One- and two-dimensional modeling of argon K-shell emission from gas-puff Z-pinch plasmas

Abstract

In this paper, a theoretical model is described and demonstrated that serves as a useful tool for understanding K-shell radiating Z-pinch plasma behavior. Such understanding requires a self-consistent solution to the complete nonlocal thermodynamic equilibrium kinetics and radiation transport in order to realistically model opacity effects and the high-temperature state of the plasma. For this purpose, we have incorporated into the MACH2 two-dimensional magnetohydrodynamic ͑MHD͒ code ͓R. E. Peterkin et al., J. Comput. Phys. 140, 148 ͑1998͔͒ an equation of state, called the tabular collisional radiative equilibrium ͑TCRE͒ model ͓J. W. Thornhill et al., Phys. Plasmas 8, 3480 ͑2001͔͒, that provides reasonable approximations to the plasma's opacity state. MACH2 with TCRE is applied toward analyzing the multidimensional implosion behavior that occurred in Decade Quad ͑DQ͒ ͓D. Price et al., Proceedings of the 12th IEEE Pulsed Power Conference, Monterey, CA, edited by C. Stallings and H. Kirbie ͑IEEE, New York, 1999͒, p. 489͔ argon gas puff experiments that employed a 12 cm diameter nozzle with and without a central gas jet on axis.Typical peak drive currents and implosion times in these experiments were ϳ6 MA and ϳ230 ns. By using Planar Laser Induced Fluorescence measured initial density profiles as input to the calculations, the effect these profiles have on the ability of the pinch to efficiently produce K-shell emission can be analyzed with this combined radiation-MHD model. The calculated results are in agreement with the experimental result that the DQ central-jet configuration is superior to the no-central-jet experiment in terms of producing more K-shell emission. These theoretical results support the contention that the improved operation of the central-jet nozzle is due to the better suppression of instabilities and the higher-density K-shell radiating conditions that the central-jet configuration promotes. When we applied the model toward projecting argon K-shell yield behavior for Sandia National Laboratories' ZR machine ͑ϳ25 MA peak drive currents, ϳ100 ns implosion times͒ ͓D. McDaniel et al., for experiments that utilize the 12 cm diameter central-jet nozzle configuration, it predicts over 1 MJ of K-shell emission is attainable.

Numerical studies of the effects of precursor plasma on the performance of wire-array Z-pinches

“…A lot of research on Z-pinches was done in one dimension during the past several decades. [38][39][40][41][42] Though the used equations of mass and momentum conservations and magnetic field evolution are basically same, the energy ͑total, electron, ion, and radiation͒ conservation and ionization processes might be treated by different schemes, as well as the transport coefficients used ͑such as electrical and thermal conductivities͒ and equation of state might also be different among those researches. It is well known that a 1D simulation of wire-array Z-pinch implosion plasma is limited because it cannot model instabilities and start with the azimuthal nonuniformities found in wire-array Z-pinches, and tends to cause radiation collapse in the simulation.…”

Fusion in a staged Z-pinch

“…Material mixing and end-losses may also reduce the target's final temperature. For our simulations the built-in radiation model and SESAME data tables are what's presently available in the code: and there may be better alternatives [50,51]. Since the target plasma is low-atomic-number, A = 1, treatment of its radiation is greatly simplified, relative to that for the high-atomic-number liner.…”

Radiation Transport in Z-Pinches

“…Ray tracing can also be used to model radiation transport in a Z-pinch [14]. Ray tracing is a deterministic method that places a grid of rays through the medium being modeled, along each of which (1) is solved.…”