Parallel Gradient Effects on ICRH in Tokamaks.

This dissertation examines the effects on Ion Cyclotron Resonance Heating of parallel nonuniformity in the magnetic field which arises from the poloidal field in a Tokamak and the universal (major radius)$\\sp{-1}$ scaling of the cyclotron frequency. The goal of the analysis is the macroscopic warm plasma current including temperature in the sense of the finite Larmor radius expansion and the quasilocal approximation of the parallel guiding center motion. Because of a particle's temporally varying instantaneous gyrofrequency, the plasma conductivity kernel is not translationally invariant. Furthermore, to treat absorption in a warm plasma, it is necessary to include parallel temperature to all orders, hence the kernel cannot be represented as a differential operator, as in the case of purely perpendicular gradients. A nonlocal, or integral kernal is required. Also because of the temporally varying average gyrofrequency, the integrals are altered in the method-of-characteristics solution which gauge relative rf-particle phase. This results in the replacement of the plasma dispersion function of Fried and Conte with a new mathematical quantity, which is surprisingly, of no greater computational difficulty. Included in this generalized dispersion function are collisional phase decorrelation effects which can play a significant role in the uniform plasma limit. The quasilocal formalism allows a mathematically rigid extension of the familiar k$\\sb\\perp$-k$\\sb\\parallel$ dependancy of the local dispersion tensor to the nonlocal problem, in which case the k$\\sb\\parallel$ factor within the plasma dispersion function is treated as an integral operator. The avenue for this development is the modal superposition technique, which need not be based on the Fourier integral basis, but is used here for its favorable analytic properties, and its intuitive appeal. A 1-D numerical application of the fully nonlocal integral dielectric is performed. Parallel gradient effects are studied for He-3 minority, 2nd harmonic deuterium, and hydrogen minority heating in Tokamaks. The results show quite significant alteration of the toroidal wavenumber absorption spectrum, and a wealth of new behavior on the local propagation scale.PhDNuclear engineeringPlasma physicsUniversity of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/161724/1/8801421.pd