PHYS 515: Plasma Physics & MHD Grade Assignments for 11/28/00 Note: This is the final set of grade assignments. They are due on Thursday December 7th. You can put them in my mailbox, or hand them in in class. 1. Alfven Waves: Consider shear (compressionless) Alfven waves in an inviscid and ideally conducting plasma without gravity and permeated by a constant magnetic field. In class and in the handouts the derivation of these waves is done in a first order perturbation analysis, with second and higher order terms ignored. Now show that for shear Alfven waves all but one of the nonlinear terms vanish. Show that the remaining term amounts to a Lorentz force parallel to the zero'th order magnetic field, and calculate its time average over one cycle for a simple propagating Alfven wave 2. Consider an isothermal plane parallel atmosphere with constant gravity g in the minus z direction. There is no magnetic field and viscosity can be ignored. Solve for the zero'th order pressure and density distribution. Find sound wave-like first order perturbation solutions in the z direction (k_x = k_y = 0). Note that in deriving these solutions one cannot simply assume that all first order variables have a z dependence that goes like exp(i*k_z*z). Find the z dependence that does work. What is the cut-off frequency for the resulting acoustic waves? What does that mean physically?