Particle-in-cell simulations of high-power cylindrical electron beam diodes

Swanekamp, S.B.; Commisso, R.J.; Cooperstein, G.; Ottinger, P. F.; Schumer, J.W.

doi:10.1063/1.1320468

Cited by 65 publications

(22 citation statements)

References 26 publications

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“…Ions present in the A-K gap introduce a bipolar ͑BP͒ flow condition which alters the SCL current as I BP Ӎ1.84I SCL for nonrelativistic electron energies and I BP Ӎ 2 I SCL /4 for relativistic electron energies ͑See Ref. 6; these results are for a one-dimensional planar diode.͒ The ion current fraction is proportional to 5,6 …”

Section: A Rod-pinch Electron Beam Diodementioning

confidence: 96%

“…5,6 The space-charged-limited phase describes the initial turn on and rise of the electron current in the diode anode-cathode ͑A-K͒ gap. As the current flowing in the gap increases to the point at which the self-electric and self-magnetic field effects on the electron flow become comparable, the diode is described as being in a weakly pinched phase.…”

Section: A Rod-pinch Electron Beam Diodementioning

confidence: 99%

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Coupled particle-in-cell and Monte Carlo transport modeling of intense radiographic sources

Rose

Welch

Oliver

et al. 2002

Journal of Applied Physics

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Dose-rate calculations for intense electron-beam diodes using particle-in-cell (PIC) simulations along with Monte Carlo electron/photon transport calculations are presented. The electromagnetic PIC simulations are used to model the dynamic operation of the rod-pinch and immersed-B diodes. These simulations include algorithms for tracking electron scattering and energy loss in dense materials. The positions and momenta of photons created in these materials are recorded and separate Monte Carlo calculations are used to transport the photons to determine the dose in far-field detectors. These combined calculations are used to determine radiographer equations (dose scaling as a function of diode current and voltage) that are compared directly with measured dose rates obtained on the SABRE generator at Sandia National Laboratories.

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Section: A Rod-pinch Electron Beam Diodementioning

confidence: 96%

Section: A Rod-pinch Electron Beam Diodementioning

confidence: 99%

Coupled particle-in-cell and Monte Carlo transport modeling of intense radiographic sources

Rose

Welch

Oliver

et al. 2002

Journal of Applied Physics

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“…Including self-magnetic field is extremely difficult analytically, especially when the electron beam is not fully insulated in the pinched regime, 17,18 or at cross-field geometry when the self-magnetic field can become important even at significantly low voltage such as 300 kV. The simple 3D relativistic CL law presented in this paper is to serve as an extension of the well-known 1D relativistic CL Law 3 to account for the effects of finite emission area, but ignoring the self-magnetic field.…”

Section: Remarksmentioning

confidence: 99%

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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“…This result can be understood if we look at the values of ␤ 2 , which for R/rϾ3 rapidly approach its asymptotic value. 1,7 However, for smaller ratios (R/rϽ3) the behavior of ␤ 2 drastically changes as it quickly decreases to zero and the fitting ͑3͒ is no longer valid.…”

mentioning

confidence: 99%

Space-charge-limited current in cylindrical diodes with finite-length emitter

Kostov

Barroso

2002

Physics of Plasmas

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In the present paper we extend to two dimensions the classical Langmuir-Blodgett law, which determines the maximum current I LB that can be accelerated by a given voltage across two infinitely long coaxial cylinders. Generalization of the I LB law is established by performing two-dimensional 2D particle-in-cell numerical experiments on a variety of cylindrical diode configurations with a finite-length emitter. It is found that the limiting current in two dimensions I 2D follows a monotonically decreasing function of the emitter length-to-outer electrode radius ratio L/R as expressed by the fitting function I 2D /I LB ϭ1ϩ0.1536/(L/R)ϩ0.0183/(L/R) 2 within 2.5% accuracy for simulation data in which the ratio of the outer to inner radii exceeds 3. © 2002 American Institute of Physics. ͓DOI: 10.1063/1.1446876͔The effect of space charge on the flow of charged particles between two parallel electrodes in vacuum is of great importance in microwave electronics, crossed-field devices, and high-power diodes. In particular, if too much charge is injected into a gap, the resulting electric field becomes sufficiently high to reflect the injected particles back to the emitter, forming a virtual cathode. Limiting currents of vacuum diodes are classical subjects with early works dating back to the beginning of the last century when onedimensional space-charge-limited flow solutions were derived. Only for simple cases, however, such as plane parallel plates, infinitely long coaxial cylinders, and concentric sphere there exist analytical solutions.1 For a planar gap with gap separation D and gap voltage V, the maximum electron current density in a space-charge-limited diode is given by the well-known Child-Langmuir law,where e and m are, respectively, the charge and the mass of the emitted particles, and ⑀ 0 is the free space permittivity. Equation ͑1͒ is derived by assuming zero electron emission velocity and neglecting relativistic effects. Later an analytical solution for limiting current of relativistic electron flow in the planar diode was found, 3 but with the generalization of Child-Langmuir law in two dimensions still remaining a formidable task analytically. So an alternative approach was adopted, namely, the use of particle-in-cell ͑PIC͒ computer simulation to investigate two-dimensional space-chargelimited flow in a planar diode.4,5 About works on cylindrical diodes, particle simulation method was successfully applied for studying the stability of divergent and convergent electron flows in 1D cylindrical Pierce diode. 6 Also numerical experiments were performed to examine electrical properties of charged-particle flows in high-power cylindrical pinchedbeam diode over a wide range of voltages. 7The electron flow between coaxial cylinders is another important topic on beam formation theory, which has laid the basis of many useful gun designs. High-power cylindrical diodes have also found application in cylindrical vircators 8 and in high-resolution radiography sources.9 Again, as for the planar diode, the specialized lit...

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Particle-in-cell simulations of high-power cylindrical electron beam diodes

Cited by 65 publications

References 26 publications

Coupled particle-in-cell and Monte Carlo transport modeling of intense radiographic sources

Coupled particle-in-cell and Monte Carlo transport modeling of intense radiographic sources

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

Space-charge-limited current in cylindrical diodes with finite-length emitter

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