Magnetohydrodynamics of laser-produced high-energy-density plasma in a strong external magnetic field

Recent progress in the generation in the laboratory of a strong ($>100$-T) magnetic field enables us to investigate experimentally unexplored magnetohydrodynamics phenomena of a high-energy-density plasma, which an external magnetic field of 200–300 T notably affects due to anisotropic thermal conduction, even when the magnetic field pressure is much lower than the plasma pressure. The external magnetic field reduces electron thermal conduction across the external magnetic field lines because the Larmor radius of the thermal electrons in the external magnetic field is much shorter than the mean free path of the thermal electrons. The velocity of a thin polystyrene foil driven by intense laser beams in the strong external magnetic field is faster than that in the absence of the external magnetic field. Growth of sinusoidal corrugation imposed initially on the laser-driven polystyrene surface is enhanced by the external magnetic field because the plasma pressure distribution becomes nonuniform due to the external magnetic-field structure modulated by the perturbed plasma flow ablated from the corrugated surface.

Figure 1

Experimental configurations for studying the hydrodynamics of HEDPs in an external magnetic field. (a) Experimental setup for the $B_{\parallel }$ geometry, in which the magnetic-field lines are parallel to the ablated plasma motion. (b) Experimental setup for the $B_{\perp }$ geometry, in which the magnetic-field lines are perpendicular to the ablated plasma motion. Tantrum plates, 50 $\mu \mathrm{m}$ thick, are placed at the bottom and top of the polystyrene foils to prevent the foils from being preheated by x rays generated at the capacitor plates. Magnetic-field structures computed using the radia code for the (c) $B_{\parallel }$ and (d) $B_{\perp }$ geometries.

Figure 2

(a) Top view of the target used in a trajectory measurement. A 25-$\mu \mathrm{m}$-thick polystyrene foil was mounted on a 25-$\mu \mathrm{m}$-thick beryllium frame. A 50-$\mu \mathrm{m}$-thick aluminum spacer was inserted between the foil and the frame. (b) Face view of a target used in the trajectory measurement. The width of the polystyrene foil was $150\mu \mathrm{m}$ along the line of sight of the diagnostics. The polystyrene foil and the beryllium frame are irradiated by the 500-$\mu \mathrm{m}$ diameter laser beam. Shadow of laser-driven polystyrene foils measured using side-on x-ray backlighting (c) with no external magnetic field and (d) in the $B_{\parallel }$ and (e) $B_{\perp }$ geometries. The rear surfaces of laser-driven polystyrene foils (black symbols) are compared with the results of simulations carried out using the pinoco-mhd code for (f) no external magnetic field and for (g) the $B_{\parallel }$ and (h) the $B_{\perp }$ geometries. Solid black and dashed lines are pinoco-mhd calculations with and without consideration of the external magnetic field, respectively. The origins of the axes are defined as the laser peak timing and initial position of the target's rear surface.

Figure 3

Two-dimensional mass density and magnetic flux density distributions at the laser peak timing for (a) $B_{\parallel }$ and (b) $B_{\perp }$. The origin of the position is defined as the initial position of the target's rear surface. (c–f) Electron temperature and pressure profiles along the target's center axis The electron temperature (solid lines) of the ablated plasmas increases notably in the external magnetic field due to anisotropic thermal conduction as shown for $B_{\parallel }$ (c) and $B_{\perp }$ (d) compared to that without a magnetic field (dotted lines). The pressure (solid lines) of the ablated plasmas also increases in the external magnetic field, as shown for $B_{\parallel }$ (e) and $B_{\perp }$ (f) compared to that without a magnetic field (dotted lines).

Figure 4

Snapshot of 50-$\mu \mathrm{m}$-wavelength perturbations on a laser-accelerated polystyrene foil simulated using the pinoco-mhd code for (a) no external magnetic field and (b) the $B_{\parallel }$ geometry. Solid black lines are lines of equal density for the target solid density of $1\mathrm{g}/{\mathrm{cm}}^3$, and dashed red lines are isotherms of the electron temperature plotted in 10-eV increments. (c) The anisotropic thermal conduction in the perturbed magnetic-field structure leads to enhancement of the perturbation growth.

Figure 5

(a) Face-on x-ray backlight image and its line-out at the laser peak timing. The origin of the axis is defined as the laser peak timing. (b) Comparison of the temporal evolution of areal density modulations measured in the experiment versus calculated by the pinoco-mhd code.