Ultrafast probing of magnetic field growth inside a laser-driven solenoid

We report on the detection of the time-dependent B-field amplitude and topology in a laser-driven solenoid. The B-field inferred from both proton deflectometry and Faraday rotation ramps up linearly in time reaching 210 $\pm$ 35 T at the end of a 0.75-ns laser drive with 1 TW at 351 nm. A lumped-element circuit model agrees well with the linear rise and suggests that the blow-off plasma screens the field between the plates leading to an increased plate capacitance that converts the laser-generated hot-electron current into a voltage source that drives current through the solenoid. ALE3D modeling shows that target disassembly and current diffusion may limit the B-field increase for longer laser drive. Scaling of these experimental results to a National Ignition Facility (NIF) hohlraum target size ($\sim 0.2{\mathrm{cm}}^3$) indicates that it is possible to achieve several tens of Tesla.

Figure 1

Schematic of the experimental setup on Omega EP. TNSA protons generated at the gold foil drift perpendicular to the longitudinal B-field direction. A small sample of the protons passes through the coil by entering a 0.1-mm-diameter hole on the front plate and exiting a $0.1*0.25$-mm slot on the rear plate. ${\mathrm{SiO}}_2$ glass (inside and outside the coil) used for Faraday rotation is shown but is not present during proton measurements.

Figure 2

(a) Normalized proton dose measured on the Radiochromic film sensitive to 29.5 $\pm$ 0.5 MeV protons without the drive beam. (b) Normalized synthetic RCF data without a magnetic field.

Figure 3

(a) Synthetic RCF data for 180 kA of total current distributed uniformly across the length of the target. (b) Proton dose measured on the Radiochromic film sensitive to 29.5 $\pm$ 0.5 MeV protons 0.65 ns after the beginning of the drive beam. (c) Synthetic RCF data for 180 kA of total current distributed equally in two $\le 100-\mu \mathrm{m}$-wide regions at the edges of the solenoid. Red arrows and dotted lines indicate the curvature of the deflection at the top edge of the target

Figure 4

(a) Normalized proton dose of the Radiochromic film sensitive to 29.5 $\pm$ 0.5 MeV showing the three metrics. Protons were delayed 0.32 ns after the beginning of the drive. (b) Contour plot of the longitudinal B-field ($B_y$) divided by the B-field value at the target center (corresponds to $[y,z]=[0,0]$).

Figure 5

(a) Squares correspond to experimentally inferred on-axis B-fields. Error bar shows the quadratic sum of each metric's uncertainty. The plain red (dashed green) line corresponds to the B-field amplitude obtained using the lumped-element circuit current for $C=$ 0.3 nF (0.06 pF) (b) B-field at $t=0.6\pm 0.1$ ns after the beginning of the laser drive. Diamonds correspond to Faraday measurements and the square to proton deflectometry. (c) Lumped-element circuit of the laser-driven solenoid with coupled equations for the voltage between the plates, $V_C$, and the current inside the loop, $I_L$. $I_S$ is the current source, $C, L$, and $R$ are the target capacitance, inductance, and resistance.

Figure 6

(a) $4\omega$ angular filter refractometer 250 ps after the beginning of the drive (b) 650 ps after the beginning of the drive. Laser is coming from the left hitting the rear plate (right plate) at $\mathrm{z}\sim 1\mathrm{mm}$, the loop center is at $z=0$ mm.