An analytic model for the dynamics of fast ignition is developed for t
he case in which the particle beam heats the fuel by generating a supe
rsonic heat wave. It shows that the beam energy and intensity required
for ignition increase with the particle range R. These results, toget
her with previous ones for the subsonic regime of heating, allow for t
he determination of an optimum particle range value (R approximate to
0.25 g/cm(2)). By decreasing the range below this value the ignition e
nergy no longer decreases. (C) 1998 American Institute of Physics. [S1
070-664X(98)04512-1].