By relaxing an assumption on the electron density in the flow layer used in magnetically insulated transmission line (MITL) theory, the theory is rescaled to match particle-in-cell (PIC) simulation results, providing a more accurate determination of the line voltage from the measurement of anode and cathode currents over a broad range of parameters. Results from the PIC simulations also show that self-limited flow is not determined by either a minimum-current or a minimum-energy condition, but rather is closer to saturated flow. In addition, analytic expressions are obtained for the first time for the self-limited flow impedance ZfSL(V)∕Z0 and the self-limited anode and cathode currents Z0IaSL(V) and Z0IcSL(V), where Z0 is the vacuum impedance of the line and V is the voltage. Similar expressions for both minimum-current flow and minimum-energy flow are also obtained. Results are compared with other models for MITL flow and show that this rescaled MITL flow model is most consistent with the PIC simulation results. Finally, it is shown that a matched load condition can never be satisfied for self-limited (or line-limited) flow.

The rod-pinch diode consists of an annular cathode and a small-diameter anode rod that extends through the hole in the cathode. With high-atomic-number material at the tip of the anode rod, the diode provides a small-area, high-yield x-ray source for pulsed radiography. The diode is operated in positive polarity at peak voltages of 1 to 2 MV with peak total electrical currents of 30–70 kA. Anode rod diameters as small as 0.5 mm are used. When electrode plasma motion is properly included, analysis shows that the diode impedance is determined by space-charge-limited current scaling at low voltage and self-magnetically limited critical current scaling at high voltage. As the current approaches the critical current, the electron beam pinches. When anode plasma forms and ions are produced, a strong pinch occurs at the tip of the rod with current densities exceeding 106 A/cm2. Under these conditions, pinch propagation speeds as high as 0.8 cm/ns are observed along a rod extending well beyond the cathode. Even faster pinch propagation is observed when the rod is replaced with a hollow tube whose wall thickness is much less than an electron range, although the propagation mechanism may be different. The diode displays well-behaved electrical characteristics for aspect ratios of cathode to anode radii that are less than 16. New physics understanding and important properties of the rod-pinch diode are described, and a theoretical diode current model is developed and shown to agree with the experimental results. Results from numerical simulations are consistent with this understanding and support the important role that ions play. In particular, it is shown that, as the ratio of the cathode radius to the anode radius increases, both the Langmuir–Blodgett space-charge-limited current and the magnetically limited critical current increase above previously predicted values.

A theoretical model for the plasma erosion opening switch (PEOS) is presented which predicts its voltage, current and impedance history as a function of the input waveforms, geometry, and switch parameters. Scaling relations for the switch operation are developed from this model. System requirements for pulse compression and power multiplication using inductive storage are derived from a simple lumped circuit analysis and a transmission line analysis. These requirements are shown to be satisfied using the PEOS as a fast opening, vacuum switch in a configuration relevant for existing high-power accelerators. The switch model is incorporated into a transmission line code for comparison with recent inductive storage experiments. Code results agree well with the data showing conduction times of ∼60 ns and switching times of ∼10 ns with peak currents of ∼600 kA.

The dynamics of long-conduction-time (r,-1 ,z+) plasma opening switches (PQS) is studied using magnetohydrodynamic (MHD) theory, including the Hall term. Plasma switches with initial electron densities of 't,= 1014-10'6 cmm3 are modeled; these densities are appropriate to recent experiments carried out at the Naval Research Laboratory using the Hawk generator (800 kA, 1.2 ,u). The conduction times obtained from the simulation studies are in the range rC=0.4-2.0 w. The POS plasma is strongly redistributed by the penetrating magnetic field. As the field penetrates, it pushes the plasma both axially and radially (i.e., toward the anode and cathode). In the higher-density regime (n,> lOI cmM3), Hall effects do not play a significant role. The magnetic field acts as a snowplow, sweeping up and compressing the plasma as it propagates through the POS plasma. In the lower-density regime (n,< 1015 cmv3), Hall effects become important in two ways: the conduction time is less than that expected from ideal MHD, and the POS plasma becomes unstable as the magnetic field penetrates, leading to finger-like density structures. The instability is the unmagnetized ion Rayleigh-Taylor instability and is driven by the magnetic force accelerating the plasma. The structuring of the plasma further decreases the conduction time and causes the penetrating magnetic field to have a relatively broad front in comparison to EMHD simulations (i.e., Vi=O). The simulation results are consistent with experimental data for conduction currents 300-800 kA.

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Initiation of an anode plasma and ion emission into a magnetically insulated transmission line can cause serious current losses unless the ions are magnetically insulated as well as the electrons. A model for magnetically insulated ion flow in a vacuum transmission line is developed. Particle-in-cell simulations are presented that show that this model accurately predicts properties of this flow. The model is applied to determine the current required to magnetically insulate ion flow for a given voltage and vacuum line impedance. Relevance of this work to system designs for Z-pinch-driven inertial confinement fusion is discussed.

The merits of several high-resolution, pulsed-powerdriven, flash X-ray sources are examined with numerical simulation for voltages up to 10 MV. The charged particle dynamics in these self-magnetically pinched diodes (SMPDs), as well as electron scattering and energy loss in the high-atomic-number target, are treated with the partic by coupling the output from LSP with the two-dimensional component of the integrated tiger series of Monte Carlo electron/photon transport codes, CYLTRAN. The LSP/CYLTRAN model agrees well with angular dose-rate measurements from positive-polarity rod-pinch-diode experiments, where peak voltages ranged from 5.2-6.3 MV. This analysis indicates that, in this voltage range, the dose increases with angle and is a maximum in the direction headed back into the generator. This suggests that high-voltage rod-pinch experiments should be performed in negative polarity to maximize the extracted dose. The benchmarked LSP/CYLTRAN model is then used to examine three attractive negative-polarity diode geometry concepts as possible high-resolution radiography sources for voltages up to 10 MV. For a 2-mm-diameter reentrant rod-pinch diode (RPD), a forward-directed dose of 740 rad(LiF) at 1 m in a 50-ns full-width at half-maximum radiation pulse is predicted. For a 2-mm-diameter nonreentrant RPD, a forward-directed dose of 1270 rad(LiF) is predicted. For both RPDs, the on-axis X-ray spot size is comparable to the rod diameter. A self-similar hydrodynamic model for rod expansion indicates that spot-size growth from hydrodynamic effects should be minimal. For the planar SMPD, a forward-directed dose of 1370 rad(LiF) and a similar X-ray spot size are predicted. These results show that the nonreentrant RPD and the planar SMPD are very attractive candidates for negative-polarity high-resolution X-ray sources for voltages of up to 10 MV.Index Terms-Bremsstrahlung, coupled electron-photon transport, electron beams, flash X-radiography, high-power diodes, ion beams, Monte Carlo, particle-in-cell.

Particle-in-cell (PIC) simulations are presented that characterize the electrical properties and charged-particle flows of cylindrical pinched-beam diodes. It is shown that there are three basic regimes of operation: A low-voltage, low-current regime characterized by space-charge-limited (SCL) flow, a high-voltage, high-current regime characterized by a strongly pinched magnetically limited (ML) flow, and an intermediate regime characterized by weakly pinched (WP) flow. The flow pattern in the SCL regime is mainly radial with a uniform current density on the anode. In the ML regime, electrons are strongly pinched by the self-magnetic field of the diode current resulting in a high-current-density pinch at the end of the anode rod. It is shown that the diode must first draw enough SCL current to reach the magnetic limit. The voltage at which this condition occurs depends strongly on the diode geometry and whether ions are produced at the anode. Analytic expressions are developed for the SCL and ML regimes and compared to simulations performed over a wide range of voltages and diode geometries. In the SCL regime, it is shown that many of the results from planar diodes provide reasonably good estimates for cylindrical diodes. In the ML regime, it is found that the critical current formula provides a better fit to the simulations than the parapotential and focused flow models. An empirical fit to the I–V characteristic was developed from the simulations that smoothly transitions from the SCL regime, through the WP regime, and into the ML regime.