Wave power flux and ray-tracing in regions of resonant absorption

Abstract

Abstract. The propagation of waves in weakly dissipative plasmas is investigated. A new expression for the wave energy flux is obtained, which is proportional to ∂λ mode /∂k, where λ mode is the real part of the eigenvalue of the dispersion tensor corresponding to the wave mode. Significant differences from the usual definition of dielectric wave energy flux occur in case of a non-negligible anti-Hermitian contribution to the dielectric tensor. This occurs, for example, near electron cyclotron resonance. The direction of the corrected wave energy flux is consistent with that of the trajectory of a wave beam crossing the EC resonance as obtained in Westerhof Plasma Phys. Control. Fusion 39 1015. It is shown that ray-tracing near cyclotron resonance can be performed with the use of λ mode as ray-Hamiltonian.

Benchmarking of codes for electron cyclotron heating and electron cyclotron current drive under ITER conditions

“…In one, the dispersion relation is calculated by the R2D2 [12] code fully relativistically without making the usual approximation that the dielectric tensor elements can be expanded as a truncated power series of k " # e . The second model for the dispersion relation is due to work by Westerhof [13] and Tokman [14], which described the breakdown of standard ray tracing when the part of the dispersion relation responsible for the absorption becomes too large, as may happen near a cyclotron resonance. This new physics was implemented in GENRAY by Smirnov and Harvey [15].…”

“…Two dispersion relations were used in the high density benchmark that were not used for the standard density case: the R2D2 code [12] called from GENRAY, which is fully relativistic and which does not expand the dielectric tensor, and the Westerhof-Tokman dispersion relation [13,14], which addresses issues which arise when the absorption becomes sufficiently strong. The R2D2 code would not be expected to produce results greatly different than a fully relativistic code that does use an expansion in this benchmark case, since the product k " # e $ v th c is small, about 0.1.…”

Electron cyclotron current drive calculated for ITER conditions using different models

“…For the Hamiltonian, H, the most general form suggested by Tokman and Westerhof [17] (which includes an "anomalous" dispersion effect) is adopted:…”

Electron Cyclotron Heating for W7-X: Physics and Technology

“…Generally, the 'cold', 'warm' non-relativistic, or weakly relativistic dielectric tensor can be used in the Hamiltonian. With the weakly relativistic dielectric tensor, the model of tracing includes those kinetic effects which become significant in the vicinity of the EC resonance, leading to 'anomalous' dispersion effects and possible wiggling and even bending of the rays there [4,5]. For example, in contrast with the 'cold' approach (which should be sufficient for many cases), the weakly relativistic model can give a quite different result in the case of (quasi-vertical) launch with the ray trajectories almost tangential to the resonance line, i.e.…”