Alfven wave collapse and the stability of a relativistic electron beam in a magnetized astrophysical plasma

The generation of Alfven waves by magnetic field-aligned electron streams, and the evolution of such streams under the action of the self-generated waves, remains an important question in theoretical radio astronomy. In this paper a simple derivation is presented of a time scale on which a nonlinear Alfven wave packet collapses. This time scale is compared with the linear growth and quasi-linear relaxation time scales for conditions appropriate to an extragalactic radio source. The nonlinear time scale can be comparable to the linear and quasi-linear time scales, which suggests that nonlinear effects may stabilize this instability and permit the propagation of anisotropic electron streams.