The Brillouin flow is widely considered as the equilibrium state in many crossed-field devices including magnetrons, crossed-field amplifiers (CFAs), magnetically insulated line oscillators (MILOs) and magnetically insulated transmission lines (MITLs). Explicit, closed form solutions, together with scaling laws have been found for the electron flows in terms of the gap voltage and the magnetic flux [1], whether the magnetic insulation is provided by the wall currents, as in a MITL and MILO, or by an external magnet, as in a magnetron and CFA, or by some combination of the two. These scaling laws, together with our recent MILO experiments, revealed some unexpected features, and pointed to the importance of the transition from magnetic insulation to nonmagnetic insulation. Also addressed are the implications on these crossed-field flows from recent extensions of the Ramo-Shockley theorem and of the Child-Langmuir law.

1. Y. Y. Lau, D. A. Packard, C. J. Swenson, J. W. Luginsland, D. Li, A. Jassem, N. M. Jordan, R. D. McBride, and R. M. Gilgenbach, “Explicit Brillouin flow solutions in magnetrons, magnetically insulated line oscillators, and radial magnetically insulated transmission lines,” IEEE Trans. Plasma Sci., vol. 49, no. 11, pp. 3418–3437, Nov. 2021.

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* Research supported by AFOSR MURI grant No. FA9550-20-1-0409 through the University of New Mexico, and by AFOSR grant Nos. FA9550-21-1-0184, and FA9550-21-1-0367.

Power flow studies on the 30-MA, 100-ns Z facility
at Sandia National Labs (SNL) have shown that plasmas in the
facility’s magnetically insulated transmission lines (MITLs)
can result in a loss of current delivered to the load. 1 During the
current pulse, thermal energy deposition into the electrodes
(ohmic heating, charged particle bombardment, etc.) causes
neutral surface contaminants layers (water, hydrogen,
hydrocarbons, etc.) to desorb, ionize, and form plasmas in the
anode-cathode (AK) gap. 2 Shrinking typical electrode
thicknesses (~1 cm) down to that of thin foils (5−200 µm)
produces observable amounts of plasma on smaller pulsed
power drivers (≤1 MA). 3 We suspect that as the electrode
material bulk thickness decreases relative to the skin depth of
the current pulse (50−100 µm for a 100−500-ns pulse in
aluminum), the thermal energy delivered to the neutral surface
contaminant layers increases, and thus surface contaminants
desorb faster from the current carrying surface.

In this talk, we review recent experimental results
using thin foil loads on the Mykonos facility at Sandia
National Labs to characterize the electrode contaminant layer
with the plasma temperature, density, and determination of the
species and their ionized states during surface desorption.
These results are collected using streaked visible spectroscopy
and a vacuum ultraviolet (VUV) spectroscopy system
developed to measure the atomic hydrogen Lyman-α line
(121.6 nm) and molecular hydrogen bands from wires and
foils with varying thicknesses (5−200 µm) and materials.
We use the VUV measurements to compare hydrogen
inventories to those predicted to be released via thermal
processes in the electrodes. The contaminant desorption,
thermal diffusion, hydrogen diffusion in the solid bulk, and
desorbed density, temperature and ionization profiles are
modeled in a new 1-D semi-analytic solver. The results from
the model are then used to run PrismSPECT simulations to
compare against experiment.

1. W.A. Stygar et al., Phys. Rev. S.T.-A.B. 12, 120401 (2009)
2. N. Bennett et al., Phys. Rev. A.B. 22, 120401 (2019)
3. T.J. Smith et al., Rev. Sci. Inst. 92, 053550 (2021)

*This work was supported by SNL and by the NNSA SSAP
under DOE Cooperative Agreement DENA0003764. SNL is a
multi-mission laboratory managed and operated by National
Technology and Engineering Solutions of Sandia, LLC., a
wholly owned subsidiary of Honeywell International, Inc., for
the U.S. D.O.E. NNSA under contract DE-NA-0003525.

Current losses in the magnetically insulated region of high-power pulsed power machines represents a major engineering challenge in the design of next-generation drivers. However, due to the difficulty of diagnostic access in the magnetically insulated transmission lines (MITLs) of drivers like the Z Machine at Sandia National Laboratories, it is very difficult to study these losses. In order to develop a better understanding of these phenomena, it is crucial to be able to conduct experiments at scale in smaller facilities. The typical power flow scaling experiment, known as the “stripline”, uses two parallel planar conductors connected in a loop such that current flows up one conductor and down the other, thus producing an environment nominally similar to a MITL. However, on university-scale pulsed power drivers (of typically ~1 MA peak current), it is difficult to produce stripline experiments with current densities and electric fields that match expected peak fields in next generation pulsed power machines, while also capturing the magnetic diffusion and other solid-state physics that may be relevant as well. In this presentation, we discuss a novel experiment that has been tested on the MAGPIE driver at Imperial College. Called the "exploding hairpin", this geometry uses wires of circular cross-section bent into slightly inductive loops. Since it is far easier to work with small-diameter wires than very thin planar foils, manufacturing costs are dramatically reduced compared to similar stripline experiments. In addition, the curvature of the wire cross-section provides field enhancement at the apex of the curve, making even higher magnetic and electric field strength attainable. Lastly, the inductance of the loop can easily be varied, providing precise tuning of the electric and magnetic field strengths in the experiment. Simulation results indicate that magnetic fields ranging from 70 T to 300 T and electric fields ranging from 30 MV/m to 650 MV/m can be produced with this geometry on MAGPIE. Several simulations of different hairpin designs are presented using COMSOL and GORGON; these simulations are then compared to the experimental results, and possible explanations for current losses in the inner MITL are then discussed in light of the experimental results.

SAND2023-02545C
This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.
Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA0003525.