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The objectives of this tutorial are as follows: 1) to help students and researchers develop a basic understanding of how pulsed-power systems are used to create high-energy-density (HED) matter; 2) to develop a basic understanding of a new, compact, and efficient pulsed-power technology called linear transformer drivers (LTDs); 3) to understand why LTDs are an attractive technology for driving HED physics (HEDP) experiments; 4) to contrast LTDs with the more traditional Marx-generator/pulse-forming-line approach to driving HEDP experiments; and 5) to briefly review the history of LTD technology as well as some of the LTD-driven HEDP research presently underway at universities and research laboratories across the globe. This invited tutorial is part of the Mini-Course on Charged Particle Beams and High-Powered Pulsed Sources, held in conjunction with the 44th International Conference on Plasma Science in May of 2017.

Herein we describe the design, simulation and performance of a 118-GW linear transformer driver (LTD) cavity at Sandia National Laboratories. The cavity consists of 20 to 24 “Bricks”. Each brick is comprised of two 80 nF, 100 kV capacitors connected electrically in series with a custom, 200 kV, three-electrode, field-distortion gas switch. The brick capacitors are bi-polar charged to a total of 200 kV. Typical brick circuit parameters are 40 nF (two 80 nF capacitors in series) and 160 nH inductance. Over the course of over 10,000 shots the cavity generated a peak electrical current and power of 1.19 MA and 118 GW.

Pulsed power accelerators compress electrical energy in space and time to provide versatile experimental platforms for high energy density and inertial confinement fusion science. The 80-TW “Z” pulsed power facility at Sandia National Laboratories is the largest pulsed power device in the world today. Z discharges up to 22 MJ of energy stored in its capacitor banks into a current pulse that rises in 100 ns and peaks at a current as high as 30 MA in low-inductance cylindrical targets. Considerable progress has been made over the past 15 years in the use of pulsed power as a precision scientific tool. This paper reviews developments at Sandia in inertial confinement fusion, dynamic materials science, x-ray radiation science, and pulsed power engineering, with an emphasis on progress since a previous review of research on Z in Physics of Plasmas in 2005.

Herein we present details of the design, simulation, and performance of a 100-GW linear transformer driver (LTD) cavity at Sandia National Laboratories. The cavity consists of 20 “bricks.” Each brick is comprised of two 80 nF, 100 kV capacitors connected electrically in series with a custom, 200 kV, three-electrode, field-distortion gas switch. The brick capacitors are bipolar charged to ±100 kV for a total switch voltage of 200 kV. Typical brick circuit parameters are 40 nF capacitance (two 80 nF capacitors in series) and 160 nH inductance. The switch electrodes are fabricated from a WCu alloy and are operated with breathable air. Over the course of 6,556 shots the cavity generated a peak electrical current and power of 1.03 MA (±1.8%) and 106 GW (±3.1%). Experimental results are consistent (to within uncertainties) with circuit simulations for normal operation, and expected failure modes including prefire and late-fire events. New features of this development that are reported here in detail include: (1) 100 ns, 1 MA, 100-GW output from a 2.2 m diameter LTD into a 0.1 Ω load, (2) high-impedance solid charging resistors that are optimized for this application, and (3) evaluation of maintenance-free trigger circuits using capacitive coupling and inductive isolation.

Complex hollow structures have been observed in the cores of single exploded wires and multiwire arrays using high-resolution X-ray radiography and laser probing. The radiographs show features supporting earlier research that suggested the core is a foamlike liquid–vapor mixture.

Implosion characteristics of cylindrical arrays of aluminum (Al) or tungsten (W) wires with low number of wires were studied on the 1-MA 100-150-ns current rise time COBRA generator at Cornell University using X-ray/extreme ultraviolet detectors, time-gated cameras, spectrometers, and electrical diagnostics. Total radiation yields ET of 2.8 and 4.1 kJ were measured for Al and W, respectively. The yield above 0.75 keV for W arrays was lower than for Al. Al spectra imply Te of 250-280 eV. X-ray spectra in the 2-3-keV range from W arrays showed only very weak spectral lines. A relatively uniform precursor plasma column was observed on time-gated images in the initial implosion phase for both Al and W. Rapid radiation cooling of W plasmas after precursor plasma formation leads to a decrease of plasma Te before the stagnation phase of the implosion. No evidence of the increased energy deposition that could be associated with the single-shell or closed toroidal magnetic structures models was found

The rebuilt COBRA pulsed-power generator, which has a variable current-pulse waveform and amplitude (95-150-ns rise time and ~1-MA peak current), has extended the range of the current-pulse parameters that can be used to study the X-pinches. X-pinches with 4-12 wires of several different wire materials (from Al to W) with diameters from 25 to 75 mum have been studied. The influence of the rate of the rise of current and the X-pinch wire mass on the X-pinch plasma formation and pinch implosion dynamics has been studied using a set of diagnostics with spatial and/or temporal resolution. Multiwire X-pinches were placed in the diode center, and/or two four-wire X-pinches were placed in one of the four parallel return-current circuits of the diode. The experiments showed that the most important factor determining the first X-ray burst timing is the linear mass density of the X-pinch wires, and an optimal value for obtaining a single high-energy X-ray burst was found. Radiographic images of the different test objects, wires in wire-array Z-pinches, and the X-pinches, themselves, were obtained using a micrometer-scale spatial resolution

The limited understanding of the mechanisms driving the mass ablation rate of cylindrical wires arrays is presently one of the major limitations in predicting array performance at the higher current levels required for inertial confinement fusion (ICF) ignition. Continued investigation of this phenomenon is crucial to realize the considerable potential for wire arrays to drive both ICF and inertial fusion energy, by enabling a predictive capability in computational modeling. We present the first study to directly compare the mass ablation rates of wire arrays as a function of the current rise rate. Formation of the precursor column is investigated on both the MAPGIE (1 MA, 250ns [Mitchell et al., Rev. Sci. Instrum. 67, 1533 (1996)]) and COBRA (1 MA, 100ns [Greenly et al., Rev. Sci. Instrum. 79, 073501 (2008)]) generators, and results are used to infer the change in the effective ablation velocity induced by the rise rate of the drive current. Laser shadowography, gated extreme ultraviolet (XUV) imaging, a...

We are investigating the development of the axial instability, a modulation of the size of the coronal plasma that develops around each wire in wire‐array Z‐pinches. The modulation is a result of nonuniform ablation of material from the relatively cold wire core. It has long been known that the wavelength of this modulation is constant late in time and, since it is unique to different materials, it has come to be known as the fundamental mode. In these experiments we imaged individual wires with laser shadowgraphy early in time primarily in low wire number, large wire diameter aluminum arrays for ease of viewing. We Observe the development of this modulation from the time of initiation of coronal plasma, obtaining its dominant wavelength and amplitude growth as a function of time. We also studied the instability on coiled wires, which modify the wire ablation mechanism and completely suppress the fundamental mode[Hall2008]. time is discussed.

A new imaging system for 1 MA scale wire-array Z-pinch experiments that produces up to five high-resolution x-ray images per experimental pulse has been developed. Calibrated areal density measurements of the Z-pinch plasma can be obtained from each pulse. The system substitutes five molybdenum (Mo) X pinches for the normal copper return-current conductors to provide point sources of x-rays for point-projection radiography. Each backlighting X pinch consists of four Mo wires, the x-ray burst timing of which was controlled by varying the wire diameter (mass) from 10.2 to 30 microm in the five X pinches. Typical images have a 16x8 mm2 field of view at the wire array and a magnification of about 6.5:1 on the x-ray-sensitive film. Titanium (Ti) filters in front of the films transmit continuum radiation in the spectral range of 3-5 keV. Inclusion on the Ti of a step wedge having known thickness increments of the same material as the wires enables the calibrated areal density measurements to be made of the exploding wire plasmas. Here, we used tungsten (W) step wedges with step thicknesses ranging from 0.015 to 1.1 microm to obtain accurate (+/-10%) areal density measurements of W plasmas from the spatial profile of film exposure. When imaging arrays that produce intense radiation pulses, a plastic monofilament "quencher" is placed on axis to avoid film saturation. Images have subnanosecond temporal resolution and about 7 microm spatial resolution.

A new, wide spectral bandwidth x-ray spectrograph, the wide-bandwidth focusing spectrograph with spatial resolution (WB-FSSR), based on spherically bent mica crystals, is described. The wide bandwidth is achieved by combining three crystals to form a large aperture dispersive element. Since the WB-FSSR covers a wide spectral band, it is very convenient for application as a routine diagnostic tool in experiments in which the desired spectral coverage is different from one test to the next. The WB-FSSR has been tested in imploding wire-array experiments on a 1 MA pulsed power machine, and x-ray spectra were recorded in the 1-20 A spectral band using different orders of mica crystal reflection. Using a two mirror-symmetrically placed WB-FSSR configuration, it was also possible to distinguish between a real spectral shift and a shift of recorded spectral lines caused by the spatial distribution of the radiating plasma. A spectral resolution of about 2000 was demonstrated and a spatial resolution of approximately 100 microm was achieved in the spectral band of 5-10 A in second order of mica reflection. A simple method of numerical analysis of spectrograph capability is proposed.

Imaging using X‐pinch backlighters has been implemented on the COBRA accelerator at Cornell University to study the early stages of wire‐array Z‐pinches. Two of four return‐current posts in the wire‐array load region are replaced by X pinches so that two images of one wire in an eight‐wire z‐pinch are obtained from different angles and at different times. High resolution images have been obtained that show the evolution of wire structure and instabilities. X‐pinch wire diameter and other parameters were varied in order to shift the timing of the X pinches relative to the start of the z‐pinch current pulse. It was found that XPBL wire diameter (mass per unit length) has the strongest influence on radiation timing.

The rebuilt COBRA pulsed power generator, which has a variable current pulse waveform and amplitude (90–150 ns rise time, 0.6 – 1 MA) has extended the range of current pulse parameters that can be used to study X pinches. X pinches with 2 to 12 wires with diameters from 25 to 75 μm of several different wire materials (from Al to W) have been studied. The influence of different current shapes on X pinch plasma formation and pinch implosion dynamics has been studied using a set of diagnostics with spatial and/or temporal resolution. Multiwire X pinches were placed in the diode center and/or two four wire X pinches were places in one of four parallel return current circuits of the diode. Radiographic images of different test objects, wires in the array and the X pinches, themselves, were obtained with μm scale spatial resolution.

Measurements of the plasma density profile near the exploding wires in 1 MA tungsten (W) wire-array Z-pinches have been made using calibrated x-ray absorption. As many as 5 x-ray images per pulse were obtained between 65 and 160 ns after the start of the 100 ns rise time current pulse. Measured W ion densities range from above 1019/cm3 close to the wire to ∼1017/cm3 about 1 mm away from the wire in the plasma stream. After accurate geometrical registration of the individual wires in each successive image in a pulse using the Genetic Algorithm, the temporal evolution of the axial modulation wavelength distribution of the ablation rate from the wires in each array and the global mass-ablation rate as a function of time are presented.

Wire core and coronal plasma formation and expansion in wire-array Z pinches with small numbers of wires have been studied on a 1MA, 100ns rise time pulsed power generator and a 500kA, 50ns generator. Two-frame point-projection x-ray imaging and three-frame laser optical imaging and interferometry were the principal diagnostic methods used for these studies. The x-ray images show that dense coronal plasma forms and is maintained close to each dense wire core in the array. A less dense, rapidly expanding (∼10μm∕ns) coronal plasma, best seen in the laser images, surrounds the ∼100μm radius dense corona. These results are in agreement with computer simulations and modeling carried out by Yu et al. [Phys. Plasmas 14, 022705 (2007)]. Results are also presented for the dependence of the wire core and coronal plasma expansion rates on the wire diameter, number of wires and current through individual wires and the overall configuration for Al, Cu, and W wire arrays. For example, the W wire dense core expansion ra...

The COBRA pulsed power generator has a variable current pulse wave form and amplitude (95–180ns rise time, up to 1MA peak current). It was designed to study wire array Z pinches and X pinches, including plasma formation, pinch implosion dynamics, and pinch plasma parameters as a function of current rise time. These loads have been studied using an extensive set of diagnostics with spatial and/or temporal resolution. The set of electrical diagnostics on the COBRA generator includes Rogowski coils to monitor the total load current and the current through individual return current posts, and there is also an inductive voltage monitor. A set of extreme ultraviolet and x-ray detectors is used to study the load radiation. Wire array and X pinch plasma formation and dynamics are studied using two-frame, point projection X-pinch x-ray imaging as well as with multiframe laser probing. Flat potassium acid phtalate crystal (KAP), convex, extreme luminosity imaging conical spectrograph, and focusing spectrograph with...

A new configuration for a two-dimensional (2D) imaging x-ray spectrograph based on a conically bent crystal is introduced: extreme luminosity imaging conical spectrograph (ELICS). The ELICS configuration has important advantages over spectrographs that are based on cylindrically and spherically bent crystals. The main advantages are that a wide variety of large-aperture crystals can be used, and any desired magnification in the spatial direction (the direction orthogonal to spectral dispersion) can be achieved by the use of different experimental arrangements. The ELICS can be set up so that the detector plane is almost perpendicular to the incident rays, a good configuration for time-resolved spectroscopy. ELICSs with mica crystals of 45×90mm2 aperture have been successfully used for imaging on the XP and COBRA pulsed power generators, yielding spectra with spatial resolution in 2D of Z pinches and X pinches.

This report contains five studies concerned with determining the costs and effectiveness of decontamination applied to postattack recovery an a fallout environment. These studies cover the following subjects: (1) The Effect of Early Decontamination of Total Dose: This study describes the effect of a single (discrete) reduction in radiation intensity (i.e., by decontamination) on an individual's dose history in a t to the -1.2 power radiation field; (2) The Effect of Early Decontamination of ERD: This analysis is like the first in describing the effect of a single reduction in radiation intensity, except that an individual's dose is measured in terms of his ERD; (3) Total Dose Approximations for Brief Exposure in a Fallout Environment: Two approximations to the expression used to calculate total dose for a finite exposure time in a t to the -Kth power radiation field developed and the resultant error is estimated. (4) The Effectiveness of Radiological Countermeasures in Accelerating Postattack Recovery: This study develops the parametric relationships that determine which radiological countermeasures could accelerate the postattack recovery process.

This study examines the effectiveness and costs associated with the application of decontamination to accelerating recovery of an activity in a postattack fallout environment. The effectiveness is measured in two ways: first, by the fractional reduction in dose rate that can be achieved by decontamination; and second, when the dose received during the activity is specified by the fractional reduction in denial time that can be achieved by decontamination. The costs are described in terms of the personnel and equipment required for decontamination, the radiation doses received by the personnel, and the water required by the operation. The recovery of an activity is defined in terms of radiation doses received by the activity personnel in performing the activity. When these doses are reduced to acceptable safety level by reducing the dose rate in the activity area, the activity is said to be recovered. The above dose constraints are expressed both in terms of the maximum total dose and in terms of the maximum equivalent residual dose. The primary conclusion reached, that decontamination is as vital to recovery as shelters are to survival in a fallout environment, is the basis for recommending further studies analyzing the application of decontamination to integrated whole-city recovery.

We present the first study to directly compare the mass ablation rates of cylindrical wire arrays as a function of the current rise‐rate. Formation of the precursor column is investigated on both the MAPGIE (1 MA, 250 ns) and COBRA (1 MA, 100 ns) generators, and results are used to infer the change in the mass ablation rate induced by the rise‐rate of the drive current. Laser shadowography, gated XUV imaging and x‐ray diodes are used to compare the dynamical behavior both generators, and x‐pinch radiography and XUV spectroscopy and provide density evolution and temperature measurements respectively. Results are compared to predictions from an analytical scaling model based on a fixed ablation rate, and the close correlation achieved suggests that the effective ablation velocity is not a strong function of the current rise rate.