N. F. Roderick

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 ...

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.

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.

Simulation of space‐charge limiting current in relativistic electron beams

A relativistic particle‐in‐cell simulation code has been used to study the space‐charge limiting currents of a solid and an annular relativistic electron beam. The resulting limiting currents are significantly higher than that given by the widely used Bogdankevich–Rukhadze interpolation formula.

Formation of plasma working fluids for compression by liner implosions

Research on the formation of a hot hydrogen working fluid, which may be used in multiple concentric solid‐density liner implosions, is reported. In such implosions, an axisymmetric outer liner is driven by a multi‐megamp axial discharge, and a coaxial inner liner is driven by a working fluid contained between the liners. The fluid is shocklessly compressed to high pressure as the outer liner implodes around it. In the work reported here a 10 to 100 Torr pressure, hydrogen filled coaxial gun discharge was used to inject plasma into a diagnostic chamber simulating an interliner volume. Spectroscopically determined electron densities of between 1017 and 1018 cm−3 and electron temperatures in the 0.5–2.0 eV range were obtained with a fair degree of reproducibility and symmetry. Two‐dimensional, time‐dependent magnetohydrodyna‐ mic computer simulations of the working fluid formation experiment have been performed, and the computations suggest that the present experiment achieves electron number densities and t...

Two‐dimensional numerical simulation of an inductively driven imploding foil plasma

A 1.9‐MJ capacitor bank with intermediate inductive energy storage for pulse shortening has been used to implode a thin cylindrical sheath in a z‐pinch geometry. Theoretical investigations of two‐dimensional axisymmetric effects in the r‐z plane, which lead to a thickening of the sheath, have been made using a two‐dimensional magnetohydrodynamics code. The results of several calculations are presented which demonstrate how imperfections in the initial sheath geometry affect development of the acceleration‐driven magnetohydrodynamic Rayleigh–Taylor instability.

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.

Swelling effects of electromagnetic waves near the critical density

Numerical techniques have been used to study the intensity pattern of a high‐frequency electromagnetic wave near the critical density for conditions typical of laser fusion plasmas. The investigation considered nonlinear density profiles, collisional absorption, and finite bandwidth effects. Using the results of these calculations as a guide, elementary analytic models were developed to describe the behavior of the intensity pattern. Results of the numerical and analytic methods indicate the following: (i) For a nonlinear but monotonic density profile, the swelling factor can be related to the Airy function pattern by a simple scale factor; (ii) for collisional absorption below 50%, a linear relation holds between the intensity and the absorption; (iii) for laser bandwidth Δω/ω0<15%, the intensity is reduced in a manner similar to that associated with collisional absorption. Within the ranges given, accuracy of the analytic models is within 10% of the numerical results. These semiquantitative models provi...

Numerical simulation of the nonlinear evolution of an exploded wire plasma

Numerical simulations of exploded wire plasmas have been conducted using a two‐dimensional (r‐z) magnetohydrodynamic computer code for several experimental configurations. Recent results with an aluminium wire showing the development of the nonlinear sausage instability are presented. Short‐wavelength modes are observed to grow and saturate initially, while longer wavelengths evolve later through nonlinear processes, particularly magnetic field diffusion. This behavior, as well as predicted energy output, appears to be consistent with experiment.

Optimization of soft x-ray emission from stagnating compact toroidal plasmas: A computational study

Computational simulations aimed at optimizing the high-energy, high-power, multikilovolt electromagnetic radiation emitted by a rapidly moving compact toroidal (CT) plasma which stagnates against a stationary “wall” are performed for argon, krypton, and xenon plasmas over a range of CT parameters. CT kinetic energies vary from 2–10 MJ, impact speeds vary from 50–200 cm/μs, and CT masses vary from 5–11 mg. It is found that a 2 MJ Ar CT optimally emits 1–1.5 MJ of essentially K-line radiation (>3 keV) for impact speeds of about 60–90 cm/μs; a 10 MJ Kr CT optimally emits about 1 MJ of essentially K-line radiation (>12.5 keV) for impact speed of about 135 cm/μs; and a 10 MJ Xe CT optimally emits about 3 MJ of essentially L-line radiation (>5 keV), about 0.5 MJ of continuum radiation above 10 keV, and about 0.1 MJ of continuum radiation above 20 keV, all also for impact speed of about 135 cm/μs. Pulse widths vary for the above optima from 7 ns at 135 cm/μs to 30 ns at 60 cm/μs.