Two-Dimensional Space-Charge-Limited Emission: Beam-Edge Characteristics and Applications

Umstattd, R.; Luginsland, J.W.

doi:10.1103/physrevlett.87.145002

Cited by 118 publications

(71 citation statements)

References 5 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: 67%

“…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: 67%

Section: Introductionmentioning

confidence: 99%

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

2005

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“…Lau 8 extended the SCL to quantum limits. Umstattd, 9 Luginsland, 10 and Rokhlenko 11 derived the semianalytic formula for two-dimensional SCL. Also, finite initial electron velocities have a strong influence on the SCL flow and have been well studied in the classical regime.…”

Section: Introductionmentioning

confidence: 99%

Consistent solution for space-charge-limited current in the relativistic regime for monoenergetic initial velocities

Feng

Verboncoeur

2008

Physics of Plasmas

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The solution for space-charge-limited (SCL) currents in electron vacuum diodes with monoenergetic initial velocity is extended to the relativistic regime. Two types of solutions are found: Type I corresponds to zero steady state surface electric field (field emission with high enhancement factor), and Type II corresponds to a finite steady state surface electric field (other emission mechanisms). Our solution compares well to the classical space-charge-limited currents with initial energy and relativistic space-charge limited currents without initial energy in the appropriate limits. The scaling law between the true SCL and the applied voltage is discussed and the two solution types are verified by particle-in-cell simulation.

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“…2 of Ref. 16. Note that the normalized average transmitted current density ͑averaged in time over the anode as shown in Fig.…”

Section: Average Transmitted Current In 2d Planar Geometrymentioning

confidence: 98%

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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Two-Dimensional Space-Charge-Limited Emission: Beam-Edge Characteristics and Applications

Cited by 118 publications

References 5 publications

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

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

Consistent solution for space-charge-limited current in the relativistic regime for monoenergetic initial velocities

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

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