Commissioning of a multi-point Bdot-Mach probe to measure the evolution of ion canonical vorticity during RFP relaxation*

Conversions between twisted magnetic and ion flow vorticity flux tubes provide an alternative viewpoint of self-organized processes in plasmas. We present simultaneous measurements of the magnetic field and ion flow, with analysis of both the equilibrium evolution and fluctuations during sawtooth relaxation in a reversed-field pinch (RFP). Data was collected during > 400 discharges on the Madison Symmetric Torus (MST) at a range of radii (r/a=0.9-0.82) covering the reversal surface (the reversal parameter F ranged from –0.3 to –0.1). We utilized a novel canonical vorticity probe consisting of four clusters of 3x magnetic (B-dot) and 4x Mach probes arranged at the vertices of a regular tetrahedron. The three-dimensional Mach vector is determined from the geometric addition of the logarithms of ion saturation currents collected by each probe cluster. These are arranged in a tetrahedral finite difference stencil so that the curl of these vectors can be determined. The propagated uncertainty in the derived 3D Mach vector due to manufacturing precision in the angular orientations of the probe clusters is also analyzed. This work will help generalize our understanding of plasma relaxation to a canonical-helicity-constrained relaxation explaining multi-scale dynamics.