Fast computer codes for evaluating non-thermal velocity
distributions are needed in
order to carry out routine analysis of neutron signals in plasmas heated
by neutral-beam injection (NBI). By neglecting the magnetic field inhomogeneity along
a field
line, i.e. neglecting trapped-particle effects, calculations of
the velocity distribution
can be made relatively rapidly. In this paper, we investigate under which
circumstances such an approximation is justified. We solve the bounce-averaged
Fokker–Planck equation, which includes particle trapping,
by expressing the solution in
terms of a series of appropriate eigenfunctions of the pitch-angle scattering
operator. The eigenfunctions, eigenvalues and time-dependent
coefficient functions are
calculated numerically. We use the solution for calculating the effect
of particle
trapping on neutron production for beam-heated deuterium plasmas.