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 (SN). 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, it is noted that relativistic plasma effects have a significant effect on the calculated growth rates, and that 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 processes should be undertaken to look for an efficient process capable of driving the stalled shock of a type II SN.