Dynamics of laser-generated magnetic fields using long laser pulses

We report on the experimental investigation of magnetic field generation with a half-loop gold sheet coil driven by long-duration (10 ns) and high-power (0.5 TW) laser pulses. The amplitude of the magnetic field was characterized experimentally using proton deflectometry. The field rises rapidly in the first 1 ns of laser irradiation, and then increases slowly and continuously up to 10 ns during further laser irradiation. The transient dynamics of current shape were investigated with a two-dimensional (2D) numerical simulation that included Ohmic heating of the coil and the resultant change of electrical resistivity determined by the coil material temperature. The numerical simulations show rapid heating at the coil edges by current initially localized at the edges. This current density then diffuses to the central part of the sheet coil in a way that depends both on normal current diffusion as well as temporal changes of the coil resistance induced by the Ohmic heating. The measured temporal evolution of the magnetic field is compared with a model that determines a solution to the coil current and voltage that is consistent with a plasma diode model of the drive region and a 2D simulation of current diffusion and dynamic resistance due to Ohmic heating in the laser coil.

Figure 1

Experimental setup of proton deflectometry for the measurement of the magnetic field which is illustrated in three and two dimensions. The magnetic field is generated with a half-loop gold sheet coil driven by one of two nanosecond OMEGA-EP beams that have an energy of 5 kJ, a power of 0.5 TW, and a duration of 10 ns. The generated magnetic field is toward the $z$-direction. The protons are generated from the thin gold foil irradiated with a picosecond OMEGA-EP beam, which have an intensity of $8\times {10}^{18}\mathrm{W}/{\mathrm{cm}}^2$. The proton beam imprint by the grid is deflected by the generated magnetic field and detected by radiochromic films.

Figure 2

Comparisons between the experimental (right half) and computed (left half) proton images in the case of (a) no laser-irradiation (cold target) and images obtained at (b) 0.62, (c) 1.15, and (d) 7.08 ns after the beginning of the laser irradiation. The computed image reproduces well the experimental proton image. The small difference in the shape of the coil shadow between left and right comes from the difference in coil shape, namely a half-loop in the experiment and a cylinder in the calculation.

Figure 3

Line-outs of the integrated current density and 2D distribution of the coil temperature at (a) 0.6 ns, (b) 1.1 ns, and (c) 3 ns after laser irradiation from the transient simulation. We also plot in (d) a line-out of the magnetic field distribution along the central axis. The integrated current density approaches a uniform distribution accompanied by current diffusion and heating from the edges to the whole body. The width of the magnetic field narrows because of the current density diffusion. The magnetic fields are normalized by the value at the center.

Figure 4

Relation between voltage and current ($V\text{−}I$) based on the laser-diode model. The current in a laser-driven coil is limited by the space-charge potential (solid and dashed black lines) and the self-magnetization of hot electron flow (blue line). The maximum current is limited to 680 kA at 21 kV. The red points show the temporal change of the $V\text{−}I$ relation in this experiment. The calculated current is mainly limited by the space-charge potential labeled as Courtois's limit.

Figure 5

Time evolution of (a) the edge magnetic field estimated from the experiment (filled squares) and calculated using the circuit model (solid black curve), and (b) the effective resistance calculated with the 2D transient simulation. We also show the predicted magnetic field resulting from including only the current diffusion (resistivity is temperature-independent). The circuit model with the time-dependent resistance estimated from the transient simulation has good agreement with the experimental data.