We have developed a relativistic-fluid model of the flow-electron plasma in a steady-state onedimensional magnetically insulated transmission line (MITL). The model assumes that the electrons are collisional and, as a result, drift toward the anode. The model predicts that in the limit of fully developed collisional flow, the relation between the voltage V a , anode current I a , cathode current I k , and geometric impedance Z 0 of a 1D planar MITL can be expressed as V a I a Z 0 h, where h 1=4 ÿ 1 1=2 ÿ lnb 2 ÿ 1 1=2 c=2 ÿ 1 and I a =I k . The relation is valid when V a * 1 MV. In the minimally insulated limit, the anode current I a;min 1:78V a =Z 0 , the electron-flow current I f;min 1:25V a =Z 0 , and the flow impedance Z f;min 0:588Z 0 . {The electronflow current I f I a ÿ I k . Following Mendel and Rosenthal [Phys. Plasmas 2, 1332 (1995)], we define the flow impedance Z f as V a =I 2 a ÿ I 2 k 1=2 .g In the well-insulated limit (i.e., when I a I a;min ), the electron-flow current I f 9V 2 a =8I a Z 2 0 and the flow impedance Z f 2Z 0 =3. Similar results are obtained for a 1D collisional MITL with coaxial cylindrical electrodes, when the inner conductor is at a negative potential with respect to the outer, and Z 0 & 40 . We compare the predictions of the collisional model to those of several MITL models that assume the flow electrons are collisionless. We find that at given values of V a and Z 0 , collisions can significantly increase both I a;min and I f;min above the values predicted by the collisionless models, and decrease Z f;min . When I a I a;min , we find that, at given values of V a , Z 0 , and I a , collisions can significantly increase I f and decrease Z f . Since the steady-state collisional model is valid only when the drift of electrons toward the anode has had sufficient time to establish fully developed collisional flow, and collisionless models assume there is no net electron drift toward the anode, we expect these two types of models to provide theoretical bounds on I a , I f , and Z f .

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.

A three-dimensional, fully electromagnetic model of the principal pulsed-power components of the 26-MA ZR accelerator [D. H. McDaniel et al., in Proceedings of the 5th International Conference on Dense Z-Pinches (AIP, New York, 2002), p. 23] has been developed. This large-scale simulation model tracks the evolution of electromagnetic waves through the accelerator's intermediate-storage capacitors, lasertriggered gas switches, pulse-forming lines, water switches, triplate transmission lines, and water convolute to the vacuum insulator stack. The insulator-stack electrodes are coupled to a transmissionline circuit model of the four-level magnetically insulated vacuum-transmission-line section and doublepost-hole convolute. The vacuum-section circuit model is terminated by a one-dimensional self-consistent dynamic model of an imploding z-pinch load. The simulation results are compared with electrical measurements made throughout the ZR accelerator, and are in good agreement with the data, especially for times until peak load power. This modeling effort demonstrates that 3D electromagnetic models of large-scale, multiple-module, pulsed-power accelerators are now computationally tractable. This, in turn, presents new opportunities for simulating the operation of existing pulsed-power systems used in a variety of high-energy-density-physics and radiographic applications, as well as even higher-power nextgeneration accelerators before they are constructed.1 Each simulation used 144 processors on the Sandia National Laboratories (SNL) Thunderbird computer system and required approximately 24 hours of total run time. This computer system was designed and built by SNL and Dell [65] and contains 8960 Intel [66] Xeon processors operating at 3.6 GHz and uses the Infiniband interconnect architecture [67].

We have developed a physics-based transmission-line-circuit model of the Z pulsed-power accelerator. The 33-m-diameter Z machine generates a peak electrical power as high as 85 TW, and delivers as much as 25 MA to a physics load. The circuit model is used to design and analyze experiments conducted on Z. The model consists of 36 networks of transmission-line-circuit elements and resistors that represent each of Zs 36 modules. The model of each module includes a Marx generator, intermediate-energy-storage capacitor, laser-triggered gas switch, pulse-forming line, self-break water switches, and tri-plate transmission lines. The circuit model also includes elements that represent Zs water convolute, vacuum insulator stack, four parallel outer magnetically insulated vacuum transmission lines (MITLs), double-post-hole vacuum convolute, inner vacuum MITL, and physics load. Within the vacuum-transmission-line system the model conducts analytic calculations of current loss. To calculate the loss, the model simulates the following processes: (i) electron emission from MITL cathode surfaces wherever an electric-field threshold has been exceeded; (ii) electron loss in the MITLs before magnetic insulation has been established; (iii) flow of electrons emitted by the outer-MITL cathodes after insulation has been established; (iv) closure of MITL anode-cathode (AK) gaps due to expansion of cathode plasma; (v) energy loss to MITL conductors operated at high lineal current densities; (vi) heating of MITL-anode surfaces due to conduction current and deposition of electron kinetic energy; (vii) negative-space-charge-enhanced ion emission from MITL anode surfaces wherever an anode-surface-temperature threshold has been exceeded; and (viii) closure of MITL AK gaps due to expansion of anode plasma. The circuit model is expected to be most accurate when the fractional current loss is small. We have performed circuit simulations of 52 Z experiments conducted with a variety of accelerator configurations and load-impedance time histories. For these experiments, the apparent fractional current loss varies from 0% to 20%. Results of the circuit simulations agree with data acquired on 52 shots to within 2%.

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