A Physical Model of Cyclotron Damping

A method for calculating the damping or growth rate of an electromagnetic wave of small amplitude propagating parallel to an external magnetic field in a fully ionized, collisionless plasma. Cyclotron damping or growth is shown to be governed by the energy exchange between the wave and those particles that feel the wave doppler-shifted in frequency to their own cyclotron frequency. The rate of change of energy of a representative particle is computed and averaged over the initial velocity distribution to yield the mean power gained/lost by the particles due to the onset of the wave. Equating the power gained by the resonant particles to the rate of decrease in the electromagnetic energy of the field and of the oscillation energy of the remaining particles in the plasma yields the conventional damping rate for the waves. Compared with the more formal procedure of solving the coupled Vlasov and Maxwell equations, this method yields insight into the physical processes involved, avoids mathematical complications, and gives the time it takes for the asymptotic values to become valid. This is roughly the time required for electrons with the thermal velocity to drift more than one wavelength.