Modeling and simultaneous sawtooth measurements of the thermal and energetic electron diffusivities from the Texas Experimental Tokamak

Abstract

Convenient mathematical models appropriate for simultaneously measuring the thermal and energetic electron diffusivities by their responses to internal disruptions are presented and compared to simultaneous soft and hard x-ray sawtooth data from the Texas Experimental Tokamak (TEXT) [Nucl. Technol./Fusion 1, 479 (1981)]. The eigenfunction expansion technique employed is first illustrated on a constant diffusivity, single sawtooth crash model that is unable to give a satisfactory fit to the TEXT soft x-ray data at disparate radii for an initial condition of a flattened temperature profile out to the mixing radius. A more sophisticated single crash model having a parabolic radial dependence for the thermal diffusivity and a flattened profile initial condition substantially improves the fit to the TEXT soft x-ray data. Simultaneous measurements of the sawtooth oscillations on the hard x-ray signal caused by runaway electrons hitting the limiter are interpreted to obtain a measure of the diffusivity of the energetic electrons in TEXT following the same crash used to measure the thermal diffusivity. A single sawtooth crash model is no longer adequate because the diffusivity of the energetic electrons may be substantially less than the thermal value. Therefore the eigenfunction expansion technique is extended to a periodic sawtooth crash model. Measurements of diffusivities far smaller than those that can be measured by a single crash model are possible and more than one value of diffusivity can fit the simultaneous TEXT hard x-ray data. The lower values of diffusivity could not have been obtained by a single crash model. Additional hard x-ray measurements having differing sawtooth periods are needed to remove the ambiguity. As more extensive hard x-ray data become available on TEXT, it may become possible to simultaneously and unambiguously measure the thermal and energetic electron diffusivities during the same crash.