Periodic Electron Structures in Gases: A Fluid Model of the “Window” Phenomenon

Nicoletopoulos, Pierre; Robson, Robert

doi:10.1103/physrevlett.100.124502

Cited by 21 publications

(34 citation statements)

References 11 publications

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“…The steady-state, spatially homogeneous balance equations, (24) and (25), are restated here for clarity:…”

Section: Modified Mttmentioning

confidence: 99%

“…While the primary aim of MTT initially was to furnish relationships between measurable quantities (e.g. the Wannier energy relations, generalized Einstein (Nernst-Townsend) relations (GER), etc), more recently it has been demonstrated to provide transport properties in good qualitative and semi-quantitative agreement with more rigorous treatments, such as Boltzmann equation solutions and Monte Carlo simulations [11,15,18,[20][21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

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On the approximation of transport properties in structured materials using momentum-transfer theory

et al. 2012

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In this paper, we present a fluid model for electrons and positrons in structured and soft-condensed matter utilizing dilute gas phase cross-sections together with a structure factor for the medium. Generalizations of the Wannier energy and Einstein (Nernst-Townsend) relations to account for coherent scattering effects present in soft-condensed matter are presented along with new expressions directly relating transport properties in the dilute gas and the structured matter phases. The theory is applied to electrons in a benchmark Percus-Yevick model and positrons in liquid argon, and the accuracy is tested against a multi-term solution of Boltzmann's equation (White and Robson 2011 Phys. Rev. E 84 031125).

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“…The steady-state, spatially homogeneous balance equations, (24) and (25), are restated here for clarity:…”

Section: Modified Mttmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the approximation of transport properties in structured materials using momentum-transfer theory

et al. 2012

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“…The "window" phenomenon, i.e., the range of voltages and gas pressures, within which electron properties oscillate, and outside of which properties simply decay monotonically in space, has been studied in Ref. [28] by means of a fluid model. The effect of magnetic field perpendicular to the electric field on the spatial relaxation of a swarm of charged particles in an idealized steady-state Townsend experiment was described by the solution of the Boltzmann equation in [29].…”

Section: Introductionmentioning

confidence: 99%

Photoelectric Franck-Hertz experiment and its kinetic analysis by Monte Carlo simulation

Magyar

Korolov

2012

Phys. Rev. E

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The electrical characteristics of a photoelectric Franck-Hertz cell are measured in argon gas over a wide range of pressure, covering conditions where elastic collisions play an important role, as well as conditions where ionization becomes significant. Photoelectron pulses are induced by the fourth harmonic UV light of a diode-pumped Nd:YAG laser. The electron kinetics, which is far more complex compared to the naive picture of the Franck-Hertz experiment, is analyzed via Monte Carlo simulation. The computations provide the electrical characteristics of the cell, the energy and velocity distribution functions, and the transport parameters of the electrons, as well as the rate coefficients of different elementary processes. A good agreement is obtained between the cell's measured and calculated electrical characteristics, the peculiarities of which are understood by the simulation studies.

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“…Thus, particular care should be taken with the closure through specification of the energy flux. Even for charged particle swarms under non-hydrodynamic conditions one must be careful how to specify the heat flux vector [35,40,41,51]. We now discuss how the fluid equations should be closed for streamers, while we stress that the method itself is applicable to a much wider range of phenomena.…”

Section: Second Order Models Including the Energy Balance Equationmentioning

confidence: 99%

“…This form of the pressure tensor was employed in all previous swarm oriented studies [35,40,41,45,51,55,56], as well as in the recent fluid models of streamer discharges [42,50]. However, if the velocity distribution significantly deviates from isotropy in velocity space, then this approximation is problematic.…”

Section: Momentum Transfer Theorymentioning

confidence: 99%

High-order fluid model for streamer discharges: I. Derivation of model and transport data

Dujko¹,

Markosyan²,

White³

et al. 2013

J. Phys. D: Appl. Phys.

102

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Abstract. Streamer discharges pose basic problems in plasma physics, as they are very transient, far from equilibrium and have high ionization density gradients; they appear in diverse areas of science and technology. The present paper focuses on the derivation of a high order fluid model for streamers. Using momentum transfer theory, the fluid equations are obtained as velocity moments of the Boltzmann equation; they are closed in the local mean energy approximation and coupled to the Poisson equation for the space charge generated electric field. The high order tensor in the energy flux equation is approximated by the product of two lower order moments to close the system. The average collision frequencies for momentum and energy transfer in elastic and inelastic collisions for electrons in molecular nitrogen are calculated from a multi term Boltzmann equation solution. We then discuss, in particular, (1) the correct implementation of transport data in streamer models; (2) the accuracy of the two term approximation for solving Boltzmann's equation in the context of streamer studies; and (3) the evaluation of the mean-energy-dependent collision rates for electrons required as an input in the high order fluid model. In the second paper in this sequence, we will discuss the solutions of the high order fluid model for streamers, based on model and input data derived in the present paper.PACS numbers: 52.25. Dy, 52.65.Kj, 52.25.Fi, 52.25.Jm Submitted to: J. Phys. D: Appl. Phys.

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Periodic Electron Structures in Gases: A Fluid Model of the “Window” Phenomenon

Cited by 21 publications

References 11 publications

On the approximation of transport properties in structured materials using momentum-transfer theory

On the approximation of transport properties in structured materials using momentum-transfer theory

Photoelectric Franck-Hertz experiment and its kinetic analysis by Monte Carlo simulation

High-order fluid model for streamer discharges: I. Derivation of model and transport data

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