A representation of a finite Larmor radius plasma is proposed, which permits the transition rL → ∞ without becoming mathematically ill-posed. It is being used in a two-dimensional guiding center plasma spectral code and may have useful analytical applications. The ions are represented as guiding centers and the Larmor radius is averaged analytically for every Fourier-mode. Finite Larmor radius densities and velocities are thus obtained from guiding center quantities by application of a filter in wave vector space.
A two-point boundary-value problem has been formulated that describes the conversion between ordinary (O) and extraordinary (X) wave modes in a cold inhomogeneous plasma. Numerical solutions to this problem have been obtained for various values of the WKB parameter k0L; where k0 is the vacuum wavenumber and L the density-gradient scale length. The results are compared with three different theoretical expressions for the O-X mode conversion efficiency derived by others in the WKB limit of k0 L ≫ l. Most of the results presented in this paper are obtained for a collisionless plasma with finite density near the plasma cut-off density. However, some examples are also given of wave propagation from vacuum. In these examples, collision effects are added to the equations in order to remove the singularity otherwise present at the position of the upper hybrid resonance layer.
A method to apply electron cyclotron resonance heating (ECRH) to a Tokamak plasma with central density higher than the critical density for cut-off of the ordinary mode (0-mode) has been investigated. This method involves two mode cqnversions, from an 0-mode via an extraordinary mode (X-mode) into an electron Bernstein mode (B-mode). Radial profiles for the power deposition and ?he wave-driven current due to the B-waves are calculated for realistic antenna radiation patterns with parameters corresponding to ?he Danish DANTE Tokamak and to Princeton's PLT.
An introduction is given to the use of spectral methods in numerical plasma simulation. As examples of the use of spectral methods, solutions to the two-dimensional Euler equations in both a simple, doubly periodic region, and on an annulus will be shown. In the first case, the solution is expanded in a two-dimensional Fourier series, while a Chebyshev-Fourier expansion is employed in the second case. A new, efficient algorithm for the solution of Poisson's equation on an annulus is introduced. Problems connected to aliasing and to short wavelength noise generated by gradient steepening are discussed.
Electromagnetic waves with ordinary polarization, propagating almost perpendicularly to the magnetic field in a tokamak with random density fluctuations, are investigated numerically. The fluctuations are assumed to be located mainly at the plasma edge, as is appropriate for drift wave type fluctuations. The wave propagation in this fluctuating plasma is described in the limit of geometrical optics by a ray tracing code. Even low levels of relative density fluctuations (around 1%) result in significant scattering of the incoming wave beam. The variations in the wave intensity are investigated by analysing the relative dispersion of rays. Caustic formation is demonstrated in localized regions, where the amplitude predictions based on geometrical optics break down. A statistical analysis of the results is performed by tracing many rays for a wide range of fluctuation parameters and subsequently averaging the ray trajectories. The results may be relevant to tokamak plasma heating experiments and current generation schemes. Analytical results for the statistics of the ray propagation are presented for simplified geometries.
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