IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 29, NO. 3, JUNE 2001 479 MHD-to-PIC Transition for Modeling of Conduction and Opening in a Plasma Opening Switch Joseph W. Schumer, Stephen B. Swanekamp, Paul F. Ottinger, Member, IEEE, Robert J. Commisso, Senior Member, IEEE, Bruce V. Weber, David N. Smithe, and Larry D. Ludeking, Member, IEEE Abstract—The plasma opening switch (POS) is a critical element of some inductive-energy-storage pulsed-power generators. De- tailed understanding of plasma redistribution and thinning during the POS conduction phase can be gained through magnetohydro- dynamic fluid (MHD) simulations. As space-charge separation and kinetic effects become important late in the conduction phase (be- ginning of the opening phase), MHD methods become invalid and particle-in-cell (PIC) methods should be used. In this paper, the applicability of MHD techniques is extended into PIC-like regimes by including nonideal MHD phenomena such as the Hall effect and resistivity. The feasibility of the PIC technique is, likewise, extended into high-density, low-temperature-MHD-like regimes by using a novel numerical cooling algorithm. At an appropriate time, an MHD-to-PIC transition must be accomplished in order to accurately simulate the POS opening phase. The mechanics for converting MHD output into PIC input are introduced, as are the transition criteria determining when to perform this conversion. To establish these transition criteria, side-by-side MHD and PIC simulations are presented and compared. These separate simula- tions are then complemented by a proof-of-principle MHD-to-PIC transition, thereby demonstrating this MHD-to-PIC technique as a potentially viable tool for the simulation of POS plasmas. Practical limitations of the MHD-to-PIC transition method and applicability of the transition criteria to hybrid fluid-kinetic simulations are discussed. Index Terms—Magnetohydrodynamic simulation, opening switches, particle-in-cell simulation. I. INTRODUCTION I MPROVEMENTS in plasma opening switch (POS) operation are crucial for the development of smaller and less expensive inductive-energy-storage, multiterawatt pulsed-power accelerators [1], [2]. A POS consists of a high-density plasma injected between the conductors of a vacuum transmission line (see Fig. 1). Operation of a POS can be divided into three phases. The first is the conduction phase, a period during which current is conducted through the plasma switch while electrical energy (initially stored in high-voltage capacitors) is converted to magnetic energy and stored in the circuit inductance between the generator and the POS. The second is the opening phase, during which plasma conditions change rapidly and in such a manner that the plasma can no Manuscript received August 25, 2000; revised February 28, 2001. This work was supported by the Defense Threat Reduction Agency. J. W. Schumer, P. F. Ottinger, R. J. Commisso, and B. V. Weber are with the Pulsed Power Physics Branch, Plasma Physics Division, Naval Research Labo- ratory, Washington, DC 20375USA (e-mail: schumer@calvin.nrl.navy.mil). S. B. Swanekamp is with JAYCOR, McLean, VA 22102 USA. D. N. Smithe and L. D. Ludeking are with Mission Research Corporation, Newington, VA 22122 USA. Publisher Item Identifier S 0093-3813(01)04961-X. Fig. 1. Plasma is injected into a coaxial transmission line and serves as a POS. The POS conducts the generator current, redistributes under the influence of magnetic pressure upstream, eventually thins and opens, and allows magnetic energy to flow downstream to a load. longer conduct large levels of current. Third is the power-flow phase, where the stored magnetic energy flows rapidly to the load. Power compression is achieved when the conduction time significantly exceeds the opening time [1]–[3]; hence, understanding how conduction phase dynamics prepare the plasma for opening may provide insight into techniques for improving POS performance. During the conduction phase, a high-density plasma ( – ) must conduct large levels of electrical current ( A) for times on the order of 1 s. Plasma redistribution (rarefaction and compression) during the con- duction phase has been well-characterized experimentally, and can be described by magnetohydrodynamic (MHD) treatments [4]–[7]. Interferometry suggests that this redistribution of mass produces a region of localized thinning in the POS [8] with plasma densities falling below , signaling the end of the conduction phase. It is in this region that the POS begins to open and space-charge dominated processes promote the formation of a vacuum gap in the plasma, allowing the stored magnetic energy to rapidly flow toward the load [9]–[12]. After opening, vacuum electron flows with densities on the order of typically accompany the energy transfer process and can account for a large fraction of the delivered energy to the load [13]. The opening and power-flow processes occur over a period lasting only tens of nanoseconds and, because of the kinetic nature of the vacuum electron flow, can only be practically modeled with particle-in-cell (PIC) methods [14]. The POS operational regime spans four orders of magnitude in density ( – ) and evolves through physical regimes with vastly different temporal ( s) and spatial scales ( cm) [1]. The smallest temporal and spatial scales in the plasma are determined by the inverse 0093–3813/01$10.00 © 2001 IEEE