Cosmic ray propagation and instabilities

The purpose of this dissertation is to extend the standard analysis of cosmic ray propagation. The standard model predicts that the combination of streaming cosmic rays in a background plasma results in the formation of Alfven waves which grow and scatter the cosmic rays until their average speed is close to the Alfven speed. What is done here is to consider the conditions under which the waves are not Alfven. The wave dispersion equation is first recalculated for wavelengths much longer than generally considered in the standard theory. Next the dispersion equation is found for physical conditions which produce a large growth rate. Two new results are found. One is a kink-mode instability which occurs if there is a net current in the wave frame which produces a helical perturbation in the background reference frame. On a scale size comparable to the twist scale length of the perturbed field the kink instability will develop. It is a purely growing instability with the smallest stable wavenumber given by: kV/sub H/ = epsilon Ωi where epsilon is the ratio of the cosmic ray number density to the number density of the electrons in the background gas and Ωi is the proton gyrofrequency. The second result is that for conditions which would result in a growth rate much larger than the wave frequency, as calculated by the results of the standard model, the wave phase velocity (and frequency) is increased markedly while the growth rate is limited in magnitude to the wave frequency. This increase in the phase velocity can be very important in cosmic ray propagation theories since the Alfven speed is no longer the limiting velocity. It can also be important in shock wave acceleration models for the production of cosmic rays