Our evolving understanding of self-magnetically insulated transmission lines and their application to future drivers

Abstract

The development of self-magnetically insulated transmission lines (MITLs) represents the single most important development in high-voltage pulsed power within the last 50 years. The use of MITLs has enabled pulsed-power drivers like Z to deliver peak electrical powers up to 80 TW to multilevel vacuum MITLs. The theoretical and experimental basis of MITLs has evolved significantly from the original theoretical work by Loveless and Ott; Creedon; Mendel; Bergeron and Poukey; Voronin and Lebedev; and too many others to conveniently acknowledge.

The initial description of MITLs started with long, self-limited, coaxial transmission lines for which the behavior of the MITLs was relatively easy to describe. In such MITLs, electron behavior is driven by the relatively low vacuum impedance of the transmission line and, in this case, the electron emission wave propagates along with the voltage pulse down the transmission line. Long, coaxial transmission lines formed the basis for the PBFA-I accelerator at Sandia National Laboratories in 1980. Load-dominated disk MITL designs were also used (Gamble II, Proto-II, DoubleEagle, Blackjack 3 and 5, Saturn, Angara V, and Z). Cathode emission in disk geometries starts at the highest electric-field locations in the interior of the disk transmission line. In such cases, the detailed, time-dependent impedance profile of the load impacts the details of steady-state vacuum insulation. Continued advances in MITL theory (Mendel, Ottinger and Schumer, and others) and in 2-D and 3-D particle-in-cell modeling (Seidel, Pointon, Welch, Rose, and others) provided continued improvements in MITL design capabilities.

Discussions of self-magnetic insulation start with the explosive emission of electrons from a conducting cathode into the anode (Fowler–Nordheim emission). Then we move to single-electron Larmor orbits, where the number of electrons is low and the interaction of individual electrons is ignored. With a sufficiently high self-magnetic field, the electron orbits do not intercept the anode. Increasing electron density then leads to the collisional description of electron flow by Creedon in which the single-particle electron orbits are replaced with a para-potential (Brillouin) flow profile. At this final point there are sufficient electrons in the vacuum flow to shield the cathode and stop electron emission. Electrons flow in the direction of the Poynting vector. Para-potential models for vacuum electron flow agree very well with data. More recently, Mendel; and Ottinger and Schumer have simplified the para-potential model using a Zflow model that approximates the electron sheath size and electron-flow current into models that are simply solved.

Higher-currents drive higher MITL voltages at all MITL locations and for all times. This leads to a number of MITL issues that must be addressed. Early-time electron current losses to the anode increase as ~V3/2 and, with sufficient voltage, these losses can raise anode plasmas, resulting in the failure of magnetic insulation. At the same time, the higher voltages (electric fields) during equilibrium MITL flow result in larger vacuum electron-flow currents and larger electron sheaths, leading to increased losses and plasma formation at the convolute. This material is based upon work supported by the Department of Energy National Nuclear Security Administration under Award No. DE-NA0003856, Sandia National Laboratories under Contract No. 2332811, the University of Rochester, and the New York State Energy Research and Development Authority.