Measurements of ion canonical cross helicity evolution during RFP relaxation using a multi-point Bdot-Mach probe

Conversions between twisted magnetic and ion flow vorticity flux tubes provide an alternative viewpoint of self-organized processes in plasmas. We present the first direct measurements of the temporal evolution of cross helicity – the scalar product of the magnetic field and ion flow velocity – taken during sawtooth relaxation in a reversed-field pinch (RFP). To do this, simultaneous and co-located measurements of the magnetic field and ion flow velocity were 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 utilize a novel canonical vorticity probe consisting of four clusters of three axis-aligned B-dot coils and four Mach probe tips 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 clusters are arranged in a tetrahedral finite difference stencil so that the curl of the vector quantities can be determined. This work represents progress made towards measuring the evolution of canonical helicity during RFP sawtooth relaxation, in an effort to generalize our understanding of plasma relaxation to a canonical-helicity-constrained framework explaining multi-scale dynamics.