Current and current density of a finite-width, space-charge-limited electron beam in two-dimensional, parallel-plate geometry

Watrous, J.J.; Luginsland, J.W.; Fresé, Michael

doi:10.1063/1.1391262

Cited by 50 publications

(29 citation statements)

References 8 publications

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“…6 In addition to the 1D models, the extension of the classical 1D planar CL law to two-dimensional ͑2D͒ models has been a subject of much interest in recent years. [8][9][10][11][12][13] For uniform cold electron emission, a 2D planar classical CL law has been derived analytically, 8 which agrees well with the simulation results. 9 Enhanced emission near to the beam edges has also been reported in various 2D nonuniform emission models.…”

Section: Introductionsupporting

confidence: 62%

“…9 Enhanced emission near to the beam edges has also been reported in various 2D nonuniform emission models. [10][11][12][13] These 2D classical CL models are focused only on simple 2D finite emitting patches with cold electron emission, where the effects of finite emission energy, 3D emitting patches, and curvature of the electrodes are not included. The 2D classical CL law for a cylindrical gap with finite width has also been simulated 14 and derived, 15 but both findings are limited and contain some discrepancies.…”

Section: Introductionmentioning

confidence: 99%

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Three-dimensional Child–Langmuir law for uniform hot electron emission

2005

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This paper presents a three-dimensional (3D) model of Child–Langmuir (CL) law for uniform hot electron emission in planar and cylindrical gap, including the effects of finite emission energy. It is found that the enhancement of 3D CL law (in terms of 1D CL law) can be written in a general form of JC[3D]∕JC[1D]=1+F×G, where F is the normalized mean position of 1D electron flow in classical, weakly relativistic, and quantum regime, and G is the geometrical correction factor depending on the geometrical properties of the finite emitting patches on the cathode. In particular, we present the analytical solutions for various emitting patches, such as rectangle, ellipse, square, circle, triangle, and polygon, which agree very well with 3D particle-in-cell simulation. For a cylindrical gap of finite width, it is also found that the convergent flow (cathode outside) has larger enhancement than the divergent flow (cathode inside) at a given aspect ratio of outer radius to inner radius of the gap. Smooth transition from various operating regimes is demonstrated.

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Section: Introductionsupporting

confidence: 62%

Section: Introductionmentioning

confidence: 99%

Three-dimensional Child–Langmuir law for uniform hot electron emission

2005

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“…The electric field at the cathode and its dependence on injection current has been earlier investigated by other researchers 15,16 using a selfconsistent numerical technique. 17 The results obtained in Refs. 15-17 are confirmed in this study using PIC simulation.…”

Section: Introductionmentioning

confidence: 78%

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

Kumar

Biswas

2009

Physics of Plasmas

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The relation between average transmitted current density (JTR) and injected current density (JIN) in a two-dimensional planar diode is investigated using particle-in-cell simulation. Beyond the space charge limited value of injected current density, JTR is found to increase slowly with JIN and finally saturate for higher values. The physics of gradual increase in JTR to the saturation value is explained using the electric field profile at the cathode surface.

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“…The space-charge-limited algorithm used in ICEPIC has been extensively validated against both theoretical predictions and experimental measurements. 9,10 The space charge limited current drawn during oscillation was calculated to be 16.3 A. The power draw was 362 kW.…”

Section: Icepic Resultsmentioning

confidence: 99%

Faceted magnetron concept using field emission cathodes

Browning¹,

Watrous²

2011

Journal of Vacuum Science &Amp; Technology B, Nanotechnology and Microelectronics: Materials, Processing, Measurement, and Phen

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Jack WatrousNumerEx A magnetron concept using field emission cathodes has been modeled with the Air Force Research Laboratory particle-in-cell code ICEPIC and the 2D particle trajectory simulation Lorentz2E. In this approach, field emitters are used to provide a distributed cathode in place of a traditional thermionic cathode. The emitters are placed below the interaction space in a shielded structure. The cathode is comprised of facet plates with slits to protect the emitters. Simulation of an L-band rising sun magnetron shows that the faceted magnetron will oscillate using both five and ten facet cathodes. The startup times are very similar to that of a cylindrical cathode magnetron. The electron trajectories of the shielded slit structure have been modeled, and the results indicate that electrons can be injected through the slits and into the interaction space using lateral edge emitters and a pusher electrode design.

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Current and current density of a finite-width, space-charge-limited electron beam in two-dimensional, parallel-plate geometry

Cited by 50 publications

References 8 publications

Three-dimensional Child–Langmuir law for uniform hot electron emission

Three-dimensional Child–Langmuir law for uniform hot electron emission

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

Faceted magnetron concept using field emission cathodes

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