Laboratory Resolved Structure of Supercritical Perpendicular Shocks

Supermagnetosonic perpendicular flows are magnetically driven by a large radius theta-pinch experiment. Fine spatial resolution and macroscopic coverage allow the full structure of the plasma-piston coupling to be resolved in laboratory experiment for the first time. A moving ambipolar potential is observed to reflect unmagnetized ions to twice the piston speed. Magnetized electrons balance the radial potential via Hall currents and generate signature quadrupolar magnetic fields. Electron heating in the reflected ion foot is adiabatic.

Figure 1

Experimental cross section. Blue shaded regions show the coverage of the Langmuir probe (wedge) and magnetic probes (rectangles). The red contour map qualitatively depicts the density during $\theta$-pinch compression, with blue dashes showing selected magnetic field lines. The four drive coils can be seen at $R=92$, $Z=\pm 15$, $\pm 40\mathrm{cm}$. Washer guns on axis supply the background plasma, which in the mirror configuration exhibits a relatively flat initial radial density profile.

Figure 2

Magnetic and Langmuir probe measurements of radially imploding $\theta$ pinch. This slice is taken at $z=0.05\mathrm{m}$, parallel to the “radial probe” in Fig. 1. The black dashed line is a linear fit to the peak of the toroidal current layer, with the dotted lines plotted for convenience at twice the speed. Note that the dotted lines border the earliest rise in density and temperature, and that the “reflection” through the axis aligns with an increase in $B_z$. Values from the starred locations are listed in Table 1, and data along the line at $t=12\mu \mathrm{s}$ are shown in Fig. 3. The radial electric field $E_r=-{\nabla }_r{V}_p$ is strongest along the current layer, as seen in Fig. 3. The drop in potential after $12\mu \mathrm{s}$ is a result of boundary conditions and electron heating in the foot, but does not affect $E_r$ in the layer.

Figure 3

$R$ profile at $z=0.05\mathrm{m}$, $t=12\mu \mathrm{s}$ showing $n_e$, $T_e$, and $V_p$ from Langmuir measurements and $J_{\varphi }$ and $B_z$ from magnetic measurements. Error bars show total error, not shot-to-shot uncertainty, which is small. The four colored areas left to right show the upstream, foot, layer, and downstream regions. The dashed red line is an adiabatic heating model, $T_e=T_{e0}(n_e/n_0{)}^{\gamma -1}$, for $\gamma =2$. The factor $\sigma \equiv {\omega }_{ce}^2/({\nu }_e^2+{\omega }_{ce}^2)$ is an experimental parameter that accounts for collisional slowing [26]. The dashed magenta line estimates the sum current of the electron and ion $E\times B$ $\widehat{\varphi }$ drifts, which is zero in MHD. Within error, the measured toroidal current is the sum of the $E\times B$ $\widehat{\varphi }$ and electron diamagnetic drifts.

Figure 4

(a) Plasma potential jump $\mathrm{\Delta }{\mathrm{\Phi }}_p$ vs convected ion kinetic energy $K_i=1/2m_i{v}_l^2$ showing a $1:1$ relationship. $\mathrm{\Delta }{\mathrm{\Phi }}_p$ was measured a distance of $d_i/2$ on either side of the layer peak with both emissive and Langmuir probes. (b) Current layer thickness against ${\beta }_e$ in the current layer for a variety of drive strengths in ${\mathrm{H}}_2$. As the magnetic piston becomes larger, the relative ${\beta }_e$ decreases, leading to weaker $\nabla B$ drifts and a thinner current layer.

Figure 5

Profile of toroidal magnetic field with arrows indicating direction of electron and ion flows. The red lobe at $(z,r)=(-0.8,0.5)\mathrm{m}$ implies current in the clockwise direction, consistent with an electron flow needed to maintain $\nabla ·\mathbf{J}=0$. The peak of the toroidal current layer is near the base of the red arrows. The axial density gradient from plasma injection at the $+\widehat{z}$ north pole skews the quadrupole slightly to the south.