Abel inversion of soft x-ray fluctuations associated with fast particle-driven fishbone instabilities in MAST plasmas

A set of soft x-ray cameras provided measurements of high frequency instabilities as well as steady-state emission in the Mega Amp Spherical Tokamak (MAST). It is shown that Abel inversion can be readily applied to fluctuating soft x-ray emission from the MAST midplane associated with fast particle-driven ‘fishbone’ instabilities, characterised by toroidal mode number n = 1. Each fishbone burst had an early phase in which high amplitude fluctuating soft x-ray signals from the plasma core were close to being in phase with each other, and there was a region close to the outboard plasma edge in which the fluctuations were relatively weak and in antiphase with those in the core. The major radius of the ‘phase axis’ at which the mode amplitude changed sign R p was initially outboard of the tokamak magnetic axis at R 0, but moved inboard during the burst, eventually becoming close to R 0, at which time the oscillations were of similar amplitude inboard and outboard of R p . The fishbone radial structure early in the burst can be understood in part by recognising that the mode is supported by energetic ions with a high average toroidal rotation rate: in a co-rotating frame, the effective magnetic axis is shifted outboard by a distance that is comparable to the difference between the major radii of the phase axis early in the burst and the laboratory frame magnetic axis. It is conjectured that the transition to a mode with R p ≃ R 0 occurred because most of the energetic ions were expelled from the plasma core region where the mode amplitude peaked, so that the instability could no longer be characterised as an energetic particle mode. Abel inversion of fishbone soft x-ray emission thus provides useful insights into the nature of energetic particle modes in tokamak plasmas and their relationship with MHD modes.