An improved space-charge-limited emission algorithm for use in particle-in-cell codes

Watrous, J.J.; Lugisland, J. W.; Sasser, G.E.

doi:10.1063/1.1329152

Cited by 42 publications

(20 citation statements)

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“…The method of overinjection requires a series of simulation in order to find the greatest value of the injection current that does not lead to the formation of a virtual cathode. Although the overinjection method has some disadvantages-in that on the assumption of spatially uniform electron emission it misses the spikes in the current density at the beam edges, as is shown for a planar diode 5 -this method provides useful estimates and can be easily applied for cylindrical geometry.…”

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confidence: 99%

“…This clearly demonstrates that for all parameters used the normalized current exhibits a general behavior, in principle, similar to that of the 2D planar diode. 4,5 The normalized space-charge-limited current density is a monotonically decreasing function of L/R, recovering the classical 1D limiting current as L/Rу5. For both aspect ratios, i.e., R/rϭ3 and R/rϭ10, and over the simulated range 0.2ϽL/RϽ5 the normalized numerical data for 2D spacecharge-limited current may be fitted empirically by a function of the single variable L/R,…”

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confidence: 99%

“…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.…”

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confidence: 99%

“…5 For the purpose of our simulation we use the so-called overinjection method. The emission current in this model is set uniform over the emitter and made to increase linearly in time from zero to its nominal value for 1 ns after that it is kept constant during the simulation.…”

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

Kostov

Barroso

2002

Physics of Plasmas

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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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