On the trapping of Alfven waves in the polar region of a compact gravitating object

Alfven wave propagation in the polar region of compact gravitating objects is studied using linear magnetohydrodynamic equations. The temperature is considered as isothermal in several Schwarzschild radii. The study demonstrates reflection and trapping of the wave from the steep gradient region of Alfven speed. The trapping efficiency depends sensitively on a dimensionless parameter βg which is proportional to the mass and inversely proportional to the temperature of the plasma. The Alfven wave in the polar region of a compact gravitating object is found to be trapped by reflection due to plasma density and magnetic field variation with the height. The reflection occurs at the frequency less than some critical frequency determining the steepness of the Alfven speed gradient depending on the temperature. Particle acceleration by Alfven waves is also examined