Electrothermal instability growth in magnetically driven pulsed power liners

Abstract

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.

Instability growth for magnetized liner inertial fusion seeded by electro-thermal, electro-choric, and material strength effects

“…A mathematical model of the ETI developed by Ryutov et al 12 and subsequently Peterson et al 13 reveals that the morphology of resultant structures is dependent on the sign of the derivative of resistivity with respect to temperature ( @g @T ). If @g @T < 0 and resistivity decreases with temperature, as in a plasma with Spitzer-like resistivity, current channels or "filaments" tend to form in the axial direction.…”

“…Figure 3 shows regions in densitytemperature space for beryllium at solid density susceptible to striations (a) and beryllium at low density susceptible to filaments (b). The dispersion relation for striations with an axial current density, J ¼ (0, 0, J z ), according to the mathematical model 13 is…”

“…One such mechanism is the electro-thermal instability (ETI). 13,14 This instability is driven by temperature dependent resistivity and alters the distribution of both current density and temperature within the liner. In the solid state, the current forms azimuthally correlated bands, which have the same orientation of wavevector as the fastest growing MRT modes.…”

Simulations of electrothermal instability growth in solid aluminum rods

“…5 Simulations of these experiments show two distinct phases of instability development. The first phase is characterized by electrothermal instabilities which begin to grow immediately after current is applied.…”

“…[1][2][3][4] In the condensed state of metals where the electrical resistivity increases with temperature, electrothermal instabilities develop striations perpendicular to the flow of current. [5][6][7] Our interest in electrothermal instabilities primarily lies in pulsed power liner inertial confinement fusion (ICF) targets such as the recently proposed magnetized liner inertial fusion (MagLIF) concept. For this concept or any other pulsed power fusion concept to succeed, instability growth must be well understood and mitigated to acceptable levels determined by both simulations and experimental measurements.…”