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We describe herein a system of self-magnetically insulated vacuum transmission lines (MITLs) that operated successfully at 20 MA, 3 MV, and 55 TW. The system delivered the electromagnetic-power pulse generated by the Z accelerator to a physics-package load on over 1700 Z shots. The system included four levels that were electrically in parallel. Each level consisted of a water flare, vacuum-insulator stack, vacuum flare, and 1.3-m-radius conical outer MITL. The outputs of the four outer MITLs were connected in parallel by a 7.6-cm-radius 12-post double-post-hole vacuum convolute. The convolute added the currents of the four outer MITLs, and delivered the combined current to a single 6-cm-long inner MITL. The inner MITL delivered the current to the load. The total initial inductance of the stack-MITL system was 11 nH. A 300-element transmission-line-circuit model of the system has been developed using the TL code. The model accounts for the following: (i) impedance and electrical length of each of the 300 circuit elements, (ii) electron emission from MITL-cathode surfaces wherever the electric field has previously exceeded a constant threshold value, (iii) Child-Langmuir electron loss in the MITLs before magnetic insulation is established, (iv) MITL-flow-electron loss after insulation, assuming either collisionless or collisional electron flow, (v) MITL-gap closure, (vi) energy loss to MITL conductors operated at high lineal current densities, (vii) time-dependent self-consistent inductance of an imploding z-pinch load, and (viii) load resistance, which is assumed to be constant. Simulations performed with the TL model demonstrate that the nominal geometric outer-MITL-system impedance that optimizes overall performance is a factor of $3 greater than the convolute-load impedance, which is consistent with an analytic model of an idealized MITL-load system. Power-flow measurements demonstrate that, until peak current, the Z stack-MITL system performed as expected. TL calculations of the peak electromagnetic power at the stack, stack energy, stack voltage, outer-MITL current, and load current, as well as the pinch-implosion time, agree with measurements to within 5%. After peak current, TL calculations and measurements diverge, which appears to be due in part to the idealized pinch model assumed by TL. The results presented suggest that the design of the Z accelerator's stack-MITL system, and the TL model, can serve as starting points for the design of stack-MITL systems of future superpower accelerators.

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We have developed a semianalytic expression for the total energy loss to a vacuum transmission-line electrode operated at high lineal current densities. (We define the lineal current density j ' B= 0 to be the current per unit electrode width, where B is the magnetic field at the electrode surface and 0 is the permeability of free space.) The expression accounts for energy loss due to Ohmic heating, magnetic diffusion, j  B work, and the increase in the transmission line's vacuum inductance due to motion of the vacuum-electrode boundary. The sum of these four terms constitutes the Poynting fluence at the original location of the boundary. The expression assumes that (i) the current distribution in the electrode can be approximated as one-dimensional and planar; (ii) the current IðtÞ ¼ 0 for t < 0, and IðtÞ / t for t ! 0; (iii) j ' 10 MA=cm; and (iv) the current-pulse width is between 50 and 300 ns. Under these conditions we find that, to first order, the total energy lost per unit electrode-surface area is given by W t ðtÞ ¼ t B ðtÞ þ t B ðtÞ, where BðtÞ is the nominal magnetic field at the surface. The quantities

The Total Immersion Particle [B. M. Marder, Math. Comput. 29, 434 (1973)] code has been used in several two-dimensional geometries to understand better the measured dynamics of annular, aluminum wire-array z-pinches. The areas investigated include the formation of the plasma sheath from current-induced individual wire explosions, the effects of wire number and symmetry on the implosion dynamics, and the dependence of the Rayleigh–Taylor instability growth on initial sheath thickness. A qualitative change in the dynamics with increasing wire number was observed, corresponding to a transition between a z-pinch composed of nonmerging, self-pinching individual wires, and one characterized by the rapid formation and subsequent implosion of a continuous plasma sheath. A sharp increase in radiated power with increasing wire number has been observed experimentally near this calculated transition. Although two-dimensional codes have correctly simulated observed power pulse durations, there are indications that three-dimensional effects are important in understanding the actual mechanism by which these pulse lengths are produced.