Generalization of the Child–Langmuir law for nonzero injection velocities in a planar diode

Puri, Rajeev K.; Biswas, Debabrata; Kumar, Raghwendra

doi:10.1063/1.1644583

Cited by 38 publications

(31 citation statements)

References 11 publications

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“…In the above scenario, the initial velocity of the electrons is zero. Generalizations for non-zero initial velocity can be found in [4,5,6]. In two dimensions, analytical and numerical studies [7,8,9] indicate that the critical current is somewhat higher than the Child-Langmuir expression and is given by [7,9] …”

Section: Introductionmentioning

confidence: 99%

Power loss in open cavity diodes and a modified Child-Langmuir law

2005

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Diodes used in most high power devices are inherently open. It is shown that under such circumstances, there is a loss of electromagnetic radiation leading to a lower critical current as compared to closed diodes. The power loss can be incorporated in the standard Child-Langmuir framework by introducing an effective potential. The modified Child-Langmuir law can be used to predict the maximum power loss for a given plate separation and potential difference as well as the maximum transmitted current for this power loss. The effectiveness of the theory is tested numerically.

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Section: Introductionmentioning

confidence: 99%

Power loss in open cavity diodes and a modified Child-Langmuir law

2005

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“…The transmitted current density J TR ≤ J SCL depends on the value of the injected current density J IN . The exact dependence of J TR on J IN (> J SCL ) is complex even for a 1-D parallel-plate geometry [20], [22].…”

Section: B Drift Tubes: Closed and Openmentioning

confidence: 98%

“…The current flowing through the diode for a given cathode potential is commonly obtained from the Child-Langmuir law which gives, as a first approximation, the maximum current density that can flow across the diode for a given anode-cathode separation (D) and potential difference (V ) [18]- [22] J CL = 4 9…”

Section: A Diodes: Closed and Openmentioning

confidence: 99%

Efficiency Enhancement of the Axial VIRCATOR

Biswas

Kumar

2007

IEEE Trans. Plasma Sci.

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We present in this paper the particle-in-cell simulation results of a modified axial virtual cathode oscillator having a metallic drum of radius R 1 placed coaxially inside the drift tube at a distance D 1 from the foil anode. The enlarged parameter space permits control of the current transmitted to the collection plate, the net diode current, and the size of the electromagnetic emission and extraction regions. The geometry allows lowfrequency radiation as well as high-frequency microwaves to leak out from the extraction region. The microwave content in the total electromagnetic power is found to be maximum when the drum is sufficiently close to the anode but far enough to allow the formation of a virtual cathode and permit a large emission region. The microwave power and efficiency also depend sensitively on the radius of the metallic drum. As the drum radius increases, the diode current and cutoff-frequency for transverse-magnetic (TM) modes increase while the extraction window shrinks in size. For parameter values studied, a peak locally time-averaged (over several periods) microwave power of 210 MW was obtained using a square voltage pulse of 250 kV at an efficiency of 7% while the peak-period averaged power was found to be 275 MW. In the absence of the drum, the peak locally time-averaged microwave power obtained was 93 MW at an efficiency of 3.3%.Index Terms-Microwave, open drift tube, particle-in-cell (PIC), virtual cathode oscillator (VIRCATOR).

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“…The average transmitted current has been predicted using electrostatic theory for the infinite parallel plate geometry of the diode. 11 For an electron beam with zero injection velocity in an infinite parallel plate diode, the average transmitted current density ͑J TR ͒ is found to saturate at the value given by the Child-Langmuir law. However, for electron beams with nonzero injection velocity in the infinite planar geometry 11 J TR does not saturate at the space charge limited value ͑J SCL ͒.…”

Section: Introductionmentioning

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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Generalization of the Child–Langmuir law for nonzero injection velocities in a planar diode

Cited by 38 publications

References 11 publications

Power loss in open cavity diodes and a modified Child-Langmuir law

Power loss in open cavity diodes and a modified Child-Langmuir law

Efficiency Enhancement of the Axial VIRCATOR

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

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