## 4. Calculation of the absorption coefficientTo study the resonant absorption of magnetosonic waves, we derive an expression for the absorption coefficient from the amplitudes of the incident and the reflected wave at . The absorption coefficient is defined as where and are the components of the energy flux densities of the incident and the reflected wave respectively. and can be expressed in terms of the components of the group velocities and the total wave energy densities as After some algebra (ade, Csík, Erdelyi & Goossens, 1997) the expression (24) for the absorption coefficient reduces to where and are amplitudes of total pressure perturbation induced by incident and reflected waves respectively. The terms 'incident wave' and 'reflected wave' are determined by the sign of the component of the group velocity in the sense that the incident waves have while the reflected waves have . According to inequalities (17), the sign of the The amplitudes of the Eulerian perturbation of total pressure and for the incident and the reflected wave are Finally, applying the boundary conditions of continuity of The absorption coefficient (26) is now completely determined by relations (27) and (28) for an incident wave of given frequency and propagation angles and . © European Southern Observatory (ESO) 1998 Online publication: September 30, 1998 |