Collisionless Dissipative Nonlinear Alfven Waves: Nonlinear Steepening, Compressible Turbulence, and Particle Trapping

The magnetic energy of nonlinear Alfven waves in compressible plasmas may be ponderomotively coupled only to ion-acoustic quasi-modes which modulate the wave phase velocity and cause wave-front steepening. In the collisionless plasma with $\beta\not=0$, the dynamics of nonlinear Alfven wave is also affected by the resonant particle-wave interactions. Upon relatively rapid evolution (compared to the particle bounce time), the quasi-stationary wave structures, identical to the so called (Alfvenic) Rotational Discontinuities, form, the emergence and dynamics of which has not been previously understood. Collisionless (Landau) dissipation of nonlinear Alfven waves is also a plausible and natural mechanism of the solar wind heating. Considering a strong, compressible, Alfvenic turbulence as an ensemble of randomly interacting Alfvenic discontinuities and nonlinear waves, it is shown that there exist two distinct phases of turbulence. What phase realizes depends on whether this collisionless damping is strong enough to provide adequate energy sink at all scales and, thus, to support a steady-state cascade of the wave energy. In long-time asymptotics, however, the particle distribution function is affected by the wave magnetic fields. In this regime of nonlinear Landau damping, resonant particles are trapped in the quasi-stationary Alfvenic discontinuities, giving rise to a formation of a plateau on the distribution function and quenching collisionless damping. Using the virial theorem for trapped particles, it is analytically demonstrated that their effect on the nonlinear dynamics of such discontinuities is non-trivial and forces a significant departure of the theory from the conventional paradigm.