J.W. Schumer

Theoretical modeling and experimental characterization of a rod-pinch diode

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 f...

Particle-in-cell simulations of high-power cylindrical electron beam diodes

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 a...

Ultra-high electron beam power and energy densities using a plasma-filled rod-pinch diode

The plasma-filled rod-pinch diode is a new technique to concentrate an intense electron beam to high power and energy density. Current from a pulsed power generator (typically ∼MV, MA, 100 ns pulse duration) flows through the injected plasma, which short-circuits the diode for 10–70 ns, then the impedance increases and a large fraction of the ∼MeV electron-beam energy is deposited at the tip of a 1 mm diameter, tapered rod anode, producing a small (sub-mm diameter), intense x-ray source. The current and voltage parameters imply 20–150 μm effective anode-cathode gaps at the time of maximum radiation, much smaller gaps than can be used between metal electrodes without premature shorting. Interferometric diagnostics indicate that the current initially sweeps up plasma in a snowplow-like manner, convecting current toward the rod tip. The density distribution is more diffuse at the time of beam formation with a low-density region near the rod surface where gap formation could occur. Particle simulations of the...

Evaluation of self-magnetically pinched diodes up to 10 MV as high-resolution flash X-ray sources

The merits of several high-resolution, pulsed-power-driven, 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.

Rescaling of equilibrium magnetically insulated flow theory based on results from particle-in-cell simulations

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...

Z pinch imploding plasma density profile measurements using a two-frame laser shearing interferometer

A laser shearing interferometer (LSI) was used to make spatially and temporally resolved measurements of the electron density profile in an imploding z pinch. Experiments were conducted on the 0.7-MA/250-ns Hawk machine, the 2.5-MA/100-ns ACE-4 machine, and the 3.8-MA/190-ns Double Eagle machine. Time and space resolved measurements of the current and plasma density are needed for better understanding of the implosion dynamics and stagnation physics of z pinches. The electron density profile can be obtained using an LSI. The LSI passes a short pulse, collimated laser beam across the imploding z pinch, which distorts the laser wavefront. the maximum wavefront distortion occurs where the density gradient is highest, such as across the current sheath. After passing through the pinch, the distorted wavefronts are split into two beams that are laterally displaced relative to one other. This shearing causes interference between these two wavefronts and produces an interferogram, from which the plasma density profiles are derived. In the experiments, a 150-ps laser pulse was split into two pulses with an interpulse delay of several tens. of nanoseconds. This pulse pair gave two snap shots of the electron density profiles during the 100-300-ns implosions. From these interferograms, electron densities and implosion velocities of the imploding plasmas were derived, the current sheath was observed, and the plasma ionization states, growth rates, and wavelengths of instabilities were estimated. The results motivate construction of an upgraded instrument with four or more frames and with an added laser polarimetry measurement (Faraday rotation) capability to obtain both electron and current profiles.

High-Power Self-Pinch Diode Experiments for Radiographic Applications

We report here on self-magnetic-pinch diode experiments at voltages from 3.5 to 6 MV. In addition to electrical diagnostics, the diode is characterized as a radiation source by dose and spot-size measurement. As the operating voltage increases, we find that a given diode geometry tends to produce a smaller spot but suffers from the reduced impedance lifetime. Optimization involves increasing the cathode diameter and diode gap as the voltage increases. We find a good quantitative agreement with the Monte Carlo code integrated tiger series over the entire data set, assuming an effective electron incidence angle of 20deg. Over this range, we observe favorable dose and spot scaling of optimized diode performance with voltage. Our best results are roughly 200-rad at 1 m with an ~2-mm-diameter spot. These were obtained at diode parameters of roughly 6 MV, 150 kA, and 30-ns radiation full-width at half-maximum.

Initialization and Operation of Mercury, A 6-MV MIVA

Mercury became operational in a stepwise manner to test the machine components after modifications and reassembly at NRL. To avoid damaging the MIVA, extensive testing of the laser and PFL output switches was performed using dummy loads. Finally, the PFLs were connected to the MIVA and Mercury was fired into a simple cylindrical diode load with a Marx charge voltage up to 75 kV. Measured MIVA currents and voltages compare well with a circuit model of the MIVA fed by the measured PFL outputs and with PIC simulations of the MIVA and the diode load.

MHD-to-PIC transition for modeling of conduction and opening in a plasma opening switch

The plasma opening switch (POS) is a critical element of some inductive-energy-storage pulsed-power generators. Detailed understanding of plasma redistribution and thinning during the POS conduction phase can be gained through magnetohydrodynamic fluid (MHD) simulations. As space-charge separation and kinetic effects become important late in the conduction phase (beginning of the opening phase), MHD methods become invalid and particle-in-cell (PIC) methods should be used. In this paper, the applicability of MHD techniques is extended into PIC-like regimes by including nonideal MHD phenomena such as the Hall effect and resistivity. The feasibility of the PIC technique is, likewise, extended into high-density, low-temperature-MHD-like regimes by using a novel numerical cooling algorithm. At an appropriate time, an MHD-to-PIC transition must be accomplished in order to accurately simulate the POS opening phase. The mechanics for converting MHD output into PIC input are introduced, as are the transition criteria determining when to perform this conversion. To establish these transition criteria, side-by-side MHD and PIC simulations are presented and compared. These separate simulations are then complemented by a proof-of-principle MHD-to-PIC transition, thereby demonstrating this MHD-to-PIC technique as a potentially viable tool for the simulation of POS plasmas. Practical limitations of the MHD-to-PIC transition method and applicability of the transition criteria to hybrid fluid-kinetic simulations are discussed.

Magnetically insulated electron flow with ions with application to the rod-pinch diode

A one-dimensional, steady-state, relativistic electron-flow model is developed that describes magnetically insulated electron flow in the presence of ions produced by space-charge-limited emission from the anode. The model is applied to the rod-pinch diode which is a cylindrical pinched-beam diode consisting of a small radius anode rod extending through the hole of an annular cathode. The diode is designed to run at critical current so that electrons emitted from the cathode are magnetically insulated and flow axially along the anode rod until they pinch radially onto the rod tip. Ions are emitted along the length of rod and flow radially outward. Without these ions, magnetically insulated electron flow cannot be established and electrons cannot propagate to the rod tip. Both fluid and Vlasov treatments of the electrons are considered. An analytic expression for the critical current is derived and is compared with the critical current determined from experimental data and particle-in-cell simulations. Rea...