Magnetosonic waves: hydrodynamics vs. kinetics

Summary form only given. Magnetosonic waves play an important role in the collisionless shock life. The shock front itself forms due to the magnetosonic wave steepening. Most of the turbulent energy in the shock front is in the low frequency waves, i.e. magnetosonic and Alfven waves and whistlers. Hydrodynamical description of magnetosonic waves works well when /spl beta/=8/spl pi/nT/B/sup 2//spl Lt/1, but produces incorrect results in the high /spl beta/ cases. In particular, the dispersion of the oblique magnetosonic wave in low /spl beta/ plasma is determined by the ion inertial length c//spl omega//sub pi/ and is positive. In the high /spl beta/ plasma the dispersion of the quasiperpendicular magnetosonic wave is determined by the ion gyroradius /spl rho//sub i/=v/sub T///spl Omega//sub i/, and is negative. Wave observations at high /spl beta/ shocks confirm the conclusion that kinetic approach is necessary to describe properly the magnetosonic wave features. Nonlinear wave equations for low-frequency waves, obtained from (semi)kinetic approach, also differ from those obtained from hydrodynamical equations. Although the main difference is in the strong dependence of the dispersive term on the plasma /spl beta/, the nonlinear interaction also becomes significantly /spl beta/ dependent.