherical reflector layer of unitary thickness in spatial point with radius-vector r; ΛR(r) is prompt neutron lifetime in spherical reflector layer of unitary thickness in spatial point with radius-vector r.The inverse-hour equation and relationship for determination of prompt neutron lifetime for continuous model of the reflector in spherically symmetrical geometry can be rewritten in the following new forms:(9)ρ=Λ-CT+∫rinroutdρR(r′)/dr′1+T/ΛR(r′)·dr′+∑i=16βi1+λi·T,(10)ΛR(r)=Λprt(r)+dΛprt(r)/drdρR(r)/dr.
Continuous model of neutron kinetics may be regarded as a model describing continuous variation of reactivity gain caused by continuous variation of prompt neutron lifetime in the neutron reflector depending on spatial coordinate within the reflector. Solution of the inverse-hour equation (9) is not a trivial task. A possible way of the solution is proposed in Appendix D.


## 7. Physical Parameters of Neutron Reflector in Continuous Model of Neutron Kinetics

Some relevant physical parameters of neutron reflector are considered here within the frames of spherically symmetrical continuous model of neutron kinetics and presented in Figure2. It follows from Figure 2(a) that the reactivity gain thanks to the reflector ρR(r) grows as the reflector becomes thicker and approaches a saturation level. Correspondingly, derivative of the reactivity gain decreases and vanishes. Derivative of the reactivity gain dρR(r)/dr defines the growth rate of contribution given by prompt neutrons to chain fission reaction as the reflector becomes thicker. So, it is natural that derivative of the reactivity gain decreases as the reflector thickness increases because contribution of neutrons coming back from more distant reflector layers into chain fission reaction in the reactor core vanishes.Physical parameters of the fast BREST-type reactor depending on thickness of neutron reflector made of208Pb.
(a)
(b)It follows from the curves shown in Figure2(b) that mean prompt neutron lifetime Λ-prt in the fast BREST-type reactor with 208Pb reflector as a whole becomes substantially longer (from ~1 μsec to ~1 msec) as the reflector thickens from 0.5 m to 6 m. Derivative of the mean prompt neutron lifetime has a weakly expressed peak at the reflector thickness of ~3 m. The latter means an important fact that elongation of mean prompt neutron lifetime becomes slower as thickness of the reflector exceeds 3 m.The following two terms of (10) are considered below, namely, ΛR(0), prompt neutron lifetime in the reflector layer of infinitesimal thickness adjacent to the reactor core, that is, practically without the reflector and Λprt(0), prompt neutron lifetime in the reactor core only. The former is larger than the latter on the second summand. This is related with the following fact. Within the frames of one-point model, all prompt neutrons in the reactor core are characterized by a common generation time Λ-C, averaged over the core volume, and it is assumed that Λprt(0)=Λ-C. Lifetime of prompt neutrons of the reflector layer of even infinitesimal thickness, adjacent to the reactor core, is relatively longer because this lifetime is defined by neutrons that came up to the very edge of the reactor core and then came back to the reactor core. The explanation is confirmed by the calculated results presented in Figure 2(b). It can be seen that prompt neutron lifetime in the reflector layer of infinitesimal thickness ΛR(0) is longer than prompt neutron lifetime in the reactor without neutron reflector Λprt(0) by above one order of magnitude.As the reflector becomes thicker, difference between prompt neutron lifetime in the reflectorΛR(r) and mean prompt neutron lifetime in the reactor with neutron reflector Λ-prt increases. When the reflector thickness reaches 6 m, the difference exceeds two orders of magnitude. It is noteworthy that lifetime of prompt neutrons coming back from 6-m-thick 208Pb reflector into the reactor core is equal to a rather long value, above 0.1 s (Figure 2(b)).


## 8. Advancement of Continuous Model from(R,T) Phase Space to (Λ,T) Phase Space

When physical parameters of physically thick neutron reflector were analyzed by using continuous neutron kinetics model, the following dependencies were calculated:(i)
Radial distribution (within the reflector thickness) of the contribution given by annular layer of unitary thickness into the reactivity gainρR(r) (Figure 2(a)).(ii)
Radial distribution (within the reflector thickness) of prompt neutron lifetime in annular layer of unitary thicknessΛR(r) (Figure 2(b)).This means that each annular layer of unitary thickness with inner radiusr is characterized by its own prompt neutron lifetime ΛR(r). Then, the contribution given by prompt neutrons with lifetime ΛR and longer into the reactivity gain may be considered as a certain generalized parameter of such a thick neutron reflector. This parameter defines capability of the reflector to generate prompt neutrons with different delay and can be calculated by using the following formulas:
(11)ρR(ΛR,Λmax⁡)≡∫rroutdρR(r′)dr′·dr′=∫ΛRΛmax⁡dρRdΛR′·dΛR′.
The contributions given by the neutron reflectors of different thickness into the reactivity gain as functions of neutron delay time in the reflector as long as ΛR and longer are presented in Figure 3. If the reflector is made of 208Pb, then the contributions of neutrons with lifetimes of 1 msec and longer into the reactivity gain can reach several dollars. For comparison, analogous dependency is shown in Figure 3 for the neutron reflector made of natural lead. In this case, the same reactivity effect caused by the reflector thickening and, as a consequence, by longer neutron lifetime remains insignificant even in the reflector with 2 m thickness.Figure 3
Radial distribution of the contribution given by neutrons of the reflector with lifetimes as long asΛR and longer into the reactivity gain ρR(ΛR,Λmax⁡). The reflector is made of 208Pb or natural lead, thickness—from 2 m to 6 m.Component of the reactivity gain—the second summand of the inverse-hour equation (9)—may be regarded as a useful characteristic parameter of the neutron reflector-converter:
(12)ρR*≡∫rinroutdρR(r′)/dr′1+T/ΛR(r′)·dr′.
One else informative function is an integrand in formula (12), whose radial distribution is shown in Figure 4.Figure 4
Differential contribution into the reactivity jump required to provide the power excursion with asymptotic time periodT (integrand of formula (12)).To analyze the contributions of neutrons with various lifetimes in the reflector into the reactivity gain, it may be helpful to transform integration over radial coordinate into integration on neutron lifetime in the reflectorΛR:
(13)∫rinroutdρR(r′)/dr′1+T/ΛR(r′)·dr′=∫Λmin⁡Λmax⁡dρR/dΛR′1+T/ΛR′·dΛR′;dρRdr=dρRdΛR·dΛRdr.
In this case, the inverse-hour equation may be re-written as follows:
(14)ρ=Λ-CT+∫Λmin⁡Λmax⁡ΛR′·(dρR/dΛR′)ΛR′+T·dΛR′+∑i=16βi1+λi·T.
It is interesting to note that the second and third summands in the inverse-hour equation have similar structures. Taking into account the fact that lifetime ΛR for major fraction of neutrons of the reflector is well below 0.1 s, we can remove this value from denominator of the second summand in the inverse-hour equation (14) for the asymptotic time periods longer than 0.1 s. As a result, the second summand becomes substantially simpler:
(15)∫Λmin⁡Λmax⁡ΛR′·(dρR/dΛR′)ΛR′+T·dΛR′=1T∫Λmin⁡Λmax⁡ΛR′·dρR=1T∫rinroutΛR′·dρR(r′).
Prompt neutron lifetime in the reflector is used here as a weighing function for the integration. Small values of the weighing function naturally decrease the calculated integrals. Since the decay constants λi of delayed neutrons cover the range from ~0.01 to ~3 inverse seconds, the third summand in the inverse-hour equation (14) could not be simplified like the second summand.Component of the reactivity gain required to provide the power excursion with asymptotic time periodT, which is defined by neutrons of the reflector layers (from short-lived neutrons of the reflector layers adjacent to the reactor core and to relatively longer-lived neutrons in distant depth r, i.e., from Λmin⁡ to current ΛR), may be calculated as follows:
(16)ρR*(r)=∫rinrdρR(r′)/dr′1+T/ΛR(r′)·dr′=∫Λmin⁡ΛdρR/dΛR′1+T/ΛR′·dΛR′.
Radial and lifetime distributions of this component are presented in Figure 5.Component of the reactivity gain required to provide the power excursion with asymptotic time periodT, which is defined by neutrons of the reflector layers adjacent to the reactor core (from 0.5 m to r, or from Λmin⁡ to ΛR).
(a)
(b)As it follows from Figures4 and 5, neutrons in distant layers of the reflector, that is, neutrons with relatively long lifetime ΛR, give a dominant contribution into the reactivity gain.If the asymptotic period of the power excursion is comparable or longer than time constant of fuel rods, then thermal energy can receive a long enough time period for its partial removal from fuel rods by coolant. Therefore, the process of fuel heating up slows down, and an opportunity arises for feedbacks on coolant density and temperature to actuate. Otherwise, if asymptotic period of the power excursion is substantially shorter than time constant of fuel rods, then fuel can be overheated and melted down. As the severest consequence, reactor can lose its ability of working. As for typical time constants of fuel rods, in experimental fast breeder reactor EBR-II (USA) fuel rods had time constants about 0.11 s [16]. If 1-$ positive reactivity is inserted into the fast BREST-type reactor with 0.5 m thick neutron reflector made of natural lead, then asymptotic period of the power excursion is considerably shorter (0.014 s) than time constant of its fuel rods. At the same time, if even 2-$ positive reactivity is inserted into the fast BREST-type reactor with 6 m thick neutron reflector made of 208Pb, then asymptotic period of the power excursion becomes considerably longer (0.1 s). That is why it is so important to develop fuel rods with quick heat transport to coolant. Then, reactor will be more stable and less vulnerable to the power excursions with short asymptotic periods caused by large reactivity jumps.


## 9. Conclusions

It is demonstrated that the use of radiogenic lead as a neutron reflector-converter makes it possible to slow down the chain fission reaction on prompt neutrons in the fast reactor and it can improve the nuclear safety of fast reactor.(1)
Multipoint model of neutron kinetics in nuclear reactors was applied to analyze time-dependent evolution of neutron population in fast reactor with physically thick neutron reflector made of weak neutron absorber (radiogenic lead with dominant content of208Pb).(2)
Multipoint model of neutron kinetics was applied to investigate a possibility for substantial elongation of prompt neutron lifetime with correct accounting for time of neutron staying in physically thick, weak neutron-absorbing reflector.(3)
The paper demonstrates how multipoint discrete model of neutron kinetics can be transformed into continuous model of neutron kinetics in the reactor core surrounded by the neutron reflector.(4)
Numerical analyses of neutron kinetics were carried out with application of multipoint and continuous models and demonstrated that physically thick and weakly neutron-absorbing reflector is able to prolong prompt neutron lifetime in the fast BREST-type reactor by several orders of magnitude (roughly, from 0.5μsec to 1 msec). This effect can be interpreted as an appearance of one else group of delayed neutrons that increases their effective fraction and, thus, improves the reactor safety.(5)
Advanced design of fuel rods with quick heat transport from fuel to coolant can remarkably enhance the reactor resistance against the power excursions with short asymptotic periods caused by large reactivity jumps.(6)
If the asymptotic period of the power excursion caused by positive reactivity jump is comparable with thermal constant of fuel rods, then heat would have a time to flow down from fuel to coolant, its density would decrease and it would be able to impact remarkably on the power excursion process (see AppendixD). This allows us to consider the question: what positive reactivity jumps are permissible for the coolant-induced reactivity feedback could actuate?



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