Mapping of power deposition zone of electron Bernstein waves externally excited in tokamak plasmas

Abstract

In toroidal plasmas, electron Bernstein (EB) waves mode-converted from X waves at the upper hybrid resonance (UHR) layer propagate toward the higher field side and are cyclotron-damped away at Doppler shifted frequency before arriving at the electron cyclotron resonance (ECR) layer. Resulting power deposition profile depends on local density, temperature and field profiles and is usually analyzed using the ray tracing technique for EB wave propagation and absorption in inhomogeneous magnetized plasmas. In axisymmetric tokamak plasmas, the ray tracing equation of EB waves can be cast into the form of equation of particle motion in a potential field. The particle trajectory and its momentum correspond to the wave trajectory and the refractive index, respectively. The potential field reflects the dispersion characteristics of EB waves, that is, the perpendicular refractive index strongly increases as the waves approach to the ECR layer from the lower field side, making a deep trench of potential along the ECR layer. Therefore the EB waves perpendicularly approach the ECR layer, which enable us to estimate the parallel refractive index and the parallel velocity of resonance electrons near the ECR layer. Thus, possible power deposition zone can be mapped and the associated current drive efficiency is roughly estimated directly from the information on wave frequency and plasma profiles without ray tracing calculations (direct mapping). The mapped zone, in the case of a moderately over dense plasma, is shown to be coincident with the ray tracing results for both XB and OXB schemes of mode conversion. In the cases of highly over dense, low safety factor and low aspect ratio plasmas, ω/Ωce is rather close to two at the UHR layer and the second harmonic cyclotron damping can take place along the ray trajectory just after OXB mode conversion, depending on the parameters. Here, ω is the wave frequency and Ωce is the local cyclotron frequency. It is shown that direct mapping also works in this case as well. The direct mapping technique is based on above picture of EB wave propagation and absorption, and is useful to guide the ray tracing analyses and cross-check the ray tracing results.