Modeling magnetically insulated power flow in mercury

Mercury is a 50-ns, 6-MV, 360-kA accelerator with a magnetically-insulated, inductive-voltage-adder (MIVA) architecture. The machine was formerly known as KALIF-HELIA [P. Hoppe et al., June 17-22, 2002] at Forschungszentrum Karlsruhe in Germany but now, with some minor modifications [R. J. Commisso et al., 2003], are sited at NRL. Mercury can be operated in either positive or negative polarity [R. J. Commisso et al., 2003; J. W. Schumer et al., 2003; R. J. Allen et al., 2003]. Voltage is added in vacuum along a magnetically insulated transmission line (MITL) from six voltage adder cells. Understanding power flow and coupling to a load in this geometry requires the application of MITL theory [C. W. Mendel et al., 1983; C. W. Mendel and S. E. Rosenthal, 1995; C. W. Mendel and S. E. Rosenthal, 1996; S. E. Rosenthal, 1991]. Because the electric field stresses on the cathode in the MITL exceed the vacuum explosive-emission threshold, electron emission occurs and current flow is divided between current flowing in the metal and in vacuum electron flow. This electron flow manifests itself as a loss current until the total current is large enough to magnetically insulate the emitted electrons from crossing the anode-cathode (AK) gap. Once insulated, the electrons flow axially toward the load. In particular, electron emission and flow along the MITL alters the impedance along the line and, thus, the power flow coupling between the machine and the load. The effective impedance is best described by the flow impedance, which is a function of both the geometry and the voltage. When electrons are emitted from regions having different voltages, such as in the adders or at different locations along the MITL itself, layered flow occurs, further complicating the picture. Analysis of power flow in this complex geometry is underway to understand the past performance of KALIF-HELIA and to assist in optimizing the future performance of Mercury in both polarities and for various load conf- gurations [J. W. Schumer et al., 2003; R. J. Allen et al., 2003]. The goal of this work is to develop physics-based MITL circuit-element models for the NRL transmission line code BERTHA [D. Hinshelwood, November 1983] to properly treat power flow in the vacuum section of mercury while modeling the full machine.