TwoDimensional Magnetohydrodynamic Equilibria with Flow and Studies of Equilibrium Fluctuations.
Abstract
A set of reduced ideal MHD (magnetohydrodynamic) equations is derived to investigate equilibria of plasmas with mass flow in general twodimensional geometry. These equations provide a means of investigating the effects of flow on selfconsistent equilibria in a number of new twodimensional configurations such as helically symmetric configurations with helical axis, which are relevant to stellarators, as well as axisymmetric configurations. It is found that, as in the axisymmetric case, general two dimensional flow equilibria are governed by a secondorder quasilinear partial differential equation for a magnetic flux function, which is coupled to a Bernoullitype equation for the density. The equation for the magnetic flux function becomes hyperbolic at certain critical flow speeds which follow from its characteristic equation. When the equation is hyperbolic, shock phenomena may exist. As a particular example, unidirectional flow along the lines of symmetry is considered. In this case, the equation mentioned above is always elliptic. An exact solution for the case of helically symmetric unidirectional flow is found and studied to determine flow effects on the magnetic topology. In the second part of this thesis, magnetic fluctuations due to the thermally excited MHD waves are investigated using fluid and kinetic models to describe a stable, uniform, compressible plasma in the range above the drift wave frequency and below the ion cyclotron frequency. It is shown that the fluid model with resistivity yields spectral densities which are roughly Lorentzian, exhibit equipartition with no apparent cutoff in wavenumber space and a Bohmtype diffusion coefficient. Under certain conditions, the ensuing transport may be comparable to classical values. For a phenomenological cutoff imposed on the spectrum, the typical fluctuatingtoequilibrium magnetic field ratio is found to be of the order of 10^{10} . Physical mechanisms to obtain decay profiles of the spectra with increasing wavenumber due to dispersion and/or different forms of damping are investigated analytically in a cold fluid approximation and numerically, with a kinetic model. The finite iongyrofrequency is identified as the leading effect determining the spectral profile shapes. It is found that the amplitude of fluctuations may be within a factor of the value suggested by the cold plasma model. The results from both models are presented and compared in low and highbeta regimes.
 Publication:

Ph.D. Thesis
 Pub Date:
 1989
 Bibcode:
 1989PhDT........15A
 Keywords:

 Physics: Fluid and Plasma;
 Flow Geometry;
 Flow Stability;
 Magnetohydrodynamic Waves;
 Magnetohydrodynamics;
 Mass Flow;
 Plasmas (Physics);
 Cyclotron Frequency;
 Ion Cyclotron Radiation;
 Stellarators;
 Plasma Physics