  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.
