Energy losses in high current density conductors

The Z accelerator at Sandia National Laboratories has reached currents in excess of 20 MA; and the new ZR accelerator, scheduled to come on line later in 2007, will generate currents greater than 26 MA. These very high currents are delivered to loads with characteristic dimensions of ∼ 1 cm or less. The resulting linear current densities can exceed 5 MA/cm. At these current densities there can be significant losses in conductors. Original studies by Singer [5] and later work by Spielman et al. [7] started to provide predictions of these conductor losses. Improved materials properties (equations-of-state and resistivities) have found their way into magneto-hydrodynamic computer codes thereby providing significant improvements in predictive capabilities. We find that the key loss mechanisms are shock heating, pdV compressive heating, ohmic heating, and dynamic material motion. In addition to the dissipative losses described above, diffusion of current into conductors and material motion acts to increase the inductance of the conductors. We describe calculations of conductor losses in stainless steel and tungsten. We show that losses generally increase with lower density material and strongly increase with current density and current pulse duration. For 100-ns rise-time current pulses at current densities of 10 MA/cm, energy losses in a stainless steel coaxial conductor can be ∼ 8%/cm.