Langmuir wave generation through a neutrino beam instability

A standard version of a kinetic instability for the generation of Langmuir waves by a beam of electrons is adapted to describe the analogous instability due to a beam of neutrinos. The interaction between a Langmuir wave and a neutrino is treated in the one-loop approximation to lowest order in an expansion in 1/M-W(2) in the standard electroweak model. It is shown that this kinetic instability is far too weak to occur in a suggested application to the reheating of the plasma behind a stalled shock in a Type II supernova. This theory is also used to test the validity of a previous analysis of a reactive neutrino beam instability, and various shortcomings of this theory are noted. In particular, relativistic plasma effects have a significant effect on the calculated growth rates, and any theoretical description of neutrino-plasma interactions must be based directly on the electroweak theory. The basic scalings discussed in this paper suggest that a more complete investigation of neutrino-plasma process should be undertaken to look for an efficient process capable of driving the stalled shock of a Type II supernova.