Relativistic wave phenomena in astrophysical plasmas
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The propagation and stability of waves in relativistic astrophysical plasmas is presented. Our investigation, using a relativistic two-fluid model, is different from previous relativistic fluid studies in that the plasma is treated fully relativistically, both in temperature and in directed speed. Much of this study is devoted to relativistic linear waves in pulsar pair plasmas, with a view to elucidating a possible mechanism for pulsar radio wave emission. We also study interesting nonlinear exact solutions in both relativistic and non-relativistic plasmas. Pulsar pair plasmas can support four transverse modes for parallel propagation. Two of these are electromagnetic plasma modes, which at high temperature become light waves. The remaining two are Alfvénic modes, split into a fast and a slow mode. The slow mode, always sub-luminous, is cyclotron (Alfvén) two-stream unstable at large wavelengths. We find that temperature effects, within the fluid model used, do not suppress the instability in the limit of large (finite) magnetic field. The fast Alfvén mode can be super-luminous only at large wavelengths; however, it is always sub-luminous at high temperatures. In this incompressible approximation, only the ordinary mode is present for perpendicular propagation. We discuss the implications of the unstable mode for radio emission mechanisms. For typical values, the instability is quite fast, and the waves can grow to sizable levels, such that, the magnetic modulation could act as a wiggler. The pulsar primary beam interacting with this wiggler, could drive a free electron laser (FEL) effect, yielding coherent radiation. Investigation of the FEL in this setting and demonstrating that the frequency spectral range, and luminosities, predicted by this mechanism is well within the observed range of radio frequency (and luminosity) emissions, is one of the principal results of this dissertation. It is tempting to speculate, then, that an FEL-like radiation effect could be responsible for the highly coherent radio wave emissions from pulsars. In the study of nonlinear exact solutions we have generalized the results to the incompressible Hall Magnetohydrodynamics (HMHD). We find that for cases when the plasma is weakly magnetized the frequencies of the modes decrease as the wave amplitude (effective mass) increases. For very strongly magnetized plasmas the light-like modes tend to be asymptotically linear; the frequency is unaffected by wave amplitude.