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Vacuum-post-hole convolutes are used in pulsed high-power generators to join several magnetically insulated transmission lines (MITL) in parallel. Such convolutes add the output currents of the MITLs, and deliver the combined current to a single MITL that, in turn, delivers the current to a load. Magnetic insulation of electron flow, established upstream of the convolute region, is lost at the convolute due to symmetry breaking and the formation of magnetic nulls, resulting in some current losses. At very highpower operating levels and long pulse durations, the expansion of electrode plasmas into the MITL of such devices is considered likely. This work examines the evolution and dynamics of cathode plasmas in the double-post-hole convolutes used on the Z accelerator [R. B. Spielman et al., Phys. Plasmas 5, 2105]. Three-dimensional particle-in-cell (PIC) simulations that model the entire radial extent of the Z accelerator convolute -from the parallel-plate transmission-line power feeds to the z-pinch load regionare used to determine electron losses in the convolute. The results of the simulations demonstrate that significant current losses (1.5 MA out of a total system current of 18.5 MA), which are comparable to the losses observed experimentally, could be caused by the expansion of cathode plasmas in the convolute regions.

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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.