Stabilities of Periodic Waves in a Cold Collision-Free Plasma in a Magnetic Field

Abstract

The existence of periodic waves propagating at an arbitrary angle to the magnetic field in a plasma is demonstrated by Stokes expansions in amplitude. Stability analysis is then made for such periodic waves with respect to side-band frequency disturbances. It is shown that waves of slow mode are unstable whereas waves of fast mode are stable if the frequency is below the cutoff frequency. The cutoff frequency depends on the propagation angle. For longitudinal propagation, the cutoff frequency is equal to one-fourth of the gyrofrequency of the electron. For transverse propagation, the cutoff frequency is so high that waves of all frequencies are stable.