Semi-analytic Shape Function of High-harmonic Electron Cyclotron Emission in Tenuous Plasma

TL;DR

This paper develops semi-analytic formulas for high-harmonic electron cyclotron emission shape functions in tenuous plasma, enabling rapid spectral analysis by fitting integrands with parameterized test functions.

Contribution

It introduces a novel semi-analytic approach to accurately approximate high-harmonic ECE shape functions for arbitrary plasma conditions.

Findings

Semi-analytic formulas match numerical results well.

The method allows rapid analysis of high-harmonic ECE spectra.

Differences between original and semi-analytic functions are minimal.

Abstract

Semi-analytic expressions for the electron cyclotron emission (ECE) shape function are developed for arbitrary high harmonics. The integrand of the ${m}^{\mathrm{th}}$ harmonic ECE shape function is fitted with the readily-integrable test function which is parameterized by plasma temperature $T_e$, harmonic number $m$ and emission angle $\theta $. Semi-analytic formulae for high harmonic ECE emissivity are obtained by integrating the test integrand with the fitting parameters gained from the regression analysis as well as the inductive studies for arbitrary cases. The developed expression matches the numerically-integrated ECE shape function very well and the overall differences between original shape functions and semi-analytic shape functions are evaluated. The expression can be used for rapid analysis of high-harmonic ECE spectra.