  Efficiency of collective beam-plasma interaction strongly depends on the
growth rates of dominant instabilities excited in the system. Nevertheless,
exact calculations of the full unstable spectrum in the framework of
relativistic kinetic theory for arbitrary magnetic fields and particle
distributions were unknown until now. In this paper we give an example of such
a calculation answering the question whether the finite thermal spreads of
plasma electrons are able to suppress the fastest growing modes in the
beam-plasma system. It is shown that nonrelativistic temperatures of Maxwellian
plasmas can stabilize only the oblique instabilities of relativistic beam. On
the contrary, non-Maxwellian tails typically found in laboratory beam-plasma
experiments are able to substantially reduce the growth rate of the dominant
longitudinal modes affecting the efficiency of turbulent plasma heating.
