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

Exact kinetic theory for the instability of an electron beam in a hot magnetized plasma