Direct computation of the growth rate for the instability of a warm relativistic electron beam in a cold magnetized plasma

The fully kinetic, fully electromagnetic dispersion equation for a warm relativistic electron beam in a cold magnetized plasma is numerically solved with no simplifying assumptions made. For magnetic fields of various strengths, the growth rate maps for the beam-plasma instability are plotted and dominant modes are identified. The exact solution is compared with available approximate solutions. The latter are shown to misinterpret the effect of the magnetic field on the instability of oblique waves.