Z pinches have long been interesting to plasma physicists because of the simplicity of their geometry. They were studied first in the 1950s as potential fusion configurations and, later, as intense X-ray sources both for military and civilian applications. The development of pulsed power technologies, some reaching energy and power levels of 3 MJ and 50 TW, respectively, by many organizations around the world has accelerated the interest in z pinches for fusion applications.

A series of specialized multidimensional resistive magnetohydrodynamic (MHD) models have been developed to tackle the different phases of evolution of wire array z-pinch implosions. Two-dimensional (r–z) “cold-start” or “wire initiation” simulations of single wires indicate the persistence of a two-component structure with a cold, dense core embedded within a much hotter, low density, m = 0 unstable corona. Cold-start simulations with similar conditions to wires in an array show a general trend in the plasma structure from discrete wires with large m = 0 perturbation amplitudes to partially merged wires with smaller perturbation amplitudes as the number of wires is increased. Two-dimensional (r–θ) simulations then show how the persistence of dense wire cores results in the injection of material between the wires into the interior of the array, generating radial plasma streams which form a precursor plasma upon reaching the axis. Higher-resolution 2-D (r–θ) simulations show similar behavior for large number wire arrays in use at Sandia National Laboratories. This model is also used to predict which modes of implosion are in operation in nested wire array experiments. Separate r–θ plane simulations of the flux of plasma imploding towards the axis from the outer array and the bombardment of the inner array by this flux are presented. Finally, 2-D (r–z) simulations of the Rayleigh–Taylor instability during the final implosion phase are used to illustrate the effect upon the power and duration of the radiation output pulse. The results of low-resolution 3-D resistive MHD simulations are also presented. The need for much higher resolution 3-D simulations of certain aspects of wire array evolution is highlighted.

Both dynamic and equilibrium z pinches are mostly described, whether in theory or in simulation, by conventional magnetohydrodynamic (MHD) fluid equations. However there are several key phases in z-pinch behavior when kinetic effects are important. Runaway electrons can occur close to the axis especially in an m = 0 neck or during the subsequent disruption. Large ion-Larmor orbits can, if sufficiently collisionless, lead to stabilizing effects. During a disruption, ion beams can be produced. For deuterium discharges, the interaction of an ion beam with the ambient plasma can lead to a significant neutron yield. If the drift velocity of the current-carrying electrons exceeds a threshold for generating microinstabilities (lower-hybrid or ion-acoustic instabilities), this leads to anomalous resistivity. This can occur not only during a disruption, but also in the low-density (usually outer) plasma boundary of an equilibrium or dynamic pinch. Related to this is the open question of whether current reconnection can occur in fully developed magneto-Rayleigh–Taylor instabilities in the low-density coronal plasma. Two other kinetic effects are new to z pinches. First, there are the collisions of low-density energetic ions from a wire array as they pass close to the axis to form a precursor plasma. Second, there is the possible erosion and ablation of wire cores in the necks of m = 0 coronal current-carrying plasma by flux-limited heat flow with its attendant deviation from a Maxwellian of the isotropic part of the distribution function.

Experiments to study plasma formation and implosion dynamics of wire array z pinches performed on MAGPIE generator (1.4 MA, 240 ns) at Imperial College are reviewed. Data from laser probing and X-ray radiography show that heterogeneous plasma structure with dense wire cores surrounded by low-density coronal plasma persists in wire arrays for a significant part of the implosion. Early implosion of the coronal plasma produces a precursor plasma column on the array axis, parameters of which depend on the rate of radiative cooling. The seeding of perturbations on the dense core of each wire is provided by nonuniform sweeping of the low-density coronal plasma from the cores by the global J × B force. The spatial scale of these perturbations (∼0.5 mm for Al, ∼0.25 mm for W) is determined by the size of the wire cores (∼0.25 mm for Al, ∼0.1 mm for W). A qualitative change in implosion dynamics, with transition to 0-D-like trajectory, was observed in Al arrays when the ratio of interwire gap to wire core size was decreased to ∼3. In experiments with nested wire arrays, two different modes of operation were identified, both giving significant sharpening of the X-ray pulse (∼10 ns) in comparison with a single array, despite the small number of wires in the arrays (16 outer, 16 inner) and the long implosion time (260 ns).

This article reviews the status of experiments directed to understanding the initial phases of exploding wire plasma formation, especially those relevant to the initiation of wire explosions and plasma formation in wire array z-pinch experiments. Thus, although we discuss experiments with ∼100 kA per wire, in which magnetic forces play a major role, our emphasis is on experiments with ∼1 kA per wire, in which magnetic forces appear to be unimportant. With high current (∼100 kA) per wire, the exploding wire consists of a rapidly expanding (1–3 cm/μs) coronal plasma surrounding a dense core that expands much more slowly. The coronal plasma exhibits strong, azimuthally symmetric instabilities driven by the high current, but the dense core appears to be stable, suggesting that it is carrying little of the current. In low-current experiments, the initial wire core expansion rate depends upon the material, the wire size, and whether or not it is coated with an insulator. For bare wires, the core diameter expands at rates which range from ≤0.03 cm/μs (for 25-μm-diameter W) to 0.46 cm/μs (for 25-μm-diameter Ag). This expansion rate increases with the energy deposited resistively in the wire before coronal plasma formation. Furthermore, expansion is more uniform as well as faster for wires in which the deposited energy is comparable to or larger than the vaporization energy. Insulating coatings increase the energy deposition, evidently by forestalling the formation of plasma around a wire. Therefore, wires coated with 1-μm thickness of plastic expand faster (e.g., by a factor of 2 for Ag) than bare wires for all wires tested so far.

The goal of the experiments on “Module A-5” and S-300 machines for some 15 years was to study the “liner-converter” inertial confinement fusion (ICF) scheme. A new class of fast instabilities of z pinches was studied both in experiments and in analytical theory. Stabilization of the light liner has been achieved by means of an extrinsic magnetic field. Formation of thin overheated current-carrying shells has been predicted analytically and seems to be really observed. Both theory and simulations predict growing Te and heat flux onto the converter by using heterogeneous z pinches with spatially separated regions of efficient energy exchange and of efficient heat conductivity. In our first experiments of this kind, impurities were inserted by means of placing thin glass fibers into a He jet. Growing intensity of the spectral lines of He-like chlorine from the cathode surface confirms the growth of heat flux. Theoretical investigations and 2.5-D simulations were devoted to some basic points of this program.

A computational study of tungsten wire array z pinches on the Z facility at Sandia National Laboratories shows that individual wires form a core–corona structure early in the current pulse. Further analysis indicates that at 1 mm or smaller interwire gap, the expanding and later merging wire plasmas prevent the growth of m = 0 sausage modes. Although a completely uniform shell is not observed in the simulations, the Hussey–Roderick profile—a characteristic of uniform shell implosions—is seen. Differences in shell characteristics between small- and large-diameter wires are observed, possibly explaining performance differences between these two arrangements.

During the last few years, we have concentrated on developing plasma radiation sources (PRS) for the longer current rise time (up to 300 ns) of the direct-drive Decade Quad (DQ; Price et al., 1999). In particular, we have developed an argon gas-puff PRS that produces a high quality pinch with an ∼200-ns implosion time, twice the implosion time of typical z pinches. We have shown that large-diameter, solid-fill (i.e., the gas density is a smooth function of the radial distance rather than a discrete shell) gas puffs can achieve adequate heating and stability for long-implosion z pinches with good K-shell yield.

To understand in detail what happens with an imploding wire array would require one to account for many different processes beginning with the wire explosion and ending with the Rayleigh–Taylor instabilities. Haines (1998) has performed a heuristic analysis of the multiwire array implosion and suggested that the dynamics and behavior of the wire array pinch be divided into four distinct phases. These phases are as follows: the electrical explosion of an individual wire (Phase 1), merging of the wire plasmas and the current shell formation (Phase 2), running-in of the wire array (Phase 3), and the stagnation of the pinch at the axis (Phase 4).

A multiwire screw pinch, a variant of a z-pinch load, is proposed as a means for further improvement of load performance for high-current 100-ns pulsed-power generators used for terawatt X-ray radiation. Wires twisted along a curved load surface are suggested to be an effective way to create an axial magnetic field and to generate and to maintain rotation of the subsequently formed plasma shell due to conservation of angular momentum. A multiwire screw pinch is predicted to mitigate the growth of the magneto-Rayleigh–Taylor instabilities, to provide a higher pinch compression ratio and more effective X-ray generation compared to classical z-pinch loads. A model based on the self-consistent simulation of the dynamics of a twisted plasma shell and the development of Rayleigh–Taylor (R-T) perturbations on a plasma surface is proposed to quantitatively study the effect of various physical factors on the generation of X rays. The model provides us with a tool for the analysis of processes that occur during the implosion of the plasma-shell–wire-core system. We plan for the R-T perturbations to break through the plasma shell at the moment when the internal radius of a shell becomes zero, where the greatest possible values of kinetic energy and X-ray radiation power ought to be obtained. The results of numerical simulations for the Sandia National Laboratories' Z generator are presented and discussed.

As a basis for this review the results of the investigations of a number of processes occurring at different stages of the fast z-pinch evolution, beginning with the electric explosion of a wire and ending with hot spot formation, have been assumed. At the same time the experimental results whose significant part had been obtained when investigating the explosion of thin aluminum and composite (W-Al-W; W-SiO2-W) wires at the high-current SIGNAL accelerator (∼220-kA current, ∼50-ns rise time) have been used.

Wire array z pinches on the Z accelerator provide the most intense laboratory source of soft X rays in the world. The unique combination of a near-Planckian radiation source with high X-ray production efficiency (10 to 15% wall plug), large X-ray powers and energies (>100 TW, ≥0.8 MJ in 6 ns to 7 ns), large characteristic hohlraum volumes (0.5 to >10 cm3), long pulse lengths (5 to 20 ns), and low capital cost (<$50–$100/radiated Joule) may make z pinches a good match to the requirements for driving high-yield scale (>200 MJ yield) ICF capsules with adequate radiation symmetry and margin. The z-pinch-driven hohlraum approach of Hammer et al. (1999) may provide a conservative and robust solution to the requirements for high yield, and is currently being studied on the Z accelerator. This paper describes a multiple-region, 0-D hohlraum energetics model for z-pinch-driven hohlraums in four configurations. We observe consistency between the model and the measured X-ray powers and hohlraum wall temperatures to within ±20% in X-ray flux, for the four configurations. The scaling of pinch energy and radiation-driven anode-cathode gap closure with drive current are also examined.

In the past few years, long-implosion-time (150 ns to 200 ns) z pinches have made significant progress in terms of their ability to make kilovolt X rays or to produce high-power subkilovolt emissions. These advances are enabling the community to utilize lower-cost pulsed power designs for high current X-ray facilities. The advances will be reviewed in historical context in this paper, plus some new physics regimes and understanding resulting from this work will be highlighted.