An algorithm for the calculation of 3-D ICRF (Ion Cyclotron Range of Frequencies) fields in tokamak geometry

Abstract

A computational scheme is developed which permits tractable calculation of three-dimensional full-wave solutions to the Maxwell-Vlasov equations under • typical Ion Cyclotron Range of Frequencies (ICRF) experimental conditions; The method is unique in that power deposition to the plasma is determined via* the anti-Hermitian part of a truncated warm-plasma dielectric operator, rather than as the result of an assumed phenomenological collisioa frequency. The-.^ resulting computer code allows arbitrary variation of density, temperature, magnetic field, and minority concentration in the poioidal plane by performing a convolution of poioidal modes to produce a coupled system of differential equations in the radial variable. By assuming no inhomogeneity along the tor. Jdal axis, an inverse transform over k, is performed to yield the full three-dimensional field solutions. The application of the code to TFTR-like plasmas shows a mild resonance structure in antenna loading related to the changing number of wavelengths between antenna and the resonance layer.

Local full-wave energy and quasilinear analysis in nonuniform plasmas

“…This fact might have been anticipated by recalling that the net area under the imaginary part of the generalized phase integral, Z ( [ , x ) . is always positive (SMITHE et al, 1988).…”

“…The time dependence of R' is especially troublesome, since the imaginary part of the phase integral in z is no longer of definite sign (FAULCONER, 1987). In SMITHE et al (1988) it is shown that this more difficult phase integral may be performed semi-analytically by doing the parallel velocity summation prior to the time integration. It is also possible to perform the perpendicular velocity summation analytically.…”

Numerical simulation of ion cyclotron heating of hot tokamak plasmas

“…According to the analysis of Smithe et al [42], this approximation could lead to overestimating somewhat the efficiency of mode conversion in the vicinity of the magnetic axis. The code is, however, modular enough so that a more accurate evaluation of the integrals could be easily incorporated if a sufficiently fast algorithm for Z" in the form (55) becomes available.…”

Electron absorption of fast waves in global wave calculations

“…In this paper we neglect the effects (PERKINS, 1977) of magnetic field variation along the field lines (poloidal magnetic field effects) on the fast wave penetration and absorption in a Tokamak plasma. These effects can influence the ion cyclotron absorption ofafastwaveatlow k,, (KOVRIZHNYKH and MOROZ, 1985 ;GAMBIER and SAMAIN, 1985 ;SMITHE et al, 1988 ;BRAMBILLA, 1989)…”