Dynamics of nanosecond spark-gap channels

S.I. Braginskii (1958) showed that the resistive collapse of a very fast spark discharge in a gas is governed in large part by the radial expansion of a cylindrical shock wave, which rapidly increases the cross-sectional area of the conducting channel. Though this model has been shown to give good qualitative agreement with experiment by a number of authors, it contains assumptions that are not a priori justified. In particular, it assumes that electrical conductivity remains constant during channel expansion, implying that hydrodynamic, radiative and thermal cooling are precisely offset by Joule heating. In this paper, the authors show that data by Sorensen and Ristic (1977) at the nanosecond timescale is not, in fact, well modeled by constant electrical conductivity. Instead, they find that conductivity must increase considerably during the first quarter cycle in order to agree well with their data. To better understand the energy balance of an expanding, Joule heated channel, they have performed 1-D magnetohydrodynamic simulations to model in detail the transport of energy out of it. They find that at the nanosecond timescale, radiation and thermal transport are insufficient to keep the channel temperature from rising rapidly at early time.