Weakly Magnetized, Hall Dominated Plasma Couette Flow

A novel plasma equilibrium in the high-$\beta$, Hall regime that produces centrally peaked, high Mach number Couette flow is described. Flow is driven using a weak, uniform magnetic field and large, cross field currents. Large magnetic field amplification (factor 20) due to the Hall effect is observed when electrons are flowing radially inward, and near perfect field expulsion is observed when the flow is reversed. A dynamic equilibrium is reached between the amplified (removed) field and extended density gradients.

Figure 1

Volumetric flow drive implemented on (left) the BRB with outward current and (right) on PCX with inward flowing current. The schematics show the electrode positions and probe scanning locations (blue wedges and red line) for the BRB and the blue dashed line shows the location of the Fabry-Perot optical diagnostic that measures chord integrated ion temperature and flow on PCX. Both devices are axisymmetric about the rotation axis. In both configurations current is sourced by ${\mathrm{LaB}}_6$ cathodes (orange) and collected by cold molybdenum anodes (gray). A weak ($<10\mathrm{G}$) externally applied magnetic field (purple) assures the plasma has an initial $\beta >10$ and that the ions are weakly magnetized.

Figure 2

Data from the BRB. (a) Time traces of the electrode currents. (b) Time traces of $B_z$ taken near the axis of the machine for four different initial field cases (0.4, 0.1, $-0.6,-1.6\mathrm{G}$). (c) Poloidal map of the magnetic field strength with lines of flux corresponding to case 1 from (b). The initial field is amplified by a factor of 20 on axis.

Figure 3

Linear profiles of the magnetic field, toroidal flow, and density during the plasma discharge for BRB and PCX. The shaded vertical bars indicate the radii of the anodes. The velocity profile for PCX was measured using the Fabry-Pérot spectrometer, with $20\mathrm{m}/\mathrm{s}$ uncertainty from the Bayesian analysis. Mach probe velocity measurements on the BRB have a roughly $100\mathrm{m}/\mathrm{s}$ error. On the BRB, profiles are measured along the cylindrical radius indicated by the red line in Fig. 1, approximately 40 cm from the equator. On PCX, the Fabry-Pérot flow measurement and density profile are made at the midplane, and the magnetic field profiles are measured slightly above the midplane (indicated by the red line in Fig. 1).

Figure 4

$|\mathbf{B}|/B_0$ and flux lines for nimrod simulations. In all cases, the initial field is uniform and has a strength of 0.5 G. The contour is plotted on a log scale. Left: case without Hall terms in Ohm’s law. Middle: case with Hall terms included in Ohm’s law and the current directed inward, which is the same direction as the PCX experiments. Right: Hall case with the current directed outward, which is the same as the experimental BRB case.

Figure 5

Scan of injected current versus normalized change in magnetic field for the two experiments. Top: the PCX case shows strong diamagnetic field removal, approaching total removal at approximately 80 A of injected current. For the BRB case, the field is amplified by nearly a factor of 20 at nearly 300 A of injected current.