Particle simulations of divergent and convergent radial electron flows in cylindrical Pierce diodes

Alves, M. V.; Gratton, F. T.; Gnavi, G.; Moreno, C.

doi:10.1063/1.872440

Cited by 5 publications

(3 citation statements)

References 18 publications

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“…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%

“…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%

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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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“…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.…”

mentioning

confidence: 99%

mentioning

confidence: 99%

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

Kostov

Barroso

2002

Physics of Plasmas

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“…The nonlinear dynamics of cylindrical Pierce-type devices has been recently investigated using particle-in-cell simulations. 17 In this paper we present a study of the nonlinear evolution of spherical Pierce-type electrodes, maintained at the same electric potential, using numerical simulations and analytical models. These systems have radial density gradients parallel or antiparallel to the electron flow, depending on whether the emitter focalizes the beam on a collector of smaller radius, or the emitter sends the beam outwards to a collector of larger radius.…”

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confidence: 99%

Nonlinear dynamics of electron flows with density gradient in spherical diodes

et al. 2000

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A variety of Pierce diodes formed by a pair of grounded concentric spheres with electrons streaming radially are investigated with particle-in-cell simulations and analytical models. The electrons flow parallel or antiparallel to a density gradient in convergent or divergent diodes, respectively. The existence and stability ͑or instability͒ of laminar steady states with space charge and nonuniform velocity that are possible for a given set of diode parameters, are crucial to determine the outcome of the numerical experiments. The dispersion relation for the stability of the initial constant velocity states and the concomitant energy flow balance are examined in relation to the nonlinear dynamical evolution. Spherical diodes have properties that are common to a dual pair of diodes with reciprocal ratios of collector to emitter radii. Stable oscillatory electrostatic states, associated with Hopf bifurcations, are observed in the simulations. The breakdown of the laminar electron flow has completely different physical characteristics in divergent and convergent diodes.

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100 years of the physics of diodes

Zhang

Valfells

Ang

et al. 2017

Applied Physics Reviews

189

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The Child-Langmuir Law (CL), discovered a century ago, gives the maximum current that can be transported across a planar diode in the steady state. As a quintessential example of the impact of space charge shielding near a charged surface, it is central to the studies of high current diodes, such as high power microwave sources, vacuum microelectronics, electron and ion sources, and high current drivers used in high energy density physics experiments. CL remains a touchstone of fundamental sheath physics, including contemporary studies of nanoscale quantum diodes and nano gap based plasmonic devices. Its solid state analog is the Mott-Gurney law, governing the maximum charge injection in solids, such as organic materials and other dielectrics, which is important to energy devices, such as solar cells and light emitting diodes. This paper reviews the important advances in the physics of diodes since the discovery of CL, including virtual cathode formation and extension of CL to multiple dimensions, to the quantum regime, and to ultrafast processes. We review the influence of magnetic fields, multiple species in bipolar flow, electromagnetic and time dependent effects in both short pulse and high frequency THz limits, and single electron regimes. Transitions from various emission mechanisms (thermionic-, field-, and photoemission) to the space charge limited state (CL) will be addressed, especially highlighting the important simulation and experimental developments in selected contemporary areas of study. We stress the fundamental physical links between the physics of beams to limiting currents in other areas, such as low temperature plasmas, laser plasmas, and space propulsion.

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Particle simulations of divergent and convergent radial electron flows in cylindrical Pierce diodes

Cited by 5 publications

References 18 publications

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

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

Nonlinear dynamics of electron flows with density gradient in spherical diodes

100 years of the physics of diodes

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