Perpendicular Subcritical Shock Structure in a Collisional Plasma Experiment

We present a study of perpendicular subcritical shocks in a collisional laboratory plasma. Shocks are produced by placing obstacles into the supermagnetosonic outflow from an inverse wire array z pinch. We demonstrate the existence of subcritical shocks in this regime and find that secondary shocks form in the downstream. Detailed measurements of the subcritical shock structure confirm the absence of a hydrodynamic jump. We calculate the classical (Spitzer) resistive diffusion length and show that it is approximately equal to the shock width. We measure little heating across the shock ($<10\%$ of the ion kinetic energy) which is consistent with an absence of viscous dissipation.

Figure 1

Cross sectional diagram of the wire array and obstacles. (a) Side-on view. Cylindrical obstacles extend into the page, and shocks are indicated where they form in the experiment. (b) End-on view showing the azimuthal configuration of wires in the array and the vector diagram for the Thomson scattering diagnostic.

Figure 2

Electron density and magnetic field measurements. (a) Electron density recorded 426 ns after current start. The edge of the wire array is at $x=0\mathrm{mm}$. (b) Magnetic field 397 ns after current start. The region sampled by the lineout in Fig. 3 is shown.

Figure 3

Thomson scattering data and plasma parameter profiles. (a) Flow velocity at 416 ns with electron density and magnetic field lineouts at $z=0\mathrm{mm}$. The region in which the magnetic field measurement was affected by shadowgraphy is shaded. (b) Temperature at $z=0\mathrm{mm}$. A characteristic error bar which includes modeling uncertainty is shown for the final data point (we expect this to be mostly systematic). (c) Velocity compared with the sound speed $C_S$, Alfvén speed $V_A$, and fast-magnetosonic speed $V_{\mathrm{MS}}$ across the subcritical shock. Values which depend on $B$ are excluded for $x=8–9\mathrm{mm}$ where Faraday rotation measurements are affected by shadowgraphy.

Figure 4

Ion temperature, electron temperatures, velocity, and $C_S$ at $z=-2\mathrm{mm}$.

Figure 5

Simulation results at 400 ns. (a) Matched shock position with $B_u=4.8\mathrm{T}$. (b) Matched $B_u$.

Figure 6

Comparison of simulated parameters, in the midplane between the obstacles, at 400 ns (solid lines) with the experimental parameters presented in Fig. 3 (data points and dashed lines). The light blue dashed line shows the experimental $B$ field scaled up by a factor of 1.3, the maximum systematic error attributable to line integration effects in the Faraday rotation data.

Figure 7

Comparison of the flow velocity with $C_S$, $V_A$, and $V_{\mathrm{MS}}$. The velocity in the simulation frame is dashed, and the velocity in the shock frame is solid ($v_{\text{shock}}=v_{\mathrm{sim}}+22.5{\mathrm{km}\mathrm{s}}^{-1}$ at 400 ns). To determine the type of shock, $v_{\text{shock}}$ should be used.

Figure 8

Position vs time data at $z=0\mathrm{mm}$ (the midplane). The maximum electron density in the simulation is compared with the maximum experimental electron density (from different shots) and the peak optical self-emission intensity (from a single shot). Optical self-emission images were recorded with a 30 ns interframe spacing and a 5 ns exposure along the same line of sight as the interferometry. In this experimental regime where the temperature is relatively constant, the optical self-emission intensity is well correlated with electron density.