Introduction

This chapter explains how Monte Carlo techniques can be used to calculate the multiplication factor K. The theories and the resulting algorithms, described in this chapter, are the basic building blocks of the later chapters, in which we investigate Monte Carlo eigenvalue perturbation methods. The multiplication factor can be defined in various ways, such as: the dominant eigenvalue of the neutron transport equation, the quantity by which $\bar{\nu}$ (the average number of neutrons per fission) must be divided to keep a non-critical system exactly critical, and the ratio between the number of neutrons in successive generations. A generation can be defined as the life of a neutron from birth by fission to death by leakage or absorption (both capture and fission). For critical systems K = 1, for subcritical systems K < 1, and for supercritical systems K > 1.

This chapter consists of four more sections. In the second section we give a mathematical basis for eigenvalue calculations. The third section describes how this mathematical basis can be transformed into Monte Carlo algorithms for the eigenvalue calculation. In the fourth section, we describe various numerical results. We conclude in the fifth section with some numerical experiments to investigate the effect of two variations of the fission matrix algorithm.