We discuss the propagation of wave packets of the form ei(ωt - kz) G(z,t) in an infinite uniform plasma (in both the formal cold plasma, and hot collision-free Vlasov plasma limit), where G(z,t) is a slowly varying function of space z and time t. One can derive the equation of change of G(z,t) (in both the above stated temperature limits) for the stable or unstable case. The terms in the equation are of physical interest and clearly define the limitations of linear theory. In particular we show that by using the model of complete stirring developed by A. C. Das, changes in apparent frequency a0/at (0 = phase of disturbance) can occur due to sharp changes in growth rate with respect to wave number. We then investigate the problem of Whistler mode wave propagation in a collisionless Vlasov plasma in a given non-uniform magnetic field. We choose the electric field to be of a W.K.B. form wad the particle distribution to be isotropic. We can express the perturbation in the particle distribution in terms of an integration along the zero order particle orbits (an integration over time). These orbits can be found correct to a term linear in a smallness parameter ε (when ε equals zero we arrive back at a uniform magnetic field). The charge and current density due to the perturbation are related through Maxwell's equations to the electric and magnetic field of the wave in the usual self consistent Boltzmann-Vlasov description. We show that the contribution to the current arises from recent events in the history of a given particle because of the finite temperature of the plasma. This result leads to an expansion of slowly varying parameters which in turn gives rise to the equation governing the motion of the wave-packet. In the final chapter the monochromatic wave case is also considered and cyclotron resonance is then investigated. It is shown that typically Fresnel integrals arise. Some light is also thrown on the magnetic beach configuration discussed by Stix. For completeness a paper on the modulation of cosmic rays, which was presented by the author at the Ninth International Conference on Cosmic Rays, is also included at the end of this thesis.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:623049 |
| Date | January 1968 |
| Creators | Houghton, Michael Joseph |
| Publisher | Imperial College London |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/10044/1/15882 |
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