**2.1 Background of the development of new technologies**

The recent decades have radically changed the opinion of scientists about laws linking the probability of an accident and its consequences and about ways to prevent technological disasters and, in particular, ways to ensure the safety of nuclear power facilities. This is based on the following objective factors:


## **2.2 The history of the issue**

After the Three Mile Island accident (1979), the work to eliminate severe accidents at NPPs was intensified in the USA and Europe. By the mid-1980s, concepts were proposed for the PIUS light-water reactor (ASEA-Atom, Sweden), high-temperature reactors KWU/Interction (Germany), GCRA (USA), DYONISOS (Switzerland), and MSGR liquid-salt reactor (China). The aim of the development was to eliminate the destruction of the core in severe accidents.

Among the technologically developed reactors, liquid metal-cooled fast reactors proved to be the most attractive, as far as possible to avoid severe accidents. In the early 1980s, in the USA research began on theoretical and experimental modeling of

#### *Accident Tolerant Materials for LMFR DOI: http://dx.doi.org/10.5772/intechopen.90703*

accident transients without scram (ATWS). By early April 1986 (a few days before the accident at Chernobyl NPP in the USSR), the work on experimental modeling of ATWS regimes at the EBR-II reactor (Argonne National Laboratory, Idaho, USA) was largely completed, demonstrating high capabilities in ensuring self-protection of lowpower reactors with sodium cooling. The results of these unique studies are published in [5–10]. Zirconium-doped metal fuel has been proposed as a possible accidenttolerant fuel for fast sodium reactors in the USA [11]. It is a high-density and heatconducting fuel. By the early 1990s, projects of modular sodium-cooled fast reactors PRISM and SAFR with such fuel were considered as promising in the USA [11, 12].

After the accident at the Chernobyl NPP (1986), Soviet scientists began to solve the problem of excluding severe accidents at reactors. It was clear that experimental modeling was limited in relation to the problem of safe reactors. First of all, this applies to the full-scale modeling of the ATWS. Such experiments are expensive and difficult to perform. They pose a potential danger to the public and the environment.

Sodium is characterized by high chemical activity. Its use requires an intermediate circulation circuit. Reactor used a three-circuit cooling systems. The melting point of metal fuel doped with zirconium is relatively low. Russia went on the way of the development of the heavy coolant (lead), much less active chemically, and more heat-resistant mixed mononitride fuel (MN). MN fuel is a reasonable compromise between heat-resistant mixed oxide (MOX) and high-density and heatconducting metal fuel (including zirconium doped).

By 1989, the Soviet Union had developed a conceptual design of the leadcooled BRS-1000 power fast reactor fueled by MN. By 1993, another conceptual design of the BRS-300 pilot reactor was proposed. It was the predecessor of the BREST-OD-300 project (JCS "NIKIET," Moscow, Russia), which has been developing to date [13–15]. The BREST uses a two-circuit cooling systems.

## **2.3 Specific hazards of fast reactors**

In addition to the general hazard factors, fast reactors are organically characterized by reactivity accidents (the reactor is prompt supercritical) and the possibility of implementing a positive void reactivity effect (VRE) when using a liquid metal coolant. VRE is realized when the core or part of it is drained. Consider these two factors.

### *2.3.1 Risk of reactivity accidents*

When entering reactivity ρ > β (β is the effective delayed neutron fraction), the reactor is prompt supercritical. The change in reactor power or neutron density *n* over time *t* can be estimated using the point kinetics equation: *dt* ≈ \_

$$\frac{dn}{dt} \approx \frac{(\rho - \beta)nk}{l},\tag{1}$$

where *k* is the effective multiplication factor, *l* is the average lifetime of prompt neutrons, *l* = *l∞P*, *l∞* is the average lifetime of prompt neutrons in an infinite medium, and *P* is the non- leakage probability.

Average lifetime of prompt neutrons in an infinite medium

$$\Lambda\_{\omega\alpha} = \text{Im } \omega \text{ платашалдае плечанани}$$

$$\Lambda\_{\omega\alpha} = \frac{\Lambda\_{\omega}}{\upsilon} = \frac{1}{\upsilon\sum\_{d}},\tag{2}$$

where <sup>Λ</sup>*a* is the average path length of a neutron until absorption.

In a fast reactor, the average neutron velocity *v* is several orders of magnitude higher than in a thermal reactors, although the macroscopic absorption cross section Σ*a* is two orders of magnitude lower. As a result, in fast reactors *l* ~ 10<sup>−</sup><sup>7</sup> –10<sup>−</sup><sup>5</sup> s, in thermal reactors *l* ~ 10<sup>−</sup><sup>3</sup> s, other things being equal (ρ, β), the *dn*/*dt* in fast neutron reactors is higher, i.e., the power or density of neutrons increases faster. Obviously, the use of a coolant with a small absorption cross section also contributes to the self-protection of a fast reactor from reactivity accidents. In this case, the advantages of thorium lead (208Pb) are obvious.

Another feature of fast reactors is the presence of 239Pu in the fuel as the main fissile nuclide. The effective delayed neutron fraction for 235U is equal 0.68%. The effective delayed neutron fraction for 239Pu is equal 0.217%. As a result, when the same reactivity is introduced, the difference (ρ – β) is greater in a reactor using 239Pu as a fissile nuclide (compared to 235U). In fast reactors, the fission of fertile nuclides (heavy nuclei with an even number of neutrons) plays an important role. Depending on the fission cross section of such nuclei (238U, 232Th) on the kinetic energy of the neutron that caused the fission, there is a threshold at *E* ≈ 1.4 MeV. In the spectrum of the thermal reactors, the contribution of the fission of fertile nuclides to the effective neutron multiplication coefficient is small: 5–7%. In fast reactors, 1/4–1/3 of the fertile nuclides are fissioned. The value of β for 238U is 1.61%, for 232Th is 2.28%. When used in a fast reactor mixed U-Pu-fuel containing dump uranium and plutonium with a high concentration of 239Pu, the effective fraction of delayed neutrons will be significantly higher than when fission isotopepure 239Pu: about 0.36–0.38%, and when using 232Th—even higher.

A certain role is played by fast neutron fission of some nuclei from among the minor actinides, for example, long-lived radioactive waste with an even number of neutrons: 237Np and 241Am, contained in small quantities (up to 5%) in the fuel of new-generation fast reactors to recycle this waste and protect the fuel cycle from proliferation. The value of β for 241Am is 0.16%. The fission threshold of these nuclei is slightly more than 1 MeV. In the fast reactor spectrum, up to 1/3 americium nuclei can fission, which leads to a decrease in the average value of β and an increase in the potential danger of reactivity accidents. From the standpoint of the deterministic approach to exclude this assident, it is necessary to prevent the input of reactivity (ρ > β). To do this, it is necessary to limit (minimize) the reactivity reserves and, first of all, the fuel burnup reactivity reserve (Δρ*b*). For a homogeneous core, the conditions breeding ratio in core BRC = 1 and Δρ*b* = 0 are equivalent. In practical cases, the total reactivity margin can be limited to β.

### *2.3.2 The problem of positive void reactivity effect*

The VRE is characterized by a strong spatial dependence. The most dangerous is the drainage of the central part of the core [4, 16]. In this case, the neutron leakage from the core is small, and, as a rule, the VRE is maximum. Draining the reflector leads to an increase in neutron leakage from the core, with the VRE < 0. During the transition to high-power reactors, the volume of the core increases, and the leakage of neutrons from it decreases, which leads to an increase in VRE. In high-power reactors with a traditional core layout, the local VRE, which is realized when its central part is drained, is positive and, as a rule, several times higher than the effective fraction of delayed neutrons.

There are several components of VRE associated with spectrum changes and neutron leakage, reduction of parasitic absorption, and changes in self-shielding factors [4]. The spectral component of the VRE and the leakage component are maximal in absolute value and opposite in sign. They are mainly and determine the VRE. From the point of view of VRE minimization, a coolant based on doublemagic nuclei (e.g., lead-208), fuel and structural materials with a high neutron capture cross section are of interest.
