Stability of a Steady, Large Amplitude Whistler Wave

The behavior of weak electrostatic waves in a collisionless magnetoplasma supporting a steady large amplitude whistler wave has been studied. All waves are assumed to propagate parallel to a uniform backgound magnetic field $B_0$ . In the presence of the whistler wave fields each particle executes an oscillatory motion parallel to $B_0$ , in addition to a translation along $B_0$ and transverse motions. This oscillation causes the Landau resonance to be replaced by a series of new resonances between particles and the electrostatic modes. A distribution function for the perturbed plasma is constructed by solving the Vlasov equation, linearized in the electrostatic wave amplitudes. A dispersion relation is obtained and solved approximately for the growth/damping rate of the perturbations. Growing electrostatic modes are found to be approximately uncoupled. Trapped particles have a strong influence on the stability of the system.