Generations Of Nonlinear Waves In Magnetized Plasmas And Their Applications To The Long-Term Unsolved Problems In Space Physics And Astrophysics

In this talk, I will briefly review two long-term unsolved problems in space physics. One of them is the velocity-shear instability. Velocity shear provides free energy to an unbounded system. One would expect the velocity-shear instability to increase with increasing shear speed. However, early theoretical and simulation studies in the 1980s indicated that the growth rate of the velocity-shear instability decreases with increasing shear speed, and the velocity shear becomes stable when the surface-wave speed becomes supersonic observed in the ambient plasma rest frame. These early studies also suggested that the most unstable eigenmode will become the dominant wave in the velocity shear layer. These theoretical solutions are inconsistent with the observed vortices in an unbounded neutral fluid. Another long-term unsolved problem to be discussed in this talk is the unique frequency gap on the observed dynamic spectra of the chorus waves, which have been reported since the 1970s. The frequency gap is always at one-half of the electron gyro frequency at the magnetic equator of the magnetic field line, where the chorus waves are observed. Possible Landau damping processes have been proposed to explain the missing waves at the given frequency band. However, it is well-known that the Landau damping should depend on the wave speed, wave amplitude, and the plasma distribution function in the phase space, but not the wave frequency. In this talk, we shall briefly summarize how we solve these controversial issues. We found that localized disturbances and anisotropic expansions of the wave energy in a magnetized plasma are responsible for the observed nonlinear waves. We shall also discuss applications of these nonlinear waves to other unsolved problems in astrophysics and solar physics.