  This paper extends the semianalytical treatment of fast ion current density
to take into account time dependence and velocity diffusion using solutions of
Boltzmann equation with a complete Coulomb collision term (Goncharov et al.
2010 Phys. Plasmas 17 112313). An arbitrary angle distribution of the fast ion
source is assumed. The results are applicable to multi-ion-species plasma.
Since analytical results provide an extra physical insight and constitute a
reliable basis for verification of numerical codes, it is desirable to obtain
exact solutions where possible. New results clarify the discrepancies between
analytical formulae in earlier bibliography and improve the physical basis of
neutral beam injection current drive.
