An analytic theory is presented that yields the maximum transmittable current across an anodecathode gap that is embedded in an arbitrary transverse magnetic field (B). The limiting current is found to be relatively insensitive to B for all B < BH, where BH is the Hull cutoff magnetic field required for magnetic insulation. The classical Child-Langmuir solution is recovered in the limit B-+0.

Pulsed power accelerators compress electrical energy in space and time to provide versatile experimental platforms for high energy density and inertial confinement fusion science. The 80-TW “Z” pulsed power facility at Sandia National Laboratories is the largest pulsed power device in the world today. Z discharges up to 22 MJ of energy stored in its capacitor banks into a current pulse that rises in 100 ns and peaks at a current as high as 30 MA in low-inductance cylindrical targets. Considerable progress has been made over the past 15 years in the use of pulsed power as a precision scientific tool. This paper reviews developments at Sandia in inertial confinement fusion, dynamic materials science, x-ray radiation science, and pulsed power engineering, with an emphasis on progress since a previous review of research on Z in Physics of Plasmas in 2005.

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It is shown that a small amount of dissipation, caused by current flow in a lossy external circuit, can produce a disruption of steady-state cycloidal electron flow in a crossed-field gap, leading to the establishment of a turbulent steady state that is close to, but not exactly, Brillouin flow. This disruption, which has nothing to do with a diocotron or cyclotron instability, is fundamentally caused by the failure of a subset of the emitted electrons to return to the cathode surface as a result of resistive dissipation. This mechanism was revealed in particle simulations, and was confirmed by an analytic theory. These near-Brillouin states differ in several interesting respects from classic Brillouin flow, the most important of which is the presence of a microsheath and a time-varying potential minimum very close to the cathode surface. They are essentially identical to that produced when ͑i͒ injected current exceeds a certain critical value ͓P. J. Christenson and Y. Y. Lau, Phys. Plasmas 1, 3725 ͑1994͔͒ or ͑ii͒ a small rf electric field is applied to the gap ͓P. J. Christenson and Y. Y. Lau, Phys. Rev. Lett. 76, 3324 ͑1996͔͒. It is speculated that such near-Brillouin states are generic in vacuum crossed-field devices, due to the ease with which the cycloidal equilibrium can be disrupted. Another novel aspect of this paper is the introduction of transformations by which the nonlinear, coupled partial differential equations in the Eulerian description ͑equation of motion, continuity equation, Poisson equation, and the circuit equation͒ are reduced to an equivalent system of very simple linear ordinary differential equations.

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