Seeding the Electrothermal Instability through a Three-Dimensional, Nonlinear Perturbation

E. P. Yu, T. J. Awe, K. R. Cochrane, K. J. Peterson, K. C. Yates, T. M. Hutchinson, M. W. Hatch, B. S. Bauer, K. Tomlinson, and D. B. Sinars

Phys. Rev. Lett. 130, 255101 – Published 22 June 2023

Abstract

Electrothermal instability plays an important role in applications of current-driven metal, creating striations (which seed the magneto–Rayleigh-Taylor instability) and filaments (which provide a more rapid path to plasma formation). However, the initial formation of both structures is not well understood. Simulations show for the first time how a commonly occurring isolated defect transforms into the larger striation and filament, through a feedback loop connecting current and electrical conductivity. Simulations have been experimentally validated using defect-driven self-emission patterns.

Received 26 October 2021
Revised 24 February 2023
Accepted 17 May 2023

DOI:https://doi.org/10.1103/PhysRevLett.130.255101

Physics Subject Headings (PhySH)

High-energy-density plasmas Magnetohydrodynamics Magnetoinertial fusion Plasma instabilities

Nonlinear DynamicsPlasma Physics

Authors & Affiliations

E. P. Yu^1,*, T. J. Awe¹, K. R. Cochrane¹, K. J. Peterson¹, K. C. Yates^1,2, T. M. Hutchinson ³, M. W. Hatch⁴, B. S. Bauer⁵, K. Tomlinson⁶, and D. B. Sinars ¹

¹Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
²Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
³Lawrence Livermore National Laboratory, Livermore, California 94550, USA
⁴University of New Mexico, Albuquerque, New Mexico 87131, USA
⁵University of Nevada, Reno, Reno, Nevada 89506, USA
⁶General Atomics, San Diego, California 92121, USA

^*epyu@sandia.gov

Three-dimensional feedback processes in current-driven metal

E. P. Yu, T. J. Awe, K. R. Cochrane, K. J. Peterson, K. C. Yates, T. M. Hutchinson, M. W. Hatch, B. S. Bauer, K. Tomlinson, and D. B. Sinars

Phys. Rev. E 107, 065209 (2023)

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Vol. 130, Iss. 25 — 23 June 2023

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Images

Figure 1
(a) Current drive (black line) applied to (b) aluminum rod, with evenly spaced hemispherical pits on the outer face (only nine are shown). (c) Periodic wedge simulation demonstrates that a $20 − μ m$ -diameter pit seeds the formation of the (d) striation and (e) filament forms of ETI. Panels (c)–(e) show temperature $T (K)$ , as well as viewing orientations. The top and side view visualize the axial midplane $z_{m}$ and cross-sectional $θ = 0$ plane, respectively.
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Figure 2
Flow around a hemispherical pit, $j_{sphere}$ . Panels (a) and (b) visualize $j (A / m^{2})$ and $j^{2} / σ (W / m^{3})$ on the rod surface ( $r = 0.5 mm$ ). Representative $j$ streamlines (in blue) divert around the pit and amplify at the equator. (c) Top view visualizes enhanced $j^{2} / σ$ around the pit. (d) $T$ at a later time, showing focusing pressure gradient $- \nabla p$ . (e)–(h) Azimuthal lineouts taken along $L$ , shown in (b) and (c). The edge of the pit lies at $x = - 10 μ m$ . Legends use exponential notation, so 1e11 corresponds to $1 \times 10^{11}$ .
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Figure 3
(a) Top view of density $ρ$ ( $kg / m^{3}$ ), showing how overheated metal around the pit’s equator has expanded, forming a bump which qualitatively changes the $j$ flow pattern. (b) Side view, showing $j$ peaking at the base of the bump. (c) Front view of $j$ near rod surface ( $r = 0.499 mm$ ). All panels show $t = 80 ns$ .
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Figure 4
(a) The Joule heating pattern arising from bump flow drives hot spots (HS) near the rod surface (visualized by $ρ_{crit} = 400 (kg / m^{3})$ contour), as well as a striation deeper in the metal. The HS, visualized in (b), are observable in (c) visible self-emission. The striation in (d)–(g) has lower electrical conductivity $σ (1 / Ω m)$ relative to surrounding metal, forcing $j$ to divert around and amplify at the edges. The resulting enhanced Joule heating drives striation growth azimuthally and radially. All panels show $t = 100 ns$ .
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Figure 5
(a) The HS explode, resulting in plumes as well as craters on the rod surface (visualized by the $ρ = 400 {kg / m}^{3}$ contour). (b)–(e) In the vapor phase, $d σ / d T > 0$ (i.e., opposite to solid-liquid phase), so the HS have enhanced $σ$ . This initiates the ETI feedback loop driving filament formation. All panels show $t = 120 ns$ .
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Figure 6
(a) The filament resides in the low- $ρ$ vapor at $r \sim 0.625 mm$ —see (c)—and dominates visible self-emission. (b),(c) The pit has seeded a $ρ$ perturbation approximately $5 \times$ wider and $4 \times$ deeper than the original size. In (d), radial lineouts along $L$ show the inward-pointing $j_{z} B_{θ}$ force overcomes the outward-pointing pressure gradient $- d p / d r$ , so the $ρ_{crit}$ contour is MRT unstable. All panels show $t = 135 ns$ , although (d) considers a separate simulation at $t = 140 ns$ , driven with enhanced $I (t)$ shown in red in Fig. 1.
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