Whistler mode electron cyclotron emission in magnetic mirror plasmas.

Electron cyclotron emission parallel to an externally applied magnetic field is theoretically investigated on an axisymmetric magnetic mirror plasma with finite mirror ratio using model distribution functions. The source function is evaluated analytically in the single-particle limit for a generalized loss cone bi-Maxwellian and a $\delta$-function pitch angle distribution, and semi-analytically for a Gaussian pitch angle distribution. The loss cone bi-Maxwellian distribution is used to calculate the index of refraction, emission coefficient and source function for the hot electrons in the end cell of the TMX-U mirror machine and the results are compared with those for the bi-Maxwellian distribution. It is discovered that at low mirror ratio the forward propagating mode breaks into two separate branches. An interactive program based on the continuation method is used to follow the multiple branches of the whistler mode dispersion equation. Whistler emission from a plasma formed by a cold Maxwellian and a hot Gaussian pitch angle distribution is calculated using an existent radiation transport code with typical plasma parameters for the MIMI mirror machine. We show that the current theory of whistler emission is inadequate to estimate the radiation emission in high density, highly anisotropic plasmas because of the existence of turning points and highly whistler-unstable regions in such plasmas, which are not accounted for in the theory. Furthermore, the extension of low density source function to high density plasmas is found to be inaccurate. Whistler emission from a low density plasma formed by a cold Maxwellian, a warm loss cone bi-Maxwellian and a hot Gaussian pitch angle distribution is calculated using a new radiation transport code. The results show that the radiation temperature lies between the parallel and perpendicular temperature of the hot electrons; however we can no longer estimate the hot electron perpendicular temperature from such calculations because the source function is no longer proportional to the temperature. A closed form representation of the generalized complete plasma dispersion function is derived in terms of the confluent hypergeometric function. This new representation may be very useful because the properties of confluent hypergeometric functions are well-known and symbolic manipulation packages can handle them.PhDNuclear EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/104683/1/9542924.pdfDescription of 9542924.pdf : Restricted to UM users only