Theory of waveguide antennas for plasma heating and current drive

Abstract

A computational model is developed that allows one to estimate in a real 3-D geometry the electrodynamic characteristics of complicated waveguide antennas ('grills') generating plasma waves in the lower hybrid frequency band. The antenna coupling efficiency and the shape of the wavenumber spectrum are found as a solution of a self-consistent problem taking into account a complete set of waveguide eigenmodes and finite waveguide dimensions in both directions and an arbitrary orientation to the plasma magnetic field. Electric and magnetic fields inside the waveguides are equated to the outside fields represented as a Fourier sum over wavenumbers Ny, Nz in the plane parallel to the plasma surface. The fields at the plasma edge are determined by the 2*2 plasma surface impedance matrix found as a numerical solution of the wave equation in the cold plasma approximation using the finite element (Galerkin) method. The solution is found on a 1-D mesh, i=1, 2, ..., N, in the form E(xi,Ny,Nz) exp(i(Nyy+Nzz- omega t)) so that the fourth order differential equation with appropriate boundary conditions is reduced to a set of 4N+2 algebraic equations. The developed model is applied to modelling a quite new antenna design for generating the fast H waves, which can be used for plasma heating and current drive in tokamaks of ITER scale. The antenna parameters are optimized to obtain the best coupling efficiency. The structure of waves excited in the plasma at various angles between the antenna and the plasma magnetic field is considered. The nature of the waves with Nz<1 excited by the grill is discussed

Quasi-linear modeling of lower hybrid current drive in ITER and DEMO

“…The antenna consists in passive/active multi-junction (PAM) array of waveguides suitably phased and feed for launching the power spectrum centred at around a certain n ||0 value and having width Δn || . The antenna spectra have been calculated using numerical code able to describe in 3-D geometry the electro dynamic characteristics of however complicated waveguide antennas, oriented at an arbitrary angle to the magnetic field of the tokamak [18,19]. The value n ||0 ≈1.8 has been chosen, as it is sufficient, following standard criterion, for having wave accessibility to the dense plasma core [20] and, together, a not too strong electron Landau damping in the outer radial half of plasma [21], where the occurrence of the LHCD effect should be compatible with electron temperatures T e ≤ 16keV ( ) .…”

“…[19]. In this case 80 MW have been launched for both the antenna configurations and keeping into account the antenna directivity (60%) only 50MW of the power is useful for the current drive.…”

“…Moreover, by controlling the shape of the spectrum, its width, the n ||0 peak and the electric field intensity (surface power density at the antenna), it is possible to control the deposition layer. This approach has been indeed routinely used in the "LH star " code, which after calculating the effects of spectral broadening produced at the edge by PI, on the coupled spectrum calculated by "grill-3D" module [19], integrate the ray tracing equations simultaneously with the Quasi-Linear Fokker-Planck evaluation of the electron distribution function in 2D velocity space including the trapped electrons. This code was successfully employed earlier for producing LH deposition profiles in agreement with available data of important experiments of JET [6], and for assessing on FTU the method for producing LHCD effects at reactor relevant high plasma density [4].…”

Lower hybrid current drive in the presence of electric field

“…Initial || spectra for the FT-2 LH two-waveguide antenna noticeably differs from the standard LH spectra because its positive and negative lobes contain comparable amounts of the LH input power. Examples of the FT-2 spectra [10] calculated for opposite waveguide phasing is present in Fig. 2.…”

ECRH on CASTOR

“…To estimate the absorbed power at oblique incidence we can use the analytic WKB formula for the penetration of the Omode through the plasma resonance and its subsequent conversion to the X mode and then the conversion to the electron Bernstein wave (EBW) [1]. We also solve the full set of Maxwell equations by the finite element method [2] for wave propagation in an inhomogeneous plasma slab. Thus we are able to numerically determine the amplitude of the reflected wave for either a cold or a warm plasma.…”