Simulations of the implosion and stagnation of compact wire arrays

Abstract

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.

Measurements of magneto-Rayleigh–Taylor instability growth during the implosion of initially solid metal liners

“…13 of Ref. 16). The feed design shown was optimized for minimal inductance using the techniques of Ref.…”

“…The original attempts at simulating the data used an ideal gas law equation of state for the aluminum, which was sufficient for modeling wire-array implosions. 16 This led to a number of unphysical effects in the high-density, low-temperature liner material, which were corrected in these simulations by the use of SESAME equation of state data tables 21 and Lee-Moore-Desjarlais electrical and thermal conductivities 22,23 for Al. Another change was that the original simulations used random density perturbations throughout the volume of the liner, while the newer calculations only perturb the mass in the outermost cells.…”

Simulations of electrothermal instability growth in solid aluminum rods

“…Most simulations of magnetically driven implosions including wires, 14 foils, 15 liners, 9 and Z-pinches, [16][17][18][19] etc. do not in general start with realistic initial conditions before current is applied and rather use assumptions of plasma conditions with empirically derived temperature or density perturbations at some time after the current has been initiated.…”

Integration of MHD load models with circuit representations the Z generator.

“…X-ray generating imploding loads can produce x-ray power pulses a few ns in duration through which electrical power may be continually delivered and radiated [2]. The energy available to continue to deliver electrical power to these loads is therefore sourced from a finite volume of the transmission lines, limited by the propagation time.…”