Mode-conversion of the extraordinary wave at the upper hybrid resonance in the presence of small-amplitude density fluctuations

TL;DR

This paper introduces a new analytical framework for studying mode-conversion of electromagnetic waves at the upper hybrid resonance in spherical tokamaks, accounting for small density fluctuations that affect conversion efficiency.

Contribution

The authors develop a simplified, analytically tractable model for X-B mode-conversion that incorporates edge turbulence and fluctuations, improving upon traditional models.

Findings

Small-amplitude density fluctuations can significantly reduce mode-conversion efficiency.

Bragg backscattering occurs when fluctuation wavenumber resonates with incident wave wavenumber.

The new model accurately reproduces key features of previous approaches and aids experimental analysis.

Abstract

In spherical tokamaks, the electron plasma frequency is greater than the electron cyclotron frequency. Electromagnetic waves in the electron cyclotron range of frequencies are unsuitable for directly heating such plasmas due to their reduced accessibility. However, mode-conversion of the extraordinary wave to the electron Bernstein wave (X-B mode-conversion) at the upper hybrid resonance makes it possible to efficiently couple externally-launched electromagnetic wave energy into an overdense plasma core. Traditional mode-conversion models describe an X-mode wave propagating in a potential containing two cutoffs that bracket a single wave resonance. Often, however, the mode-conversion region is in the edge, where turbulent fluctuations and blobs can generate abrupt cutoffs and scattering of the incident X-mode wave. We present a new framework for studying the X-B mode-conversion which makes the inclusion of these fluctuations analytically tractable. In the new approach, the high-field cutoff is modelled as an infinite barrier, which manifests as a boundary condition applied to a wave equation involving only one cutoff adjacent to the resonance on the low-field side. The new model reproduces the main features of the previous approach, yet is more suitable for analyzing experimental observations and extrapolating to higher dimensions. We then develop an analytical estimate for the effect of small-amplitude, quasi-monochromatic density fluctuations on the X-B mode-conversion efficiency using perturbation theory. We find that Bragg backscattering of the launched X-mode wave reduces the mode-conversion efficiency significantly when the fluctuation wavenumber is resonant with the wavenumber of the incident X-mode wave. These analytical results are corroborated by numerically integrating the mode-conversion equations.