Compression Waves in a Plasma in a Static Magnetic Field

The propagation of small amplitude compression waves through a plasma in a static magnetic field is discussed In contrast to the usual treatment of this type of problem we shall not treat the ions as a fixed neutralizing back-ground but shall include them in the dynamics of the problem The problem is discussed in the general case in which the thermal velocity distribution is not negligible The method of solution is to use the linearized Boltzmann equation in conjunction with Maxwell's equations to obtain a distribution function and dispersion relation To obtain the dispersion relation an approximation method is used and it is shown that over the greater part of the frequency range the oscillations are of a characteristic wave number We show that the inclusion of the ions in the dynamics is justified by the fact that at integral multiples of the ion gyrotrequency the ions play the dominant role. The results obtained show that the waves are undamped The graph of the distribution function for particles with large velocities shows a fine structure which indicates that at these velocities collisions become important, especially for particles moving perpendicular to the field and direction of propagation