Diocotron instability of a warm electron beam in crossed fields

The warm-fluid equation derived from the drift kinetic equation is solved numerically to investigate the electrostatic low-frequency stability of an electron ribbon beam drifting in the crossed-fields of a planar magnetron. The temperature effect is manifested only for oblique propagation with respect to the drifting beam direction. The dispersion relation takes the form ω = ω(k/ks) = ω(ks/k), where k and k are respectively the components of the surface wave vector k parallel and perpendicular to the magnetic field. The obliqueness of the propagation direction and the non-zero temperature give rise to a resonant instability, in addition to the diocotron instability, and the wavenumber corresponding to the maximum diocotron growth rate shifts as the temperature changes.