Azimuthal magnetic field distribution in gas-puff $Z$-pinch implosions with and without external magnetic stabilization

An experimental study of the magnetic field distribution in gas-puff $Z$ pinches with and without a preembedded axial magnetic field ($B_{z0}$) is presented. Spatially resolved, time-gated spectroscopic measurements were made at the Weizmann Institute of Science on a 300 kA, 1.6 μs rise time pulsed-power driver. The radial distribution of the azimuthal magnetic field, $B_{\theta }$, during the implosion, with and without a preembedded axial magnetic field of $B_{z0}=0.26\mathrm{T}$, was measured using Zeeman polarization spectroscopy. The spectroscopic measurements of $B_{\theta }$ were consistent with the corresponding values of $B_{\theta }$ inferred from current measurements made with a B-dot probe. One-dimensional magnetohydrodynamic simulations, performed with the code trac-ii, showed agreement with the experimentally measured implosion trajectory, and qualitatively reproduced the experimentally measured radial $B_{\theta }$ profiles during the implosion when $B_{z0}=0.26\mathrm{T}$ was applied. Simulation results of the radial profile of $B_{\theta }$ without a preembedded axial magnetic field did not qualitatively match experimental results due to magneto-Rayleigh-Taylor (MRT) instabilities. Our analysis emphasizes the importance of MRT instability mitigation when studying the magnetic field and current distributions in $Z$ pinches. Discrepancies of the simulation results with experiment are discussed.

Figure 1

Profile of load current and response of UV-visible photodiode. The inductive current notch and peak photodiode signal occur close to 700 ns. The photodiode peaks at 250 and 555 ns are signals from timing monitors for the laser and imaging ICCD, respectively.

Figure 2

Diagram of the experimental arrangement. The elements are as follows: (a) polarizing beam splitter cube, (b) λ/4 wave plate, (c) lenses, (d) flat mirrors, (e) spherical mirror, and (f) bifurcated fiber bundle.

Figure 3

Example of a spectral image for $B_{\theta }$ measurement (a). The rectangles correspond to the positions from which the spectral sample was taken and correspond to the edge of emission for that spectral line. Plots of the lineouts are shown for O III (b) and O VI (c).

Figure 4

Images obtained from the time-gated ICCD for eight shots, each taken at different times relative to the pinch. The top four images correspond with $B_{z0}$ and the bottom four without $B_{z0}$. The $z=0\mathrm{mm}$ position corresponds to the edge of the nozzle injector (anode).

Figure 5

Implosion trajectories for cases with and without initial axial magnetic field. Each data point is taken from a separate shot and axially integrated between 3 and 9 mm from the anode. The horizontal error bars correspond to the 5 ns integration time of the detector while the vertical error bars account for the resolution limitation of the imaging camera. The solid curves represent the motion of the outer plasma radius from the trac-ii simulation results.

Figure 6

Evolution of $B_{\theta }$ at the outer plasma radius for the cases (a) with a preembedded axial magnetic field and (b) without a preembedded axial magnetic field. The expected (Ampere's law) curve represents the range of calculated values of $B_{\theta }$ based on the B-dot measured current and outer plasma radius at the time of the $B_{\theta }$ measurement. The horizontal error bars correspond to 30 ns integration time of the detector.

Figure 7

Measured (dashed lines with points) and simulated (solid lines) radial profiles of the azimuthal magnetic field for various points in time for experiment and simulation with (a) axial magnetic field and without (b). The wide band of the gray curve denoted as “Ampere's law” is such to account for the range of current values measured for all discharges. Circular points were measured from O III, while square points were measured from O VI.