Nonlinear Alfven wave propagation in the solar wind

We derive a self-consistent set of equations that describe the propagation of nonlinear shear Alfven waves in the solar wind. The equations include the interaction between the waves and wind plasmas and has an exact energy conservation law. Using a truncated Fourier series, we further reduce the system to a simplifed nonlinear model with multiple waves. We solve the model numerically in a radially expanding box with a finite angular size. We find that for linear waves in a time-varying plasma background, the conditions for the WKB approximation are violated in practically the entire radial domain (even at high frequencies), although the scaling of wave amplitudes (delta B) with radial distance and the equipartition between the magnetic and kinetic energy are similar to the WKB results. For nonlinear waves, equipartition still holds, but nonlinear wave reflection enhances the backward propagating waves (in the rest frame of the wind), which leads to a faster drop in delta B than the linear waves. As a result, there is a ''soft'' saturation in which delta B approaches the background magnetic field gradually at large distance. The simplified nonlinear model produces reasonably high wind speed (between 600 and 700 km s(-1)).