A distributed parameter wire model for transient electrical discharges

Journal Article · Fri Jun 15 04:00:00 EDT 1990 · Journal of Applied Physics; (USA)

DOI:https://doi.org/10.1063/1.344556· OSTI ID:7036428

Maier, II, W B; Kadish, A; Sutherland, C D ^[1]; Robiscoe, R T ^[2]

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1. Los Alamos National Laboratory, Los Alamos, New Mexico (USA)
2. Montana State University, Bozeman, MT (USA)

A model for freely propagating transient electrical discharges, such as lightning and punch-through arcs, is developed in this paper. We describe the electromagnetic fields by Maxwell's equations and we represent the interaction of electric fields with the medium to produce current by {partial derivative}{bold J}/{partial derivative}{ital t}={omega}{sup 2}({bold E}{minus}{ital E}*{ital {cflx J}})/4{pi}, where {omega} and {ital E}* are parameters characteristic of the medium, {bold J}{equivalent to}current density, and {ital {cflx J}}{equivalent to}{bold J}/{vert bar}{bold J}{vert bar}. We illustrate the properties of this model for small-diameter, guided, cylindrically symmetric discharges. Analytic, numerical, and approximate solutions are given for special cases. The model describes, in a new and comprehensive fashion, certain macroscopic discharge properties, such as threshold behavior, quenching and reignition, path tortuosity, discharge termination with nonzero charge density remaining along the discharge path, and other experimentally observed discharge phenomena. Fields, current densities, and charge densities are quantitatively determined from given boundary and initial conditions. We suggest that many macroscopic discharge properties are properly explained by the model as electromagnetic phenomena, and we discuss extensions of the model to include chemistry, principally ionization and recombination.

• OSTI ID: 7036428
• Journal Information: Journal of Applied Physics; (USA), Journal Name: Journal of Applied Physics; (USA) Vol. 67:12; ISSN 0021-8979; ISSN JAPIA
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700108* -- Fusion Energy-- Plasma Research-- Wave Phenomena
ANALYTICAL SOLUTION
BOUNDARY CONDITIONS
CURRENTS
DIFFERENTIAL EQUATIONS
ELECTRIC ARCS
ELECTRIC CURRENTS
ELECTRIC DISCHARGES
ELECTROMAGNETIC FIELDS
EQUATIONS
LIGHTNING
MATHEMATICAL MODELS
MAXWELL EQUATIONS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
TRANSIENTS