T. W. Hussey

Scaling of (MHD) instabilities in imploding plasma liners

The dynamics of imploding foil plasmas is considered using first‐order theory to model the implosion and to investigate the effects of magnetohydrodynamic instabilities on the structure of the plasma sheath. The effects of the acceleration‐produced magnetohydrodynamic (MHD) Rayleigh‐Taylor instability and a wall‐associated instability are studied for a variety of plasma implosion times for several pulsed power drivers. The basic physics of these instabilities is identified and models are developed to explain both linear and nonlinear behavior. These models are compared with the results of detailed two‐dimensional magnetohydrodynamic simulations. Expressions for linear Rayleigh‐Taylor growth are developed showing its dependence on driving current, plasma conductivity, and density gradient scale length. A nonlinear saturation model, based on magnetic field diffusion, is developed. The model for a wall instability involves the interaction of the plasma sheath with the electrode wall and the material ablated ...

Efficient x‐ray production from ultrafast gas‐puff Z pinches

The Proto‐II accelerator has been used to implode krypton and xenon annular gas puffs. A significant fraction of the machine electrical energy was converted first to plasma kinetic energy and then to x rays when the plasma pinched on axis. Quantitative measurements using time‐resolved bolometers have shown as much as 10% of the total radiation yield near 1 keV in Xe and 2 keV in Kr. We have compared this radiation yield to the predictions from one‐dimensional magnetohydrodynamic code calculations. The implosions were also observed with both time‐integrated pinhole cameras and spectrographs. No hard x‐ray (E>10 keV) output was observed.

Two‐dimensional simulation of the hydromagnetic Rayleigh‐Taylor instability in an imploding foil plasma

Two‐dimensional (r‐z) magnetohydrodynamic simulations of the electromagnetic implosion of metallic foil plasmas show, for certain initial configurations, a tendency to develop large‐amplitude perturbations characteristic of the hydromagnetic Rayleigh‐Taylor instability. These perturbations develop at the plasma magnetic field interface for plasma configurations where the density gradient scale length, the characteristic dimension for the instability, is short. The effects on the plasma dynamics of the implosion will be discussed for several initial foil configurations. In general, the growth rates and linear mode structure are found to be influenced by the plasma shell thickness and density gradient scale length, in agreement with theory. The most destructive modes are found to be those with wavelengths of the order of the plasma shell thickness.

Large-scale-length nonuniformities in gas puff implosions

Because they are less susceptible to the hydromagnetic Rayleigh–Taylor instability than other fast Z‐pinch imploding liner systems, gas puffs offer the possibility of higher implosion velocity. This higher specific energy appears necessary for optimizing high‐energy x rays required in a photoionization‐pumped soft x‐ray laser. Nevertheless, large‐scale‐length nonuniformities created as the gas flows from the nozzle across the electrode gap are a potential problem. One‐ and two‐dimensional calculations suggest that gas near the nozzle will implode before that which is further from the nozzle, leading to an effect described as ‘‘zippering.’’ Because the number of such two‐dimensional calculations that can be done is limited and because the density distribution of nozzles is uncertain, we have developed a simple quasi‐two‐dimensional interface code that is able to quickly survey the effect of arbitrary initial gas distributions on the implosion dynamics. Results of this survey suggest that zippering contributes significantly to thermalization time, and we propose two methods to counteract this problem. These techniques, each of which involves tailoring the initial density distribution to offset effects of nonuniformities, appear promising. Nevertheless, we will never completely eliminate these nonuniformities, therefore, they must be accounted for in x‐ray laser target design.

Z‐pinch implosions onto extremely low‐density foam cylinders

We have imploded xenon gas‐puff Z pinches onto small diameter, extremely low‐density foam cylinders ( ρ=0.0045 g/cm3). The presence of the foam on the cylindrical axis had little effect on the radiation production efficiency, pulse width, or spectral details, but it significantly improved the symmetry and uniformity of the stagnation. These experiments confirm that we can stagnate and thermalize a high velocity (5×107 cm/s) plasma onto a cold, low‐density target and suggest the feasibility of creating a homogeneous plasma for x‐ray laser studies.

A model for the saturation of the hydromagnetic Rayleigh–Taylor instability

The saturation of the hydromagnetic Rayleigh–Taylor instability is caused by the reduction of driving current in the bubble region between the spikes formed as the instability develops. For short wavelengths linear magnetic field diffusion provides the necessary smoothing of the magnetic field to reduce the driving force. For wavelengths longer than the magnetic field diffusion length, the current is shorted through material which expands into the bubble region. This initially low density accumulates in the bubble and eventually provides a source of sufficiently high conductivity plasma which reduces the magnetic field penetration to the front of the bubble. Simple analytic models have been developed to verify and and quantify these predictions. These models have been compared with two‐dimensional magnetohydrodynamic calculations for imploding plasma shells and give good agreement with these more detailed simulations.

Diffusion of magnetic field into an expanding plasma shell

A simple theory is developed to describe the density profile of an electromagnetically imploded hollow plasma liner. The model gives a good analytic means of determing density gradient scale length and sheath thickness for use in linear and nonlinear analysis of the Rayleigh–Taylor instability.

Magnetic diffusion smoothing with application to the hydromagnetic Rayleigh–Taylor instability

An analytic model has been developed to quantify the effects of magnetic field diffusion on plasmas accelerated by magnetic J×B forces. We examine the penetration of equilibrium and perturbed magnetic fields into a conducting plasma. Analytic solutions are found for both fields for a power law time dependence of the equilibrium field at the field plasma interface. Results show that wavelengths longer than the magnetic field diffusion length penetrate the plasma shell faster than the equilibrium field. For wavelengths shorter than the magnetic diffusion length the perturbed field remains confined to the original field plasma interface and falls off rapidly inside the plasma. Application to imploding linear plasmas show good agreement with detailed two‐dimensional magnetohydrodynamic simulations.

Plasma‐implosion‐driven, photoionization‐pumped, soft x‐ray laser targets

Designs are proposed, based on a series of one‐dimensional calculations, for layered, hollow cylindrical targets to be placed on the axis of an imploding, hollow Z‐pinch plasma that can create the approximate plasma conditions, as well as radiation spectrum, for a photoionization pumped, Ne‐like recombination laser. The lasant must reach the Ne‐like state and be at the appropriate density at the same time that the photoionizing pump radiation is present, placing severe constraints on designs for such targets. Target designs are further constrained by the fact that the 3s‐2p resonance line, which depopulates the lower lasing state, must not be highly trapped and by the fact that the upper lasing state must not be collisionally depopulated. We find that hollow, cylindrical targets consisting of a few‐micron‐thick CH strongback, coated on the inside with a thin layer of Ni lasant and on the outside with an Al converter layer, can be optimized to achieve appropriate conditions for lasing and modest levels of ...

A simple model for plasma temperature in imploded hollow plasma liners

Existing theory for the Rayleigh‐Taylor instability in imploding hollow plasma liners has assumed a constant electrical resistivity during most of the implosion. While this is qualitatively justified by the competition between joule heating and field‐diffusion‐driven expansion of the plasma shell; one, nevertheless, expects the temperature and, therefore, electrical conductivity to rise during the implosion. A simple model for plasma temperature as a function of time, based on the neglect of radiative losses and using approximate fits to equation‐of‐state information, is presented here. The results are used to compute the minimum allowed wavelength, a parameter used to assess instability effects, and agreement with magnetohydrodynamic calculations to well within a factor of 2 is obtained.