The Z-pinch, perhaps the oldest subject in plasma physics, has achieved a remarkable renaissance in recent years, following a few decades of neglect due to its basically unstable MHD character. Using wire arrays, a significant transition at high wire number led to a great improvement in both compression and uniformity of the Z-pinch. Resulting from this the Z-accelerator at Sandia at 20 MA in 100 ns has produced a powerful, short pulse, soft x-ray source >230 TW for 4.5 ns) at a high efficiency of ~15%. This has applications to inertial confinement fusion. Several hohlraum designs have been tested. The vacuum hohlraum has demonstrated the control of symmetry of irradiation on a capsule, while the dynamic hohlraum at a higher radiation temperature of 230 eV has compressed a capsule from 2 mm to 0.8 mm diameter with a neutron yield >3 × 1011 thermal DD neutrons, a record for any capsule implosion. World record ion temperatures of >200 keV have recently been measured in a stainless-steel plasma designed for Kα emission at stagnation, due, it was predicted, to ion-viscous heating associated with the dissipation of fast-growing short wavelength nonlinear MHD instabilities. Direct fusion experiments using deuterium gas-puffs have yielded 3.9 × 1013 neutrons with only 5% asymmetry, suggesting for the first time a mainly thermal source. The physics of wire-array implosions is a dominant theme. It is concerned with the transformation of wires to liquid-vapour expanding cores; then the generation of a surrounding plasma corona which carries most of the current, with inward flowing low magnetic Reynolds number jets correlated with axial instabilities on each wire; later an almost constant velocity, snowplough-like implosion occurs during which gaps appear in the cores, leading to stagnation on the axis, and the production of the main soft-x-ray pulse. These studies have been pursued also with smaller facilities in other laboratories around the world. At Imperial College, conical and radial wire arrays have led to highly collimated tungsten plasma jets with a Mach number of >20, allowing laboratory astrophysics experiments to be undertaken. These highlights will be underpinned in this review with the basic physics of Z-pinches including stability, kinetic effects, and finally its applications.

A review of the dense Z-pinch

The enhancement of magnetic‐field penetration into short‐duration plasmas by the dissipationless Hall field is examined. Magnetic‐field penetration along a background magnetic field is focused on, where the inductive Hall electric field enables the magnetic field to penetrate as a whistler wave. It is shown that the magnetic‐field evolution, when governed simultaneously by both whistler wave propagation and collisional diffusion, is described by a diffusion equation with a complex diffusion coefficient. The imaginary part of this coefficient is proportional to the Hall resistivity associated with the background magnetic field. In the collisionless limit the governing equation is equivalent to the Schrodinger equation for a free particle, and the magnetic field propagates the way a free‐particle wave packet expands by dispersion rather than by diffusion. This study was motivated by the enhanced magnetic‐field penetration recently observed in the anode plasma of a magnetically insulated ion diode.

Fast magnetic-field penetration into plasmas due to the Hall field

The authors report recent results in the polytron devices with an additional vertical magnetic field. This field is used to control the radial expansion of the accelerated toroidal plasma. The structure of the double electrostatic sheaths present at the separatrix plane of each ring cusp was also measured, and found to be consistent with a resistive model. Evidence is presented for viscous heating of the ions to a temperature of about 100 eV, well in excess of the electron temperature. This occurs because of the spatial non-uniformity of the accelerating forces. Further the Ti5/2 dependence makes viscosity an attractive method for heating ions to high temperatures. A method for reducing electron thermal conduction by increasing the Mach number of toroidal ion flow is considered, and a modified field structure is proposed to reduce the initial plasma loss.

https://iopscience.iop.org/article/10.1088/0032-1028/23/4/003/pdf

Toroidal equilibrium, acceleration and ion heating in the polytron

Computer simulations have been performed for the Toroidal Cusp Experiment (TCX), a plasma device built and operated at the University of California, Los Angeles. TCX is a toroidal MacKenzie machine with an external magnetic field provided by 48 magnetic cusps arranged in poloidal rings. A transformer generates a toroidal electric field which causes a current to flow in the plasma. Experimentally, the following parameters are observed in hydrogen: ne = 2 × 1013cm− 3, Te = 10 – 20 eV, Ti = 40 – 110 eV. The toroidal current is carried mostly by the ions. A computer model of TCX has been developed, using a two-and-one-half-dimensional electromagnetic particle code. Basically, the simulation results (the electrons are restrained by the magnetic cusp fields, the ions are free to move, there is ion heating, and a relatively large fraction of the current is ion current) agree with those of the experiment and are explained by simple physical theoretical arguments. These provide the scalings observed in the simulation model.

https://iopscience.iop.org/article/10.1088/0029-5515/23/8/001/pdf

Computer simulations of the Toroidal Cusp Experiment

Computer Simulations of the Toroidal Cusp Experiment.

The Polytron is a toroidal plasma configuration, using 36 magnetic cusps joined point-to-point. This paper presents observations of the acceleration and containment of the plasma. Measurement of the force on the plasma shows that the initial acceleration is given by a particle equation mi(dvphi /dt)=ZeEphi and occurs in thin sheaths in the ring cusp planes. The concept of a non-magnetic effective inductance is experimentally verified. However rapid, although not complete loss of plasma occurs after 1 mu sec for argon, limiting the electron temperature to 30 eV at an electron density of 1020 m-3. This loss is expected and an energy balance at this time implies that electron thermal conduction causes the principal loss of energy. After this loss, the rest of the plasma drifts to the outer wall of the vacuum vessel after about 3 mu sec.

https://iopscience.iop.org/article/10.1088/0032-1028/15/12/004/pdf

Experiments on the Polytron, a toroidal Hall accelerator employing cusp containment

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Experiments on the Polytron, a toroidal Hall accelerator employing cusp containment