Approximate analytical solutions for the space-charge-limited current in one-dimensional and two-dimensional cylindrical diodes

Chen, Xupeng; Dickens, J.; Hatfield, L.L.; Choi, Eun-Ho; Kristiansen, M.

doi:10.1063/1.1743309

Cited by 30 publications

(25 citation statements)

References 8 publications

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“…[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. Simple extension of the classical 2D CL models to other regimes, such as relativistic and quantum regime has not been developed.…”

Section: Introductionmentioning

confidence: 98%

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: Introductionmentioning

confidence: 98%

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

2005

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“…Approximate analytical solutions for the space-charge limited current in 1D and 2D cylindrical diodes have been also calculated by various authors. 7,8 Our observation can be described by a simple model for the electron space-charge limited current in the presence of the plasma expanding from the cathode and anode surfaces. The anode plasma is formed from the desorbed and ionized gases.…”

Section: Space-charge Limited Electron Flow In a Cylindrical Diodementioning

confidence: 94%

Intense relativistic electron beam generation and prepulse effect in high power cylindrical diode

Roy

Menon

Mitra

et al. 2008

Journal of Applied Physics

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Intense gigawatt relativistic electron beam has been generated in a high power cylindrical diode in the presence of prepulse. A bipolar prepulse voltage, recorded at the diode, varies both in amplitude and time duration with the Marx generator voltage. It was found that only at the accelerating gap ⩽1.65cm there is some shot to shot variation in the diode voltage and current for the same Marx generator voltage. The anode and cathode plasma expansion velocities were calculated using the perveance data. The plasma expands at 5cm∕μs for 1.85cm radial anode-cathode gap and the plasma velocity decreases for smaller gap. It was found that the effect of the prepulse is less pronounced in the cylindrical diode as compared to planar diode that allows one operation of the cylindrical diode with the gap ⩽1.85cm.

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“…9 Let us examine how the I-V characteristics look like for a typical voltage pulse from KALI 5000 pulse power system. The cylindrical diode having dimensions r a = 4.25 cm, r c = 5.25 cm, and h = 2 cm.…”

Section: ͑6͒mentioning

confidence: 99%

Electron beam current in high power cylindrical diode

et al. 2010

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Intense electron beam generation studies were carried out in high power cylindrical diode to investigate the effect of the accelerating gap and diode voltage on the electron beam current. The diode voltage has been varied from 130 to 356 kV, whereas the current density has been varied from 87 to 391 A/cm2 with 100 ns pulse duration. The experimentally obtained electron beam current in the cylindrical diode has been compared with the Langmuir–Blodgett law. It was found that the diode current can be explained by a model of anode and cathode plasma expanding toward each other. However, the diode voltage and current do not follow the bipolar space-charge limited flow model. It was also found that initially only a part of the cathode take part in the emission process. The plasma expands at 4.2 cm/μs for 1.7 cm anode-cathode gap and the plasma velocity decreases for smaller gaps. The electrode plasma expansion velocity of the cylindrical diode is much smaller as compared with the planar diode for the same accelerating gap and diode voltage. Therefore, much higher voltage can be obtained for the cylindrical diodes as compared with the planar diodes for the same accelerating gap.

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Approximate analytical solutions for the space-charge-limited current in one-dimensional and two-dimensional cylindrical diodes

Cited by 30 publications

References 8 publications

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

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

Intense relativistic electron beam generation and prepulse effect in high power cylindrical diode

Electron beam current in high power cylindrical diode

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