Reflection and trapping of Alfvén waves in the open field lines of a neutron star

We have studied Alfvén wave propagation in the polar cap region of a neutron star at isothermal atmosphere using linear MHD equations. The study demonstrates reflection and trapping of the wave from the steep gradient region of Alfvén speed. The trapping efficiency depends sensitively on a dimensionless parameter $\beta_{g}$ which is proportional to the mass and inversely proportional to thetemperature of the plasma. A scaling of radius, Schwarzchild radius and acceleration due to gravity of neutron stars of different masses are performed. The effective temperature of hydrostatic equilibrium is also scaled. For a neutron star with mass 1.4 solar mass and radius 10 km the temperature is to be of $10^8$ degree K. The Alfvén wave propagation near the event horizon is investigated. It is found that the wave length of Alfvén wave is shorter near the horizon while it becomes longer away from it. Pulsar wind acceleration by Alfvén wave is also examined. It is found that wave pressure force is predominant for low temperature but for higher temperature, thermal pressure is the main driving force.