Abstract
The combined effect of modulational instability and nonlinear Landau damping on a circularly polarized MHD wave is studied. When the wave gets modulated, the magnetic mirror force as well as the parallel electric field associated with the modulations, transfer energy to the charged particles with velocity near the Alfvén velocity, to cause a nonlinear Landau damping. Our mathematical model is a DNLS equation extended with a nonlocal term representing the resonant particles. This irreversible model allows a conservation law which in a slowly varying wave train limit corresponds to conservation of wave action. In addition to the modulational instability already known from the DNLS model, the Landau damping term introduces a modulational instability in the wave number range where the wave would otherwise be stable. We present numerical studies of the development of the instabilities and the subsequent wave damping in both ranges. One of our principal findings is that the wave frequency decreases in the same proportion as the energy density. This can be understood in terms of the conservation of action law.
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