Seeding and Evolution of Magnetohydrodynamic Instabilities

of aMetal Surface Driven by Intense Current*

Co-PI’s: M. Gilmorea, B. Bauerb, B. Srinivasanc

Students: M. Carrierc, M. Hatcha, T. Hutchinsonb, A. Klemmerb, S. Kreherb, R. Mastic, K. Toddb

Collaborators: K. Yatesd, T. Awee, E. Yue, I. Lindemuthb, D. Yeager-Elorriagae

*Supported by NNSA Stewardship Sciences Academic Programs under award numbers DE-NA0003870, DE-NA0003872, and DE-NA0003881

aUniversity of New Mexico, bUniversity of Nevada, Reno, cVirginia Tech, dLosAlamos National Laboratory, eSandia National Laboratories

Personnel and National Lab InteractionsStudents

Matthew Carrier, PhD candidate, VA TechMaren Hatch* , PhD student, UNMTrevor Hutchinson*, PhD candidate, UNRAidan Klemmer*, PhD student, UNRSeth Kreher**, PhD student, UNRRobert Masti, PhD candidate, VA TechKelby Todd, Undergrad. student, UNR

Faculty

Bruno Bauer, UNRMark Gilmore, UNMBhuvana Srinivasan, VA Tech

* Performing PhD research on site at SNL

** Performing PhD research on site at LANL

No-Cost Collaborators

Tom Awe, SNLIrv Lindemuth, UNRKevin Yates, LANLDavid Yeager-Elorriaga,

SNLEdmund Yu, SNL

Mykonos Experimental Team

(UNR, UNM, SNL, LANL)

L to R: E. Yu (SNL), K. Yates (LANL), T. Hutchinson (UNR), M. Gilmore (UNM), M. Hatch (UNM), T. Awe (SNL), A. Klemmer (UNR). Not shown: B. Bauer (UNR)

4

Bhuvana SrinivasanVirginia Tech PI

Robert MastiVirginia Tech PhD student

Matthew CarrierVirginia Tech PhD student

Computational Team

Virginia Tech Team

UNR/LANL Team

Seth Kreher, UNR PhD StudentBruno Bauer, UNR PII. Lindemuth, UNR Faculty

1. To understand the seeding, formation, and evolution of the Electro-Thermal Instability (ETI) in a thick wire regime in the solid, liquid, vapor, and plasma phases

2. To understand the seeding of late time MHD instabilities via early time ETI

3. To understand the effect of hydrodynamics on the growth rate of ETI and the formation of plasma

4. To understand the development of azimuthal correlation of MHD instabilities

5. Through numerical effort, deepen the understanding of metal driven by intense current and of the influence of various modeling assumptions

6. Educate students in high energy density (HED) laboratory plasma physics and train them in experimental and numerical methods for working with magnetized HED plasma

Project Objectives

Motivation/Approach

Question: Does nonuniform Joule heating provide the seed for Magneto-Rayleigh-Taylor (MRT) instability growth in magnetically-driven, solid liner implosions?

Nonuniform Joule Heating of

Solid Liner

Electrothermal Instability (ETI)

Azimuthally-correlated structures

Seed for MRT?

Nonuniform Implosion

• We will investigate (continue to investigate) the detailed physics of ETI evolution in a simplified geometry on a well-diagnosed, 1 MA-scale driver, using defect-controlled loads, together with 3D MHD simulations

ETI

For conductors thicker than electrical skin depth, ETI can be undermined by diversion of j around resistive (e.g., low density or high T) regions

Electrothermal instability can occur when material resistivity η depends on temperature T or density ρ

Condensed metals form

strata Ʇ j

Plasmas form

filaments || j

TJA, BSB 6/24/18

K.J. Peterson et al., Phys. Plasmas 19, 092701 (2012)

• Five stage Linear Transformer Driver (LTD) voltage adder

• 1 MA• 500 kV pulse• Rise time (10%-90%)

~ 80 ns (barbell load)• Pulse width (FWHM)

~ 160 ns

Experiments Being Conducted on the MYKONOS 1 MA Driver at SNL

To study ETI, 0.8 MA are driven through 0.8 -1 mm-diameter metal rods on Mykonos

TMH, BSB 6/26/19

Al-5N, Al-6061, Cu-5N, Ni-4N rod radii >> electrical skin depth Parylene-N coated (5, 17, 41 µm thick) & uncoated rods Surface defects, inclusions, and machining periodicity varied

12-Frame ICCD imager shows

instability structure and evolution

Photonic Doppler velocimetry (PDV) measures expansion of

ohmically heated surface

Photodiodes measure emission history

Streaked visible spectroscopy

Single-Frame ICCD imagers provide high-resolution imaging

D0=1.0 mm

Coatings Reduce Expansion Speed

TMH, BSB 6/25/19

Thick coatings slow expansion more than thinner ones Surface finish under 41-µm coatings does not much affect speed Velocity continuously increases (no shock jumps, though shock in plastic may

be pinned to accelerating aluminum) Apparent acceleration is constant just after melt, then increases, becomes

constant again, and then decreases at peak current

• Photonic Doppler Velocimetry (PDV) used to measure expansion velocity of the expanding surface

T. Hutchinson, B. Bauer, UNR, et al

New Experiments Have Utilized Engineered Defect Loads and Have Improved Diagnostics

• High purity Al (99.999%) barbell with discrete, engineered (machined) defects

• New high resolution, multi-frame, multi-angle visible imaging and shadowgraphy

• Imaging resolution: ~ 1 µm

M.W. Hatch, T. Awe, et al.

Shot 10325, load 6-007

New Data: Engineered Defect Loads Generate Features that Suggest Heating Around Defects and Axial Striations

D0=1.0 mm

Depth ProfilesConfocal

Microscope Image

Pre-shot Camera

View

Shot data: Time @ approx. ½ peak current

Defects

Virginia Tech Simulation Overview

Goal: Reproduce quantitative measurements of experimental results (i.e. explosion velocity) through simulationTools used: ● Ares: MHD code developed by Lawrence Livermore National

Labs● Flash: MHD astrophysics code developed by University of

ChicagoProgress:● Developed SESAME table reader and interpolation algorithm● Implemented QLMD table interpolation in Flash, and developed

a 2D simulation setup ● 2D uncoated/coated simulations of wire electrical explosion

using Ares● Explored the effect of anomalous resistivity (AR) on the ETI

growth rate

Ref: LLNL-POSTER-793884; LLNL-TR-801198

Density [gcc] drdt [cm/μs]

Jz [10 MA/cm^2]T [keV]

Ref: LLNL-POSTER-793884; LLNL-TR-801198

5μm pert. uncoated simulations at 77 ns (Ares)

Density [gcc]

Density [gcc]

30μm pert. Coated vs uncoatedResults:- Uncoated

simulations show ETI growth

-Coated simulations show qualitative reduction of ETI growth

Future work:-Run with higher

resolution with larger Δr

2D ARES Results

- Run coated simulations with a more realistic dielectric resistivity (≠∞)

-Obtain quantitative results from simulations and compare with exp.

Given the right conditions (large jz) AR can stabilize against ETI growth

dηdT > 0

dηdT < 0

LMD aluminum table w/o AR LMD aluminum table w/ Tanaka AR

Ref: LLNL-POSTER-793884; LLNL-TR-801198; PhysRevLett.47.714; PhysRevE.66.025401

dηdT < 0

dηdT > 0

Results: - Explored if AR can contribute to ETI growthFuture Work:- Run wire sims w/ AR, and limit AR influence in non

applicable regime (high ρ, low T)

E.q. ETI (T perturbed) growth

Anomalous Resistivity

Validating the Rod Expansion Velocity against PDV data with ASC-FLAG (LANL)

• FLAG has been used to calculate the 1D expansion dynamics

• Both new LANL Conductivity Table (23715) and DesjarlaisSNL Table (29371) used

• Calculated Velocities are ~175% measured values

• Melt time consistent with SNL ALEGRA sims and PDV liftoff (~58-60ns)

LA-UR-20-20871

S. Kreher, B. Bauer, , et al.

FLAG Lineout plots at times of interest during expansion using LANL Conductivity (23715)

Melt 58ns

Loss of Signal 98ns

Middle Rise 80ns

Melt Line

Melt LineMelt Line

LA-UR-20-20871

Status/Progress• Experiments utilizing PDV to study expansion dynamics of coated and

uncoated barbells are ongoing

• First experiments with engineered-defect “barbell” rod loads, utilizing improved imaging diagnostics, completed on 2/17/2020

● Developed a SESAME table reader and interpolation algorithm

● Implemented QLMD table interpolation in Flash, and developed a 2D simulation setup

● 2D uncoated/coated simulations of wire electrical explosion using Ares

● Explored the effect of anomalous resistivity (AR) on the ETI growth rate

• FLAG simulations modelling 1D expansions relevant to Mykonos experiments

• Current he focus is to understand early-time ETI growth. Subsequent work will follow its development into late-time MHD instabilities

• Seven U.S. citizen students (3 working on site at SNL, 1 working on site at LANL) and one Post-Doc (TBD) are/will be fully supported.

Backup Slides

MHD Modeling Shows Development of Experimentally-Observed Strongly Azimuthally-Correlated MRT

Structures When an Initial Liner Perturbation is Included

axial magneticfield

cold DTgas (fuel)

azimuthal drive field

Liner (Al or Be)

compressedaxial field

laserbeampreheated

fuel

~1 cm

MAGLIF

Isolated pits merge to form striations

Simulations detail how current redistribution drives ETI

• Current bends around pits or resistive inclusions, driving enhanced Joule heating and T at edge, thus locally reducing the conductivity. This effectively widens the perturbation; in this way neighboring perturbations merge.

Electrothermal instabilities are driven by Joule heating and arise when resistivity (η) depends on temperature (T)

Allegra simulations by E. Yu, SNL

Equation of State (EOS)

● Developed an Equation of State (EOS) Viewer to provide an aid in analyzing various Equation of States.○ Can take EOS

information from supported filetypes and provide a visual data comparison.

○ Provides user a means to identify how EOS A differs from EOS B and in various regimes.

● Currently using SESAME for Ares and IONMIX for FLASH.

22Comparison of SESAME Al93721 and with equations of state generated by PrOpacEOS for energy as a function of density and temperature for aluminum 6061.

Lee-More-Desjarles Conductivity

Using Lee-More-Desjarlais (LMD) electrical conductivity (resistivity) table to calculate magnetic field diffusion in Ares and FLASH.

● Ares contains built-in interpolation algorithms (birational included).

● For FLASH, interpolating conductivity tables using an order N=9 birational interpolant, where weights vijand wij found using a least squares fit to LMD data.

23

Calculated error of birational interpolant relative to bicubic spline interpolation at 20,000 random points (black). All interpolation points demonstrated <8% for all points.

Phase Space plot shows Calculation’s outer surface enters Vapor Dome (~100ns)• Crude Overlay of EOS

boundaries correlate loss of signal with entry into Vapor Dome

• Dashed Line represents Thermodynamic Values of outermost cell in calculation over time

• Tmelt 23715 is melt line in conductivity table

• 401, 411, 412 phase boundaries from EOS used

t = 98 ns

LA-UR-20-20871

t = 58 ns