On the saturation in the average transmitted current in two-dimensional planar diodes

Kumar, Raghwendra; Biswas, Debabrata

doi:10.1063/1.3234246

Cited by 4 publications

(1 citation statement)

References 18 publications

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“…For two-dimensional (2D) geometry, particle simulations by Luginsland et al, 8 and a simple theory by Lau, 9 have demonstrated that the 2D rearrangement of the equipotential profiles allows the extracted current to exceed the Child-Langmuir limit as the distance to the anode is increased. Further 2D simulations by Kumar and Biswas 10 have addressed the time-dependent behavior encountered for large injection currents. They also find that, on average, the transmitted currents can exceed the Child-Langmuir limit.…”

Section: Introductionmentioning

confidence: 99%

Plasma flows generated by an annular thermionic cathode in a large magnetized plasma

et al. 2019

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A LaB 6 thermionic emitter of annular shape is used in the Large Plasma Device at the University of California, Los Angeles to create off-axis heating conditions for various transport studies. Since the emitter is biased relative to a distant anode, which is many collision lengths away, the entire magnetized plasma develops a self-consistent, potential structure that simultaneously generates transverse and axial flows with shear. This study uses swept Langmuir probe techniques and Mach probes to map the flow patterns and their dependence on bias and plasma parameters. By implementing additional biasing configurations, it is possible to control the magnitude of the flows and their shear strength. The experimental measurements, including the selfconsistent currents, are compared to predictions of a model that incorporates the boundary conditions associated with thermionic injection, combined with a Braginskii transport code for the electron temperature.

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Section: Introductionmentioning

confidence: 99%

Plasma flows generated by an annular thermionic cathode in a large magnetized plasma

et al. 2019

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On the Child–Langmuir law in one, two, and three dimensions

Lau,

Li,

Chernin

2023

Physics of Plasmas

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We consider the limiting current from an emitting patch whose size is much smaller than the anode–cathode spacing. The limiting current is formulated in terms of an integral equation. It is solved iteratively, first to numerically recover the classical one-dimensional Child–Langmuir law, including Jaffe's extension to a constant, nonzero electron emission velocity. We extend to two-dimensions in which electron emission is restricted to an infinitely long stripe with infinitesimally narrow stripe width so that the emitted electrons form an electron sheet. We next extend to three-dimensions in which electron emission is restricted to a square tile (or a circular patch) with an infinitesimally small tile size (or patch radius) so that the emitted electrons form a needlelike line charge. Surprisingly, for the electron needle problem, we only find the null solution for the total line charge current, regardless of the assumed initial electron velocity. For the electron sheet problem, we also find only the null solution for the total sheet current if the electron emission velocity is assumed to be zero, and the total maximum sheet current becomes a finite, nonzero value if the electron emission velocity is assumed to be nonzero. These seemingly paradoxical results are shown to be consistent with the earlier works of the Child–Langmuir law of higher dimensions. They are also consistent with, or perhaps even anticipated by, the more recent theories and simulations on thermionic cathodes that used realistic work function distributions to account for patchy, non-uniform electron emission. The mathematical subtleties are discussed.

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