The experimental determination of the volume recombination rate in tokamak divertors

Abstract

A method for evaluating the volume recombination rate within a cold ( T e≲1 eV), relatively dense ( n e≳1×10 21 m −3) plasma is described. These conditions often exist in the detached divertor plasmas of the Alcator C-Mod Tokamak. Temperatures ≲1 eV are measured spectroscopically. Densities in the 0.4 × 10 21–2.5 × 10 21 m −3 range are measured using the Stark-broadened D 0 Balmer series lines. D 0 line emissions in both the Lyman and Balmer series show that the D 0 excited state populations ( n≳3) in the recombining regions are close to those given by the Saha–Boltzmann distribution and are essentially independent of the ground state density. The intensities of lines from these excited states are related to the recombination rate. The number of recombinations per D 0 photon is a function of opacity of the Lyman series lines, T e and n e. Determinations of the recombination rates corresponding to the line intensities are made by using a collisional radiative model describing the level populations, ionization and recombination of D 0 and a model which accounts for the radiation transfer of the Lyman lines. The effects of the trapping of Lyman photons on the `recombinations per photon' curves have been calculated using both modelling which considers only spatial diffusion of the photons and modelling by a radiative transfer code which calculates photon transport in space and frequency. Subject to imperfect knowledge of the 2D profiles of opacity and temperature, total recombination rates in the detached divertor plasma are determined. In the Alcator C-Mod divertor region, volume recombination can be a significant sink for ions under detached conditions.