Reactor kinetics is represented by the time-dependent Boltzmann equation (4.2) associated to a set of equations expressing the balance of the delayed neutron precursors.

For our practical applications a diffusion theory approximation is usually sufficient. We obtain in this way(1)

The symbols are those of the diffusion equation (4.39) with m = number of delayed neutron groups,

Ci = concentration of delayed neutron precursors of group /,

A, = decay constant for delayed neutron precursors of group i, f3i = fraction of the total number of fission neutrons emitted as delayed neu­trons of group i,

p=’Zpu

і = I

X(E) = fission spectrum of prompt neutrons,

Xi(E) = spectrum of delayed neutrons of group і (often assumed to be the same for all groups),

v = neutron velocity corresponding to energy E.

This equation is suitable for computer calculations after discretizing the space, time and energy coordinates. Energy is discretized in groups, space in mesh points, and time in time steps (see § 12.12).