Wire dynamics model of the implosion of nested and planar wire arrays

Abstract

This paper presents the wire dynamics model (WDM), which can effectively replace the generic 0D (zero-dimensional) model in simulation of the implosions of arbitrary shaped wire arrays, including high-wire-number nested and planar array loads at multi-MA generators. Fast and inexpensive WDM modeling can predict the array implosion time and the rate of thermalization of the kinetic energy, and can estimate the timing of the x-ray pulse. Besides serving the purposes of the design and optimization of the wire array loads of complex configurations, the WDM reproduces the specific features of the wire array implosion dynamics due to the inductive current transfer, which makes the WDM a valuable amplification of the magnetohydrodynamic models.

Compact wire array sources: power scaling and implosion physics.

“…For a cylindrical array, this is equivalent to the standard thin-shell 0D implosion model, but this approach is more general. Inductive current division still allows current to be distributed throughout the wires in a planar array, but causes current to peak in the few wires near the edge of the array with the outermost wires carrying a factor of 2-3 times more current than the innermost wires [11]. We expect this to be the most reasonable assumption for planar arrays, given the observations that the inner wires ablate and so must carry some current [8], but also that the inner wires experience little acceleration while the implosion commences at the outer wires and cascades inward [11,13] implying that somewhat less current flows in the inner wires.…”

“…This could be a detrimental effect, leading to large MRT spatial broadening of the imploding mass, or it could be a positive effect leading to robust gap formation and high convergence in the MRT bubble regions. At the same time, the distributed mass in planar wire arrays is expected to help stabilize MRT growth during the implosion as the implosion front continues to snowplow wire material [11,12,13] (analogous to nested cylindrical arrays). It is not clear which of these effects will dominate the performance of planar wire arrays.…”

“…A. Esaulov (University of Nevada, Reno) in collaborative design of the planar array loads for the May-June 2007 Saturn shots. Termed the "wire dynamics model" [11], the technique can be applied to single or multiply nested cylindrical arrays, or planar wire arrays. The model implicitly includes inductive division of current between the wires at each time step, and essentially applies Newton's second law to each wire (modeled as a 0D current-carrying filament with some prescribed mass per unit length) in order to track its trajectory.…”

“…The planar array distributes the initial mass profile radially, which is not intuitively optimal for providing high implosion velocity. Numerical modeling [11,12] and laser shadowgraphy measurements [13] indicate, however, that the wires implode in a cascade, with magnetic Rayleigh-Taylor implosion instabilities being stabilized to some extent as the implosion front impacts each adjacent wire on its way toward the axis. This suggests that a linear array mitigates instabilities in a manner analogous to a multiply nested wire array; nested cylindrical wire arrays have been previously demonstrated to enhance the radiated x-ray power and shorten the pulse due to mitigation of the magnetic Rayleigh-Taylor (MRT) implosion instability [2] as the current is switched from the outer to the inner array during the implosion [14].…”

Planar wire array performance scaling at multi-MA levels on the Saturn generator.

“…A. Esaulov (University of Nevada, Reno) in designing the planar array loads for the May-June 2007 Saturn shots. Termed the "wire dynamics model" [27], the technique can be applied to single or multiply nested cylindrical arrays, or planar wire arrays. The model implicitly includes inductive division of current between the wires at each time step, and essentially applies F=ma to each wire in order to track its trajectory.…”