Theory of the initial stage of streamer propagation

Lozansky, E. D.; Firsov, O. B.

doi:10.1088/0022-3727/6/8/310

Cited by 43 publications

(66 citation statements)

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“…the equations for the three moments of Boltzmann equation are written, respectively, as 8pl~+ V"(njvJ)=SJ at (2) for the transport equation of density nj for particle j, where int is the source term for particle j, It is obvious that Eqs. (2) -(4) represent the discharge only if it is possible to close the set of equations and to de-fine the force I (that is to say the electric field) and the is the mean speed of the particles j, where dwj is the volume element &n the velocity space dwI =dwj"dw j~dw j, Pjnjmj(WJVJ)(WJVJ) is the kinetic pressure tensor, and interaction terms S&, R~,E.2. So it is clear that a macroscopic description of the discharge is necessarily linked to an a priori description of the microscopic behavior of the particles inside the collective phenomena.…”

Section: Introductionmentioning

confidence: 99%

Propagation of ionizing electron shock waves in electrical breakdown

Bayle

Cornebois

1985

Phys. Rev. A

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A numerical solution of a hydrodynamic second-order model shows that the propagation of the first ionizing wave arises from an overgrowth of hot electrons in the wave front in a zone of a greatly disturbed electric field. This gives rise, in the electron shock zone ahead of the wave, to a precursor phenomenon, whose effect is to accelerate the channel propagation. Inside the shock zone, the electronic energy differs from the characteristic energy; the nonequilibrium between the electrons and the electric field, as a result of the electron pressure gradient, induces a heating of electrons in this zone. The space-charge electric field is calculated assuming that the discharge evolves in a variable ellipsoidal envelope with revolution symmetry around the propagation axis. The electron shock-wave structure is shown to maintain itself and to propagate during the evolution of the discharge. The results obtained from this second-order model are compared to those obtained from a classical first-order model in which the electron temperature is a function of the reduced electric field alone. This comparison allows us to define the concept of electron nonequilibrium in an electron shock wave and to show that it is the source of the high-speed propagation of the streamer. The close agreement of the results obtained from the second-order model with the experimental data justifies the formulation of the model, particularly that of the interaction operators of the energy equation.

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Section: Introductionmentioning

confidence: 99%

Propagation of ionizing electron shock waves in electrical breakdown

Bayle

Cornebois

1985

Phys. Rev. A

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“…In previous theoretical work, it is implicitly assumed that streamers in a uniform background field propagate in a stationary manner [6][7][8]. This view seems to be supported by previous simulations [9,10].In this paper we present the first numerical evidence that anode directed (or negative) streamers do branch even in a uniform background field and without initial background ionization in the minimal fully deterministic "fluid model" [1,[6][7][8][9][10], if the field is sufficiently strong. We argue that this happens when the streamer approaches what we suggest to call the Lozansky-Firsov limit of "ideal conductivity" [6].…”

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confidence: 99%

“…We argue that this happens when the streamer approaches what we suggest to call the Lozansky-Firsov limit of "ideal conductivity" [6]. The streamer then can be understood as an interfacial pattern with a Laplacian instability [11], qualitatively similar to other Laplacian growth problems [12].…”

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confidence: 99%

“…We investigate the minimal streamer model, i.e., a "fluid approximation" with local field-dependent impact ionization reaction in a non-attaching gas like argon or nitrogen [1,[6][7][8][9][10][11]. In detail, the dynamics is as follows: (i) an impact ionization reaction in local field approximation: free electrons and positive ions are generated by impact of accelerated electrons on neutral molecules ∂ τ n e + ∇ R · j e = ∂ τ n i + ∇ R · j i = |µ e En e | α 0 α(|E|/E 0 ); n e,i and j e,i are particle densities or currents of electrons or ions, respectively, and E is the electric field; in all numerical work, we use the Townsend approximation α 0 α(|E|/E 0 ) = α 0 exp(−E 0 /|E|) with parameters α 0 and E 0 for the effective cross-section.…”

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confidence: 99%

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Spontaneous Branching of Anode-Directed Streamers between Planar Electrodes

2002

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Non-ionized media subject to strong fields can become locally ionized by penetration of fingershaped streamers. We study negative streamers between planar electrodes in a simple deterministic continuum approximation. We observe that for sufficiently large fields, the streamer tip can split. This happens close to the limit of "ideal conductivity". Qualitatively the tip splitting is due to a Laplacian instability quite like in viscous fingering. For future quantitative analytical progress, our stability analysis of planar fronts identifies the screening length as a regularization mechanism.Streamers commonly appear in dielectric breakdown when a sufficiently high voltage is suddenly applied to a medium with low or vanishing conductivity. They consist of extending fingers of ionized matter and are ubiquitous in nature and technology [1,2]. The degree of ionization inside a streamer is low, hence thermal or convection effects are negligible. However, streamers are nonlinear phenomena due to the space charges inside the ionized body that modify the externally applied electric field. While in many applications, streamers by a strongly nonuniform background electric field are forced to propagate towards the cathode through complex mixtures of gases [2-4], we here investigate the basic phenomenon of the primary anode-directed streamer in a simple nonattaching and non-ionized gas and in a uniform background field as in the pioneering experiments of Raether [5]. In previous theoretical work, it is implicitly assumed that streamers in a uniform background field propagate in a stationary manner [6][7][8]. This view seems to be supported by previous simulations [9,10].In this paper we present the first numerical evidence that anode directed (or negative) streamers do branch even in a uniform background field and without initial background ionization in the minimal fully deterministic "fluid model" [1,[6][7][8][9][10], if the field is sufficiently strong. We argue that this happens when the streamer approaches what we suggest to call the Lozansky-Firsov limit of "ideal conductivity" [6]. The streamer then can be understood as an interfacial pattern with a Laplacian instability [11], qualitatively similar to other Laplacian growth problems [12]. For future quantitative analytical progress, we identify the electric screening length as a relevant regularization mechanism. Our finding casts doubts on the existence of a stationary mode of streamer propagation with a fixed head radius. FIG. 1. Evolution of spontaneous branching of anode directed streamers in a strong homogeneous background field at times t = 300, 365, 420 and 450. Model, initial and boundary conditions are discussed in the text. The planar cathode is located at z = 0 and the planar anode at z = 2000 (shown is 0 ≤ z ≤ 1400). The radial coordinate extends from the origin up to r = 2000 (shown is 0 ≤ r ≤ 600). The thin lines denote levels of equal electron density σ with increments of 0.1 or 0.2 as indicated by the labels. The thick lines denote the higher electron de...

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“…For a self-sustained discharge for each initial electron, an average of more than one electron should appear [8]. This leads to formation of secondary streamers in the vicinity of the original one.…”

Section: Discussion and Resultsmentioning

confidence: 99%

Initiation of pulsed corona discharge under supercritical conditions

Lock

Saveliev

Kennedy

2005

IEEE Trans. Plasma Sci.

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Supercritical carbon dioxide is a medium with unique properties and variety of applications in modern green chemistry.The generation of pulsed corona discharge in supercritical CO 2 is studied experimentally for point-to-plane and wire-to-plane geometries. The low breakdown voltages recorded near the critical point are attributed to peculiarities of electron kinetics in a medium characterized by high spatial inhomogeneity and enhanced cluster formation.

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Theory of the initial stage of streamer propagation

Cited by 43 publications

References 2 publications

Propagation of ionizing electron shock waves in electrical breakdown

Propagation of ionizing electron shock waves in electrical breakdown

Spontaneous Branching of Anode-Directed Streamers between Planar Electrodes

Initiation of pulsed corona discharge under supercritical conditions

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