Short Course

Speaker: Rick B. Spielman, Laboratory for Laser Energetics, University of Rochester, Rochester, NY 14623-1299
Title: Design and Modeling of Multi-TW Magnetically Insulated Transmission Lines


Magnetically insulated transmission lines (MITLs) have been a fixture on all TW+ pulsed-power drivers over the last 45 years. Our design understanding and use has gone from purely empirical (1972-1985), to ideal MITL theory (1975–1980), to Z-flow models of MITLs, and finally to particle-in-cell (PIC) validation tools (1990–today). The computing overhead for high-resolution PIC simulations is quite high, even with modern massively paralleled codes, and this limits the use of PIC codes (MAGIC, LSP, Quicksilver, CHICAGO, and TriForce) for iterative design. These codes always provide extremely useful insight into MITL operation. Higher-power computer clusters permit very high spatial resolutions (~few microns), thereby resolving the sheath at the cathode, and allow the use of more macroparticles that give much better statistics for losses.

Nevertheless, the basic understanding of the operation of complex, conical-disk MITLs has progressed to the point that initial MITL designs can be generated with intuition and simple circuit codes using Z-flow models (Screamer and BERTHA) and then validated with a more-limited number of expensive PIC simulations. Design evolution with circuit codes are possible with hundreds of iterations per day possible.

We will follow history to the first discussions of coaxial MITLs with the understanding of self-limited flow, then to losses generated by impedance mismatches, and to the generic concept of constant (geometric) impedance MITLs. Next, we will examine the “actual” operation of MITL’s in systems that do not have a constant impedance load (reactive loads). We find in these cases that the local “running” impedance of the MITL is not a constant in time or space. This is a vastly different viewpoint than the simple picture of self-limited flow in long MITLs.

The implications of even higher current drivers on MITL design are just now being considered. It should be obvious that reaching a higher peak current (for a fixed load geometry and current rise time) always forces a higher voltage on all locations in a MITL for all times. This affects both the electron losses during the setup phase of the MITL and the equilibrium MITL operational parameters (flow impedance, vacuum electron current, electron sheath thickness, etc.) At some point in peak current, the voltages (and electric fields) on the MITL cause issues with the magnitude of electron losses (plasma formation on the anode) during the startup phase and a much larger vacuum electron flow current (such flow can be lost at convolutes). Taken together, we see that MITL physics drives the design of these high-voltage MITLs.

Participants will leave this short course understanding the issues that drive MITL design over a wide range of electrical and mechanical parameters. You should be able to see how simple circuit simulations can provide equilibrium MITL operating parameters and know the danger limits.