Numerical simulation of ion cyclotron heating of hot tokamak plasmas

Abstract

The authors have written a code for the solution of the integro-differential equations describing coupling, propagation and absorption of high frequency waves in the ion cyclotron frequency range in tokamak plasmas, taking into account finite Larmor radius effects and parallel dispersion. The wave equations are discretized by a semi-spectral approach, using cubic Hermite finite elements in the radial direction and an expansion in Fourier modes in the poloidal direction. The latter permits analytic evaluation of the orbit integrals along magnetic field lines in the presence of a poloidal component of the static magnetic field. Thus, the code describes mode conversion to ion Bernstein waves, ion cyclotron damping at the fundamental and at the first harmonic, and electron transit time and Landau damping in full toroidal geometry. A few simulations of ion cyclotron heating of the ASDEX tokamak are presented. They show generally good agreement with the predictions of simpler models, namely plane layered models and ray tracing. Furthermore, the simulations can be used to identify a few interesting toroidal effects, particularly regarding the efficiency of mode conversion and the propagation of ion Bernstein waves.

An assessment of full wave effects on the propagation and absorption of lower hybrid waves

“…(5a) is solved by a variational technique 25 that results in a block tri-diagonal stiffness matrix. The electric field as expressed in the basis given in Eq.…”

Full wave simulations of fast wave mode conversion and lower hybrid wave propagation in tokamaks

“…The TORIC code uses an FLR expansion to convert this vector integro-differential equation into a sixth order partial differential equation. 5,8 This approximation retains the second harmonic wave frequency and is second order in the ion gyro-radius, (ρ i = v ti /Ω ci ), for plasma interactions with the wave.…”

“…While the approximation to the integral plasma current response is done to second order in the normalized perpendicular wavenumber, k ⊥ ρ i , the damping for the IBW is good to all orders. This is done by modifying the imaginary part of the plasma dispersion to account for the IBW damping, while leaving the real part unchanged 8 .…”

Modelling RF-plasma interaction in ECR ion sources

“…Several full-wave numerical simulation codes have been developed to describe waves in fusion toroidal devices [1][2][3], exploiting symmetry or ray-tracing technique; at the same time, only few methods have been developed to obtain selfconsistent solutions for nonaxisymmetric ECRIS plasma [4][5][6].…”