Semi-analytic shape function of high-harmonic electron cyclotron emission in magnetically confined plasma

Abstract

Semi-analytical expressions for the electron cyclotron emission (ECE) shape function are developed for arbitrary high harmonics. The integrand of the mth harmonic ECE shape function is fitted with the readily integrable test function parameterized by plasma temperature T-e, harmonic number m, and emission angle theta. Semi-analytical formulae for high harmonic ECE emissivities are obtained by integrating the test integrand with the fitting parameters obtained from regression analysis. The semi-analytical expressions match with the numerically integrated ECE shape functions very well for a wide range of T-e (100 eV-12 800 eV), m (2-10), and theta (10.0 degrees -89.9 degrees) values. The expressions can be applicable for rapid analysis of ECE spectra in magnetically confined fusion plasmas. Published under license by AIP Publishing.