Nonlinear Alfvén Wave Propagating In MHD Plasmas

The nonlinear evolution equations of Alfvén wave and fast’slow magneto-acoustic waves propagating in magnetized plasmas with isotropic resistive and viscous dissi-pation mechanism are presented analytically. The LCPFCT algorithm is extended to a multidimensional case using direct time integration method, and then employed to solve governing MHD equations and investigate nonlinear Alfvén waves propagating in plasmas with different boundary conditions numerically.Firstly, the behavior of nonlinear Alfvén waves propagating in one-dimensional ideal plasmas is studied. It is found that in a weakly nonlinear system, an Alfvén wave train can excite two longitudinal disturbances, namely an acoustic wave and a pon-deromotively driven disturbance, which behave differently for high/low β(the ratio of plasma-to-magnetic pressures). For periodic boundary condition, weakly nonlinear Alfvén waves excite longitudinal disturbances with periodically changing amplitudes, and the changing rate is related with β.The nonlinear effects can be enhanced by increasing the driven Alfvén wave am-plitude. In a strongly nonlinear system, the Alfvén wave train is modulated and can steepen to form shocks, leading to significant dissipation due to appearance of current sheets at magnetic-pressure minima. For periodic boundary condition, we find that the Alfv en wave transfers its energy to the plasma and heats it by doing work via Lorentz force during the shock formation. Besides, the strong nonlinear effects can be gener-ated through resonance between Alfvén and acoustic waves. When Alfvén speed equals acoustic speed, the Alfvén wave train transfers its energy to the longitudinal disturbance continuously, leading to form shocks finally. For periodic boundary condition, we find that the Alfv en wave heats the plasma by resonance heating initially and shock heating later.The addition of resistive/viscous effects naturally leads to resistive/viscous damp-ing and thus to resistive/viscous heating. It is found that in a weakly nonlinear system, the damping efficiency of the Alfvén wave train depends on dissipation coefficients and frequency of the Alfvén wave, as well as the background magnetic field and plasma den-sity. The behavior of the Alfvén wave train propagating in resistive plasmas is similar to that in viscous plasmas, while the behavior of the longitudinal disturbances is differ-ent from each other, and related with β. In strong dissipative plasmas, we find that the first pulse of the Alfvén wave train damps more slowly, and gradually transforms to a Gaussian shaped damping soliton. The influence of a steady flow U0 along the back-ground magnetic field is considered. It is found that the damping efficiency is reduced when direction of U0 is consistent with that of the Alfvén wave train, and vice versa.In two-dimensional systems, the behavior of nonlinear Alfvén waves propagating in inhomogeneous plasmas is studied, and fast magneto-acoustic wave generation due to Alfvén wave phase mixing is considered. For periodic boundary condition, we find that the amplitude of the fast magneto-acoustic waves grows linearly with time dur-ing the initial stages in ideal plasmas, and they soon saturate at driven wave amplitude squared levels. The process depends on the amplitude and frequency of the Alfvén waves, as well as their speed gradients and the pressure of the background plasma. It is also found that the resistive/viscous damping efficiency of the Alfvén wave train is significantly enhanced by Alfvén wave phase mixing in non-ideal plasmas, and Gaus-sian shaped damping soliton arises as in one-dimensional systems. The plasma heating is composed of two processes:resistive/viscous heating in boundary region with high plasma density, and phase mixing enhanced resistive/viscous heating, the latter of which is dominated. By comparison with the case caused by velocity inhomogeneity, we find that the damping efficiency of the Alfvén wave train is different due to the background plasma density, even though the velocity of the Alfvén wave train remains the same.Lastly, the effects of a steady flow, a stratified plasma density, and a diverging magnetic field to the efficiency of Alfvén wave phase mixing are considered respec-tively. It is found that the influence of a steady flow along the background magnetic field is similar to that in one-dimensional systems, but it affects not only the viscous-resistive damping but also the phase mixing damping. It is also shown that the decrease in density lengthens the oscillation wavelengths and thereby diminishes the efficiency of phase mixing, whereas a diverging magnetic field enhances the mechanism.