Edmund P. Yu

Electrothermal instability growth in magnetically driven pulsed power liners

This paper explores the role of electro-thermal instabilities on the dynamics of magnetically accelerated implosion systems. Electro-thermal instabilities result from non-uniform heating due to temperature dependence in the conductivity of a material. Comparatively little is known about these types of instabilities compared to the well known Magneto-Rayleigh-Taylor (MRT) instability. We present simulations that show electrothermal instabilities form immediately after the surface material of a conductor melts and can act as a significant seed to subsequent MRT instability growth. We also present the results of several experiments performed on Sandia National Laboratories Z accelerator to investigate signatures of electrothermal instability growth on well characterized initially solid aluminum and copper rods driven with a 20 MA, 100 ns risetime current pulse. These experiments show excellent agreement with electrothermal instability simulations and exhibit larger instability growth than can be explained by MRT theory alone.

Feedback stabilization of resistive shell modes in a reversed field pinch

A reactor relevant reversed field pinch (RFP) must be capable of operating successfully when surrounded by a close-fitting resistive shell whose L/R time is much shorter than the pulse length. Resonant modes are largely unaffected by the shell resistivity, provided that the plasma rotation is maintained against the breaking effect of nonaxisymmetric eddy currents induced in the shell. This may require an auxiliary momentum source, such as a neutral beam injector. Nonresonant modes are largely unaffected by plasma rotation, and are expected to manifest themselves as nonrotating resistive shell modes growing on the L/R time of the shell. A general RFP equilibrium is subject to many simultaneously unstable resistive shell modes; the only viable control mechanism for such modes in a RFP reactor is active feedback. It is demonstrated than an N-fold toroidally symmetric arrangement of feedback coils, combined with a strictly linear feedback algorithm, is capable of simultaneously stabilizing all intrinsically u...

Improved evolution equations for magnetic island chains in toroidal pinch plasmas subject to externally applied resonant magnetic perturbations

An improved set of island evolution equations is derived that incorporates the latest advances in MHD (magnetohydrodynamical) theory. These equations describe the resistive/viscous-MHD dynamics of a nonlinear magnetic island chain, embedded in a toroidal pinch plasma, in the presence of a programmable, externally applied, resonant magnetic perturbation. A number of interesting example calculations are performed using the new equations. In particular, an investigation is made of a recently discovered class of multiharmonic resonant magnetic perturbations that have the novel property that they can lock resonant island chains in a stabilizing phase.

Nonlinear dynamo mode dynamics in reversed field pinches

The nonlinear dynamics of a typical dynamo mode in a reversed field pinch, under the action of the braking torque due to eddy currents excited in a resistive vacuum vessel and the locking torque due to a resonant error-field, is investigated. A simple set of phase evolution equations for the mode is derived: these equations represent an important extension of the well-known equations of Zohm et al. [Europhys. Lett. 11, 745 (1990)] which incorporate a self-consistent calculation of the radial extent of the region of the plasma which corotates with the mode; the width of this region being determined by plasma viscosity. Using these newly developed equations, a comprehensive theory of the influence of a resistive vacuum vessel on error-field locking and unlocking thresholds is developed. Under certain circumstances, a resistive vacuum vessel is found to strongly catalyze locked mode formation. Hopefully, the results obtained in this paper will allow experimentalists to achieve a full understanding of why the...

Optimal design of feedback coils for the control of external modes in tokamaks

A formalism is developed for optimizing the design of feedback coils placed around a tokamak plasma in order to control the resistive shell mode. It is found that feedback schemes for controlling the resistive shell mode fail whenever the distortion of the mode structure by the currents circulating in the feedback coils becomes too strong, in which case the mode escapes through the gaps between the coils, or through the centers of the coils. The main aim of the optimization process is to reduce this distortion by minimizing the coupling of different Fourier harmonics due to the feedback currents. It is possible to define a quantity α0 which parametrizes the strength of the coupling. Feedback fails for α0⩾1. The optimization procedure consists of minimizing α0 subject to practical constraints. If there are very many evenly spaced feedback coils surrounding the plasma in the poloidal direction then the optimization can be performed analytically. Otherwise, the optimization must be performed numerically. The...

Angular momentum injection into a Penning–Malmberg trap

It is demonstrated using conventional fluid theory that angular momentum can be injected into a single component plasma confined in a Penning–Malmberg trap via an externally generated, oscillating, nonaxisymmetric, electric field. The torque exerted on the plasma by the electric field is a highly nonmonotonic function of the plasma angular rotation velocity. The torque vs angular velocity curve is dominated by sharp resonances at which the angular phase velocity of a particular poloidal harmonic of the external field matches the plasma angular rotation velocity. The torque exerted on the plasma by a given poloidal harmonic is negative when the field rotates faster than the plasma, and vice versa. This rather surprising behavior is shown to be entirely consistent with a standard result in hydrodynamic theory, but is generally not observed in present-day experiments.

Scaling of X pinches from 1 MA to 6 MA.

This final report for Project 117863 summarizes progress made toward understanding how X-pinch load designs scale to high currents. The X-pinch load geometry was conceived in 1982 as a method to study the formation and properties of bright x-ray spots in z-pinch plasmas. X-pinch plasmas driven by 0.2 MA currents were found to have source sizes of 1 micron, temperatures >1 keV, lifetimes of 10-100 ps, and densities >0.1 times solid density. These conditions are believed to result from the direct magnetic compression of matter. Physical models that capture the behavior of 0.2 MA X pinches predict more extreme parameters at currents >1 MA. This project developed load designs for up to 6 MA on the SATURN facility and attempted to measure the resulting plasma parameters. Source sizes of 5-8 microns were observed in some cases along with evidence for high temperatures (several keV) and short time durations (<500 ps).