Nuclear Criticality Calculations with Monte Carlo

Abstract

In order to address multiplying assemblies we must include fission events. The time-dependent, homogeneous transport equation (eqn 3.11) can be expressed in operator notation by

$$ \frac{{\partial \Psi }} {{\partial t}} = L\Psi $$

(8.1)

where Ψ(r,Θ,E,t) is the neutron angular density of eqn 3.6 and

$$ L = - v\Omega \bullet \nabla - v\Sigma _t + v\smallint \Sigma ^* (r;\Omega ',E' \to \Omega ,E)d\Omega 'dE' $$

(8.2)

Here Σ^* is the total cross section for neutron transfer from Ω’,E’ to Ω,E, including fission events. Eqn 8.1 has solutions of the form

$$ L = - v\Omega \bullet \nabla - v\Sigma _t + v\smallint \Sigma ^* (r;\Omega ',E' \to \Omega ,E)d\Omega 'dE' $$

(8.3)

where αis an eigenvalue of eqn 8.1.