Reconstruction of superthermal electron velocity distribution function from electron cyclotron spectra at down-shifted frequencies in tokamak T-10

P.V Minashin,V.I Poznyak,A.B Kukushkin

doi:10.1051/epjconf/20123201015

Abstract

A model is developed to quantitatively interpret the electron cyclotron (EC) spectra in tokamak T-10 at frequencies lower than the first EC harmonic at the plasma edge. The model is based on the almost free propagation and isotropy of EC radiation in between the vacuum chamber wall and the cut-off zone in plasma. The inverse problem for the reconstruction of the velocity distribution function of superthermal electrons (in parallel and perpendicular momenta, and magnetiс flux surfaces at the plasma edge) is formulated and solved. It is shown that in the Ohmic discharges in the tokamak T-10 the superthermal electrons are the trapped particles at the low magnetic field side of toroid. Their mean kinetic energy lies in the range ~ 150-200 keV, and the density fraction is about ~ 10 -4 relative to the main plasma.

Highlights

Observations of electron cyclotron (EC) radiation spectra in tokamak T-10 simultaneously in the range of the first and second EC harmonics of thermal plasma EC emission, including relativistically downshifted frequencies for both harmonics, suggested the presence of a fraction of superthermal electrons with energies in the range up to few hundreds of keV [1]
The characteristic feature of the experiments in tokamak T-10 is the smallness of the plasma density at the periphery, that allows the propagation of the 1st harmonic O-mode EC radiation at the periphery
We consider the case when superthermal electrons are localized within 3 cm layer at the plasma edge as suggested by the experiments [1]

Summary

Introduction

Observations of electron cyclotron (EC) radiation spectra in tokamak T-10 simultaneously in the range of the first and second EC harmonics of thermal plasma EC emission, including relativistically downshifted frequencies for both harmonics, suggested the presence of a fraction of superthermal electrons with energies in the range up to few hundreds of keV [1]. The model is based on the almost free propagation and isotropic intensity of the EC radiation in between the vacuum chamber wall and the cut-off zone in plasma This allows us to apply the calculation method formerly developed for the ECR power losses in tokamak-reactors where the radiation at high frequencies, responsible for the EC power losses, is trapped in between the vacuum chamber wall and the inner region of high optical opacity. Such a freedom in solving the inverse problem is possible due to a strong dependence of the ECR spectrum for superthermal electrons in a nonuniform magnetic field in a tokamak on the radiation frequency in the range of relativistically down-shifted frequencies. The calculations, carried out for the case of the Ohmic discharges in tokamak T-10, enable us to determine the type of the trajectory of the radiating electrons (either they are the trapped or circulating particles), mean kinetic energy and the ratio of superthermal electron density to the main plasma density at the plasma edge

Modeling of EC radiation spectrum

Algorithm of VDF reconstruction

Inverse problem solution

Conclusions