A relativistic electron beam in the presence of a whistler wave excites a negative‐energy beam space charge mode and a high frequency laser radiation (&ohgr;1≫&ohgr;c). The instability is explosive for a copropagating beam and the whistler pump, resulting in the excitation of an intense laser in a short pulse. The explosion time &tgr;={(4/kv0)[(&ohgr;1−k1vb−&ohgr;c) &ggr;0&ohgr;1/(&ohgr;1−k1vb)&ohgr;’pb]1/2}. For both the counterpropagating beam and the whistler wave, the instability is nonexplosive. The laser frequency in this case is somewhat larger, whereas the exponentiation time is comparable to the explosion time of the earlier case.