Plasma Oscillations Perpendicular to a Weak Magnetic Field

The propagation of electrostatic waves perpendicular to a uniform magnetic field, the so‐called Bernstein modes, are discussed. It is shown, in the limit as the strength of the magnetic field approaches zero, that these modes, which themselves are undamped, collectively act so as to form a single damped mode identical to the usual Landau damped mode appropriate to zero magnetic field. The behavior of the plasma for small but finite magnetic field is also considered. It is shown that damping due to phase mixing exists for a time short compared to ωc−1, the reciprocal of the cyclotron frequency. In times long compared to this, the plasma exhibits a quasi‐periodic behavior with period 2π/ωc.