Abstract
Kinetic simulations of Sandia National Laboratories’ Z machine are conducted to understand particle transport in the highly magnetized environment of a multi-MA accelerator. Joule heating leads to the rapid formation of electrode surface plasmas. These plasmas are implicated in reducing accelerator efficiency by diverting current away from the load [M.R. Gomez et al., Phys. Rev. Accel. Beams 20, 010401 (2017), N. Bennett et al., Phys. Rev. Accel. Beams 22, 120401 (2019)]. The fully-relativistic, electromagnetic simulations presented in this paper show that particles emitted in a space-charge-limited manner, in the absence of plasma, are magnetically insulated. However, in the presence of plasma, particles are transported across the magnetic field in spite of being only weakly collisional. The simulated cross-gap currents are well-approximated by the Hall current in the generalized Ohm’s law. The Hall conductivities are calculated using the simulated particle densities and energies, and the parameters that increase the Hall current are related to transmission line inductance. Analogous to the generalized Ohm’s law, we extend the derivation of the magnetized diffusion coefficients to include the coupling of perpendicular components. These yield a Hall diffusion rate, which is equivalent to the empirical Bohm diffusion.
Highlights
The pulsed-power TW-class accelerators driving fast Z-pinch experiments generate magnetic fields of 100– 1000 T by transporting multi-MA currents to mm-diameter loads [1,2]
While kA-class accelerators typically transition from vacuum operation to magnetically insulated transmission lines (MITLs) during the pulse, multi-MA accelerators progress from vacuum to MITL to dense electrode plasma formation within 10s of ns [8,9]
Electrode surface plasmas form during the pulse rise and evolve a Hall-currentrelated conductivity that scales with electron density and enables current to cross the gap in the presence of a strong magnetic field [9]
Summary
The pulsed-power TW-class accelerators driving fast Z-pinch experiments generate magnetic fields of 100– 1000 T by transporting multi-MA currents to mm-diameter loads [1,2] These high current densities create a charged particle environment in the accelerator transmission lines that is significantly denser (1015–1017 cm−3 [3,4]) than found in kA-scale accelerators (1010–1012 cm−3 [5,6,7]). Electrode surface plasmas form during the pulse rise and evolve a Hall-currentrelated conductivity that scales with electron density and enables current to cross the gap in the presence of a strong magnetic field [9]. The Hall conductivity is derived in a fluid description that assumes Maxwell distributions, we extract the densities and electric fields from kinetic simulations (with arbitrary distributions) to calculate the analogous cross-gap current. IV to show magnetized transport persists at larger radius (r ≥ 5 cm) such that even enhanced space-charged-limited (SCL) emission is largely insulated
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