Fokker–Planck studies of high power electron cyclotron heating in tokamaks

Abstract

A Fokker–Planck formalism has been developed to interpret experimental data from high power electron cyclotron heating of tokamak plasmas in which the electron distribution function can be substantially distorted. The Fokker–Planck equation is solved using a 2-D code which incorporates electron trapping, a steady Ohmic electric field and a bounce averaged electron cyclotron heating term. The quasilinear RF diffusion coefficient is calculated using a single particle model which includes the mildly relativistic resonance condition and takes into account localized RF power injection and tokamak rotational transform effects. Comparisons are presented of the calculated and observed soft X-ray spectra from 60 GHz second harmonic electron cyclotron heating experiments on the CLEO tokamak. Good agreement between theory and experiment is found. In addition, predicted RF current drive efficiencies for the COMPASS tokamak are presented.

Consequences of plasma rotation for neoclassical tearing mode suppression by electron cyclotron current drive

“…This equation describes the evolution of the bounce-averaged electron distribution function under the influence of both collisions and the EC driven quasi-linear diffusion. [30][31][32] Because the island evolution is incompressible, the evolution of the island will not affect the bounce-averaged distribution function f e ðS X Þ as a function of the total area enclosed by the flux surface as indicated in Fig. 1.…”

Kinetic modeling of nonlinear electron cyclotron resonance heating

“…Instead, it satisfies the quasilinear evolution equation [19][20][21][22]11,12,2,[23][24][25][26] where the effect of the resonant wave-particle interaction on the unperturbed distribution function is described by diffusion terms with coefficients which are quadratic in the wave amplitude. Instead, it satisfies the quasilinear evolution equation [19][20][21][22]11,12,2,[23][24][25][26] where the effect of the resonant wave-particle interaction on the unperturbed distribution function is described by diffusion terms with coefficients which are quadratic in the wave amplitude.…”

Positivity-preserving scheme for two-dimensional advection–diffusion equations including mixed derivatives

“…In general, the time evolution of the distribution function can be solved under multiple effects, such as collisions, electric fields and plasma-wave interactions [14,15,16], and this method could easily be extended to include these additional terms. We will only consider the effect of collisions, for which the Fokker-Planck equation can be written as the divergence of a flux, ∂f ∂t = ∇ · S c If we assume steady-state, or that the distribution is in local thermal equilibrium, particle number is exactly conserved if the flux S c = 0.…”

“…with A g and B g given by (14). A similar approach is used for the flux in the v -direction in order to obtain solutions for δ , but in this case there are four possibilities,…”