  Electron beams in two-dimensional systems can provide a useful tool to study
energy-momentum relaxation of electrons and to generate microwave radiation
stemming from plasma-beam instabilities. Naturally, these two applications
cannot coexist: if beam electrons do relax, the beam is stabilized; if
instability exists, it strongly distorts the distribution function of beam
electrons. In this paper, we study the competition of beam relaxation due to
electron-electron (e-e) collisions and development of plasma beam instability
in graphene. We find that unstable plasma mode associated with a beam is
stabilized already by weak e-e collisions. At intermediate e-e collision
frequency, the instability re-appears at the ordinary graphene plasmon mode.
Such instability is interpreted as viscous transfer of momentum from beam to 2d
plasmons. Its growth rate reaches its maximum at hydrodynamic-to-ballistic
crossover, when plasmon wavelength and electron mean free path are of the same
order of magnitude.
