Resistive magneto-hydrodynamic (MHD) simulations are used to evaluate the influence of three-dimensional inhomogeneities on x-ray power production in wire array Z-pinches. In particular, we concentrate on simulations of wire array Z-pinch experiments on the MAGPIE generator at Imperial College. An initial temperature perturbation is used to stimulate variations in wire core ablation rates that result in a highly non-uniform final implosion. Results indicate that x-ray power production is governed by the symmetry of the implosion surface and by the rate at which current can transfer to the axis through a threedimensional debris field that trails behind the main implosion. The peak power is ultimately limited by the growth of MHD instabilities in the stagnated pinch. The individual contributions of the implosion kinetic energy, compression of the stagnated pinch, ohmic heating and MHD instabilities to the radiation yield are quantified. The onset of m = 1 instabilities is found to provide an efficient mechanism for dissipation of the magnetic energy surrounding the stagnated pinch. The formation of a helical plasma column not only allows the magnetic field to do work in driving an expansion of the helix but also enhances the ohmic heating by elongating the path of the current through the pinch. The effect of these energy sources combined is to increase the radiation yield to typically 3 1 2 times the kinetic energy of the implosion. Simulations of arrays with different wire numbers, wire material and with nested arrays are used to examine the mechanisms that influence the peak soft x-ray power. In the simulations, peak power can be increased by: increasing the number of wires (which improves the implosion symmetry), by increasing the atomic number of the material (which increases the compressibility of the plasma) and by using a nested inner array (which brings the mass and the current to the axis more efficiently than a single array).

We present the first results of high energy density laboratory astrophysics experiments which explore the evolution of collimated outflows and jets driven by a toroidal magnetic field. The experiments are scalable to astrophysical flows in that critical dimensionless numbers such as the Mach number, the plasma β and the magnetic Reynolds number are all in the astrophysically appropriate ranges. Our experiments use the MAGPIE pulsed power machine and allow us to explore the role of magnetic pressure in creating and collimating the outflow as well as showing the creation of a central jet within the broader outflow cavity. We show that currents flow along this jet and we observe its collimation to be enhanced by the additional hoop stresses associated with the generated toroidal field. Although at later times the jet column is observed to go unstable, the jet retains its collimation. We also present simulations of the magnetic jet evolution using our two‐dimensional resistive magnetohydrodynamic laboratory code. We conclude with a discussion of the astrophysical relevance of the experiments and of the stability properties of the jet.

A review of recent experiments on the MAGPIE generator (1 MA, 250 ns) aimed at studying the implosion dynamics of wire array Z-pinches is presented. The first phase of implosion is dominated by the gradual ablation of stationary wire cores and gradual redistribution of the array mass by the precursor plasma flow. It is found that the rate of wire ablation depends on the magnitude of the global (collective) magnetic field of the array, and increases with the field. The existence of the modulation of the ablation rate along the wires leads to the presence of a 'trailing' mass left behind by the imploding current sheath. The trailing mass provides an alternative path for the current, reducing the force available for compression of the pinch at stagnation. The observed dependence of the ablation rate on inter-wire separation suggests an explanation for the existence of the optimal wire number maximizing the x-ray power. Axially resolved spectroscopy shows the presence of the x-ray 'bright' spots (<150 µm) emitting intense continuum radiation.

Wire array z-pinches have been used successfully for many years as a powerful x-ray source, as a dynamic hohlraum, and as an intense K-shell radiation source. Significant progress has been made in the effective modeling of these three-dimensional ͑3D͒ resistive plasmas. However, successful modeling also requires an accurate representation of the power delivered to these loads from the generator, which is an uncertainty potentially as large as the magnetohydrodynamic ͑MHD͒ implosion dynamics. We present 3D resistive MHD simulations of wire arrays that are coupled to transmission line equivalent models of the Z generator, driven by voltage sources derived directly from electrical measurements. Significant ͑multi-mega-ampère͒ current losses are shown to occur in both the convolute and the final feed. This limits the array performance and must be correctly accounted for to accurately represent the generator response to the load. Our simulations are validated against data for compact: 20 mm diameter, 10 mm long wire arrays that have produced the highest x-ray power densities on Z. This is one of the most comprehensive experimental data sets for single and nested wire arrays and includes voltage, current, x-ray power and energy, and multiple mass distribution measurements. These data tightly constrain our simulation results and allow us to describe in detail both the implosion and stagnation, and how energy is delivered to, and radiated from z-pinch loads. We show that the radiated power is consistent with the kinetic energy delivered to a distributed 3D mass profile over its implosion and stagnation. We also demonstrate how the local inductance of the transmission line connecting to the wire array is responsible for delivering more than 50% of the total radiated power. This makes the power output dependent on the design of specific elements of the generator, and their response to the imploding load, and not just on the peak current that can be delivered.

We have developed conceptual designs of two petawatt-class pulsed-power accelerators: Z 300 and Z 800. The designs are based on an accelerator architecture that is founded on two concepts: single-stage electrical-pulse compression and impedance matching [Phys. Rev. ST Accel. Beams 10, 030401 (2007)]. The prime power source of each machine consists of 90 linear-transformer-driver (LTD) modules. Each module comprises LTD cavities connected electrically in series, each of which is powered by 5-GW LTD bricks connected electrically in parallel. (A brick comprises a single switch and two capacitors in series.) Six water-insulated radial-transmission-line impedance transformers transport the power generated by the modules to a six-level vacuum-insulator stack. The stack serves as the accelerator's water-vacuum interface. The stack is connected to six conical outer magnetically insulated vacuum transmission lines (MITLs), which are joined in parallel at a 10-cm radius by a triple-post-hole vacuum convolute. The convolute sums the electrical currents at the outputs of the six outer MITLs, and delivers the combined current to a single short inner MITL. The inner MITL transmits the combined current to the accelerator's physics-package load. Z 300 is 35 m in diameter and stores 48 MJ of electrical energy in its LTD capacitors. The accelerator generates 320 TW of electrical power at the output of the LTD system, and delivers 48 MA in 154 ns to a magnetized-liner inertial-fusion (MagLIF) target [Phys. Plasmas 17, 056303 (2010)]. The peak electrical power at the MagLIF target is 870 TW, which is the highest power throughout the accelerator. Power amplification is accomplished by the centrally located vacuum section, which serves as an intermediate inductive-energy-storage device. The principal goal of Z 300 is to achieve thermonuclear ignition; i.e., a fusion yield that exceeds the energy transmitted by the accelerator to the liner. 2D magnetohydrodynamic (MHD) simulations suggest Z 300 will deliver 4.3 MJ to the liner, and achieve a yield on the order of 18 MJ. Z 800 is 52 m in diameter and stores 130 MJ. This accelerator generates 890 TW at the output of its LTD system, and delivers 65 MA in 113 ns to a MagLIF target. The peak electrical power at the MagLIF liner is 2500 TW. The principal goal of Z 800 is to achieve high-yield Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.