Diffusive radial expansion effect on long-Rail spark dynamical impedances

Abstract

Summary form only given. By close examinations over the numerical simulations based on Rompe and Weisel (R&W) spark gap model, the calculated peaks and rise times of gap transient currents are significantly lower and slow than the empirical data extracted from recent experimental works for the preliminary designed prototype Direct Strike Lightning (DSL) Test Facility. This implies the gap dynamical resistance R<;sub>;s<;/sub>;(t) implemented for employed Rail Gap Switch (RGS) in our SPARKGAP computational code is quite larger and decreasing slower than interpreted data from DSL experiments. These discrepancies are mainly originated from the RGS features of specific geometric structure and triggering schemes. First, it is discharged physically through multi-channels (i.e., plasma columns) rather than only one plasma column across the long rail gap within hemi-cylindrical electrodes as breakdown initiated by the rapid rising electric pulse imposed from a knife-edged triggering plate. Meanwhile the numbers of plasma columns across the gap are inevitably fudged input to the code in order to cope with empirical data. Secondly, in R&W model, the plasma column(s) formed are considered conductive only along axial z-direction with fixed radius r across the gap ± electrodes; however, the (charged) particles in (each) plasma column(s) propagating along radial r-direction through diffusion mechanism. Though radial diffusive process of order over micro-second (μs) is much slower than axial drift process of order less than nano-second (ns) due to electron diffusion v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">diffuse</sub> ≪ drift velocity v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">diffuse</sub> for high axial field E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z</sub> , but the dramatic temperature increasing in plasma columns and long-sustained bank discharging over μs will enhance diffusion (coefficient D <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</sub> ) resulting in significant increasing in v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">diffuse</sub> . This effect is negligible for short-lived pulses of ns range but will definitely augment the RGS discharging of μs range. Thus, plasma radial r-expansions will be particularly manifested in RGS impulses. The primary purpose here is to improve the deficiencies in R&W model as described for diffusive radial expansion phenomena across long rail gap by means of characteristic method for electron continuity equation involving ionized sources and corrections with photo-ionizations and radiation losses from accelerated charged particles ignored previously.