Laser astrophysics experiment on the amplification of magnetic fields by shock-induced interfacial instabilities

Laser experiments are becoming established as tools for astronomical research that complement observations and theoretical modeling. Localized strong magnetic fields have been observed at a shock front of supernova explosions. Experimental confirmation and identification of the physical mechanism for this observation are of great importance in understanding the evolution of the interstellar medium. However, it has been challenging to treat the interaction between hydrodynamic instabilities and an ambient magnetic field in the laboratory. Here, we developed an experimental platform to examine magnetized Richtmyer-Meshkov instability (RMI). The measured growth velocity was consistent with the linear theory, and the magnetic-field amplification was correlated with RMI growth. Our experiment validated the turbulent amplification of magnetic fields associated with the shock-induced interfacial instability in astrophysical conditions. Experimental elucidation of fundamental processes in magnetized plasmas is generally essential in various situations such as fusion plasmas and planetary sciences.

Figure 1

Side-view sketch of the arrangement for the RMI experiment driven by a laser-induced shock in a weak ambient magnetic field. The GEKKO laser irradiates a polystyrene foil target in nitrogen gas. A permanent magnet applies the initial seed field at the target position.

Figure 2

Optical shadowgraph images of the target in shot no. 41767 (a) before the shot and (b) 40 ns after the shot. A modulated CH target was used in this shot so that the rear surface is subjected to the RMI. In the later evolutionary stage shown by panel (b), a fluctuated contact surface and a smooth transmitted shock emerged as a shadow. The field of view is 4.63 mm in diameter. The red arrow and mark in panel (a) denote the drive laser injection and the center of the laser focal spot, respectively. The indicated coordinate is for the three-axis induction coil probe.

Figure 3

Optical shadowgraph images of the target in shot no. 41765 (a) before the shot and (b) 40 ns after the shot. A flat CH target was used in this shot so that the rear surface is stable for the RMI. The indicated marks are the same as in Fig. 2.

Figure 4

Growth velocities of the modulation amplitude obtained in the GEKKO-laser experiment. The closed and open circles are the results of the shots with and without the initial magnetic field applied by a permanent magnet. The corresponding data shown in this figure are listed in Table 1. The red dashed curve is the linear growth velocity of the Wouchuk-Nishihara formula [49] using an experimentally obtained interface velocity given by Eq. (2). Here, the numerical factor is assumed to be $\left|\xi \right|=0.3$ (see Appendix pp1).

Figure 5

Interface velocities obtained in the experiment of the flat target with the seed magnetic field. The corresponding data shown in this figure are listed in Table 2. The blue dashed curve is the power-law fitting of the data given by Eq. (2). Here the interface velocity is fitted by a function $a{I}_L^b$ where $a$ and $b$ are the fitting parameters. (Inset) Streaked image of the shadowgraph for shot no. 41765. The silhouette of the interface between the CH foil and ${\mathrm{N}}_2$ gas is captured in this figure. The boundary is indicated by the red dashed line.

Figure 6

Streaked image of the self-emission from the shocked gas in shot no. 41765. The origin stands for the initial target position and the laser timing. The time profile of the shock velocity is obtained from the trajectory of the shock front. The shock-front position obtained from the shadowgraph image [Fig. 3] is plotted by the black mark at (3.9 mm, 40 ns). The white dashed line is the interface location measured by the shadowgraph streak image of this shot shown by the inset of Fig. 5. The blank data near 1.2 mm is due to the damage of the camera.

Figure 7

Time profiles of the signals in voltage detected by the inductive coil probes. The amplitude indicates the time derivative of the magnetic field strength for (a) a modulated-target case with the magnet, (b) a flat-target case with the magnet, and (c) a modulated-target case without the magnet. The shot number is indicated at the right bottom of each panel. Each component of the signals is shown in different colors. The later-phase signals in the highlighted period ($1.93<t \left[\mu \mathrm{s}\right] <3.57$) are used for the Fourier analysis shown in Fig. 8. The significant amplitude of signal noise at the laser timing $t=0$ can be seen in all cases.

Figure 8

Frequency spectra of the magnetic field energy calculated by the Fourier transform of the B-dot data for three types: (red) the modulated-target shots with the seed magnetic field, (green) the flat-target shots with the magnetic field, and (blue) the modulated-target shots without the magnet. Each spectrum is the average of two different shots with the same experimental conditions. The shot-by-shot fluctuation is indicated with the light color for the modulated-target (light red) and flat-target (light green) cases with the magnet. The light-color thickness stands for the deviation from the average for each shot. The selected period for the Fourier analysis is from 1.93 to 3.57 $\mu \mathrm{s}$ (see Fig. 7). The reference slope proportional to $f^{-11/3}$ is for the Kolmogorov turbulence. The dashed gray curve indicates the noise level calculated from the reference data taken before the shot.

Figure 9

Mach-number dependence of the linear growth velocity of the RMI. The relation between the growth velocity of the WN model $v_{\mathrm{wn}}$ and the interface velocity $v_i$ shown as a function of the incident Mach number $M$. The vertical axis is the ratio defined by a nondimensional factor $\xi =v_{\mathrm{wn}}/\left(k{\psi }_0{v}_i\right)$. The experimental parameters are adopted here for the evaluation of $v_{\mathrm{wn}}$, which are the density jump ${\rho }_{a0}/{\rho }_{b0}={10}^{-5}$ and the corrugation amplitude ${\psi }_0/\lambda =0.05$. The isentropic index is assumed to be $\gamma =5/3$.

Figure 10

Snapshots of the density distribution at 50 ns after the laser irradiation calculated by the FLASH code. The initial conditions of these radiation MHD simulations are almost the same as the experimental parameters for the cases of (a) a modulated target and (b) a flat target. Finger-like structures of the interface indicate the growth of the RMI with the wavelength of the initial modulation. Although there are tiny fluctuations of the interface in the flat-target case, the contact discontinuity is relatively smooth, the same as seen in the experiment.

Figure 11

Spatial distributions of the magnetic field at the nonlinear regime of the RMI in the modulated-target case. The color denotes the strength of the magnetic field in the unit of Tesla for (a) $B_x$, (b) $B_y$, and (c) $B_z$. The snapshots are taken at 50 ns after the laser hits the target. The $x$ and $z$ components are amplified by the RMI growth from a weak seed field. On the other hand, the $y$ component is generated only through the Biermann battery effect.

Figure 12

Time evolutions of the maximum strength of the magnetic field for each component in (a) the modulated-target case and (b) the flat-target case. The laser irradiation is from $t=0$ to 2.5 ns. The amplified magnetic fields $|B_x{|}_{max}$ and $|B_z{|}_{max}$ are depicted by the red circles and blue squares, respectively. The green triangles indicate the self-generated magnetic field $|B_y{|}_{max}$. The time profiles of the self-generated magnetic field in the reference simulations without the initial magnetic field are also shown by the gray circles.