Fast neutron multiplication factor

The fast neutron multiplication coefficient μ is an indicator that takes into account the effect of fission of ²³⁸ U nuclei by fast neutrons on the course of a chain reaction in a thermal neutron reactor .

Content

1 Fast neutron propagation
- 1.1 Homogeneous environment
- 1.2 Heterogeneous environment
2 See also
3 Literature

Fast neutron

In thermal neutron reactors with nuclear fuel from slightly enriched uranium (<5%), the concentration of ²³⁸ U is many times higher than the concentration of ²³⁵ U. Fission of ²³⁵ U nuclei by fast neutrons is very small, and they are usually not taken into account. However, the number of fission of ²³⁸ U nuclei by neutrons with an energy E _n > 1.0 MeV can be significant, and they have a noticeable effect on the course of the chain reaction.

Homogeneous environment

In a homogeneous core, ²³⁸ U nuclei are surrounded by a large number of moderator nuclei. Penetrating neutrons through the environment, they are more likely to experience collisions with light nuclei and slow down to energies below the fission threshold of ²³⁸ U. As a result, the fast neutron multiplication coefficient in homogeneous reactors differs little from unity.

Heterogeneous environment

In a heterogeneous reactor, fast neutrons move first in fuel rods among ²³⁸ U nuclei. Therefore, the probability of collision with the ²³⁸ U nucleus and its fission in a heterogeneous reactor is much greater than in a homogeneous reactor. It depends on the path of a fast neutron in nuclear fuel, that is, on the size of the fuel elements, the concentration of ²³⁸ U, and also on the lattice pitch a . In a thick fuel rod, a fast neutron travels a greater path than in a thin one, which means that the multiplication coefficient for fast neutrons in the first case is greater than in the second. If the lattice pitch a far exceeds the scattering length of the fast neutron in the moderator $\lambda _{S}$ ${\ displaystyle \ lambda _ {S}}$ $\lambda _{S}$ , then most fast neutrons fall into another fuel rod, slowing down to energies E _n <1.0 MeV. Therefore, the coefficient μ for gratings with a step $a\gg \lambda _{S}$ ${\ displaystyle a \ gg \ lambda _ {S}}$ $a\gg \lambda _{S}$ determined only by the size and composition of the fuel rod. For example, for rods of natural uranium with a radius of R cm

μ ≈ 1 + 1.75⋅10 ⁻² R.

In water-cooled reactors, fuel elements form a tight lattice ( $a\ll \lambda _{S}$ ${\ displaystyle a \ ll \ lambda _ {S}}$ $a\ll \lambda _{S}$ ) Such an arrangement of fuel elements reduces the absorption of thermal neutrons in water. In cramped lattices, fission neutrons manage to pass several fuel rods until they slow down below the threshold fission energy of ²³⁸ U. The fastest neutron multiplication coefficient in VVER is highest. For the ratio of hydrogen nuclei and ²³⁸ U N _H / N ₈ > 3, the fast neutron multiplication coefficient is calculated by the approximate formula:

μ ≈ 1 + 0.22 ( N ₈ / N _H ).

We calculate the multiplication factor for fast neutrons:

For a uranium-graphite lattice with a = 14 cm and a rod diameter of natural uranium 3 cm. The scattering length in graphite is λ _S = 2.5 cm. Therefore, the pitch of the uranium-graphite lattice $a\gg \lambda _{S}$ ${\ displaystyle a \ gg \ lambda _ {S}}$ . Hence, $\mu =1+1,75\cdot 10^{-2}\cdot 1,5\approx 1,026.$ ${\ displaystyle \ mu = 1 + 1.75 \ cdot 10 ^ {- 2} \ cdot 1.5 \ approx 1,026.}$
for VVER with N _H / N ₈ = 5. Coefficient μ for VVER is σ = 1 + 0.22 · 0.2 = 1.044.

Literature

Klimov A.N. Nuclear physics and nuclear reactors. M. Atomizdat , 1971.
Levin V.E. Nuclear physics and nuclear reactors. 4th ed. - M .: Atomizdat , 1979.
Petunin V.P. Thermal energy of nuclear installations M .: Atomizdat , 1960.