Quasistationary magnetic field generation with a laser-driven capacitor-coil assembly

Recent experiments are showing possibilities to generate strong magnetic fields on the excess of 500 T with high-energy nanosecond laser pulses in a compact setup of a capacitor connected to a single turn coil. Hot electrons ejected from the capacitor plate (cathode) are collected at the other plate (anode), thus providing the source of a current in the coil. However, the physical processes leading to generation of currents exceeding hundreds of kiloamperes in such a laser-driven diode are not sufficiently understood. Here we present a critical analysis of previous results and propose a self-consistent model for the high current generation in a laser-driven capacitor-coil assembly. It accounts for three major effects controlling the diode current: the space charge neutralization, the plasma magnetization between the capacitor plates, and the Ohmic heating of the external circuit—the coil-shaped connecting wire. The model provides the conditions necessary for transporting strongly super-Alfvenic currents through the diode on the time scale of a few nanoseconds. The model validity is confirmed by a comparison with the available experimental data.

Figure 1

Scheme of the capacitor coil target with notations used in the paper. The materials commonly used for target fabrication are aluminum, copper, nickel, and gold.

Figure 2

Measurements of magnetic fields at the coil center of nickel targets with different diagnostics as reported in Refs. [8] (a) and [9] (b).

Figure 3

Potential (a) and density (b) distribution in the diode. Stationary distribution is shown with solid lines, and dashed lines show the transient distribution before the potential equilibration.

Figure 4

Optical shadowgraphy (at 532 nm) of the coil expansion. On the left, 0.65-ns-gated images corresponding to a cold coil (top, $t=0$) and two different timings after laser driving of the capacitor-coil target. On the right, the ns-scale expansion is resolved in a single shot by imaging the coil diameter into the slit of a streak camera. The average expansion velocity of the coil rod was measured to be $11\pm 3\mu \mathrm{m}$/ns (as indicated by the dashed orange line). Data acquired on the experimental campaign [8].

Figure 5

Dependence of the parameter $g$ on the plasma flow divergence ${\alpha }_0$ and the ratio $d/r_h$ according to Eq. (17). The values of ${\alpha }_0$ are shown with numbers near the correspondent curves.

Figure 6

Current-voltage characteristic of the diode $V_c\left(I\right)$ accounting for the effects of the space charge and magnetization. The chosen set of parameters corresponds to the experiments [5] (a), [6] (b), and [10] (c). The distance between the diode plates is set to 1 mm and the resistance $R_c=1\mathrm{\Omega }$.

Figure 7

Temporal dependence of the current $I_c$ (a) and tension (b) in the diode-coil circuit (a) and the circuit impedance $Z_c=V_c/I_c$ (c). The parameters correspond to the experiment [8].