A Novel Study of Warm Dense Matter Using Hybrid PIC/MD ......Hybrid PIC/MD Simulation Approaches Combined With Hybrid Ultrafast DAC Based Experiments Douglass Schumacher The Ohio State

A Novel Study of Warm Dense Matter Using Hybrid PIC/MD Simulation Approaches Combined

With Hybrid Ultrafast DAC Based ExperimentsDouglass Schumacher

The Ohio State UniversityStewardship Science Academic Programs Symposium

Washington DC, February 26-27

Goals

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• Drive microexplosions and develop suitable time resolved diagnostics

• Study a range of target types and materials: free standing films, embedded targets, target in diamond anvil cells

• Develop a new approach to WDM using the particle-in-cell method based on atomic pair potentials, including careful bench mark experiments

• Combine these facets to better understand material and plasma evolution at the high pressures and temperature facilitated by microexplosions.

Graduates now at national labs

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• Dr. Anthony LinkPostdoc at LLNL 2011-2014, Applied Physicist 2014

• Dr. Gregory Elijah KempLawrence Fellow 2011Postdoc at LLNL 2013Research Scientist 2015

• Dr. Matthew McMahonPostdoc at LLNL 2015Research Scientist

• Dr. Sheng JiangPostdoc at LLNL 2014Research Scientist

• Dr. Patrick PoolePostdoc at LLNL 2016

• Dr. Andrew KrygierPostdoc at LLNL 2016

• Dr. Kyle KafkaResearch Scientist at LLE 2016

• Mr. Abraham HandlerSenior Mechanical Technologist at LLNL2016

• Dr. Ginevra CochranPostdoc at LLNL 2019

• Dr. Jeffrey PigottAgnew Nat’l Security Postdoctoral FellowLANL 2018Panero Group

Warm dense matter using microexplosions

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This study brings together a diverse collection of experimental and computational capability.

Enam Chowdhury Wendy Panero

Abdallah AlShafey

AlexanderKlepinger

Noah Talisa Justin Twardwoski

Microexplosions – a path to WDM

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Near IR single pulse @ 760 nm

Possible structure added, eg. 20 µm Polystyrene spheres

T = +9.6 nsT = +7.3 ns

20 µm

20 µm

Time resolved microscopy images

100 um substrate

390 nm fs probe

Intensity 1014 W/cm2

3 km/s expansion

Polystyrene spheresexpansion

Vailionis, et al., Nature Comm. (2011).Gamaly, et al., High Energy Density Phys. 8, 13 (2012).Rapp, et al., Nature Comm. (2015)Gamaly, et al. Nanomaterials (2018)

Experimental program: free standing samples

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Hybrid DAC experiments

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Scarlet Laser Facility and Gray

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Gray Laser

Femto-Solid Laboratory

Specifications

3 mJ energy per pulse

30 fs pulse duration

Center wavelength at 800 nm

1 kHz repetition rate

0.4 mJ per pulse @ 5 fs

OPAs @ 1.1 – 2 μm, 3-5 μm

Scarlet Laser

HEDP & high field science

Specifications

10 J energy per pulse

30 fs pulse duration

2 μm spot size

Center wavelength at 815 nm

1 shot per minute

Intensity of >5 x 1021 W/cm2

300 TW

Exp. ChamberAFOSR DURIP

Poole, et al., Applied Optics 55, 4713 (2016)

Pump-probe setup

2 µm

• Energy/pulse 12 uJ• Pulse duration 50 fs• Focal spot FWHM: 2.2 um• Estimated projected Intensity in bulk 2 x 1015 Wcm-2

• If intensity is too high, will cause dielectric breakdown, filamentation and channeling

390 nm

780 nm

GDD measurement setup for objective lenses

GDD measurement spectrum GDD ~ 1000 fs2 Compensating chirped mirror

GDD measurement for HR objective

Time-resolved micro-explosion inside bulk fused silica (0.4 mm thick)

1311 ps678 ps

0 fs 333 fs 51 ps

Post Magnification:0.38 um/px

pixe

l

10 µm

Reduce energy/pulse and increase SNR• 3.5 uJ/pulse• Tighter spot and more symmetric –

likely suppression of filament

0 ps 35 ps 69 ps

700 ps 700 ps + 66 fs 700 ps + 132 fs 700 ps + 198 fs 700 ps + 264 fs 700 ps + 330 fs

700 ps + 396 fs 700 ps + 462 fs 700 ps + 528 fs 700 ps + 594 fs 700 ps + 660 fs post

10 µm

Two step rapid signal change

• Step 1 : ~35 ps to ~70 psApprox. speed 39, 45 km/s

• Step 2: 700 ps to 701 psApprox. speed 10,000 km/s

0.00E+00

5.00E-07

1.00E-06

1.50E-06

2.00E-06

2.50E-06

3.00E-06

0 1E-13 2E-13 3E-13 4E-13 5E-13 6E-13

Dist

ance

(m)

delay time (s)

y = 1E+07x + 1E-08R² = 0.9745

0.00E+00

5.00E-07

1.00E-06

1.50E-06

2.00E-06

2.50E-06

3.00E-06

0 5E-14 1E-13 1.5E-13 2E-13 2.5E-13 3E-13

35 ps 69 ps

delay time (s)

700 ps

10 µm

Particle-in-cell modeling (PIC)

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• PIC’s speed relies on two key simplificationso Particles have continuous

position, finite sizeo Fields, densities, currents,

etc live only at grid nodes

• The PIC method is a widely used method for the simulation of plasmas• Directly integrates Maxwell’s equations• Has been used to study laser plasma

interactions, laser driven fusion, ionosphere …

Modeling solids with PIC

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• Without modification, PIC cannot model stable configurations of atoms

• Pair potential algorithm developed by Rob Mitchell to model the ablation process (coded in LSP)

1. Use density, density gradient to calculate approximate nearest neighbor distances

2. Use the pair potential to calculate force due to these neighbors on the atom.

3. Use forces to find new particle positions and momenta

Δr1 Δr2𝑛𝑛,𝑑𝑑𝑛𝑛𝑑𝑑𝑑𝑑UL-J(Δr1) UL-J(Δr2) �̅�𝑟 = 1

𝑛𝑛1/3 , 𝜕𝜕�̅�𝑟𝜕𝜕𝜕𝜕

= −𝜕𝜕𝜕𝜕𝜕𝜕𝜕𝜕

3𝑛𝑛4/3∆𝑟𝑟1,2= �̅�𝑟 1 ±

12𝜕𝜕�̅�𝑟𝜕𝜕𝑑𝑑

−1

Mitchell, et al., Optics Letters 40, 2189 (2015).

Use multiple stages to model an interaction

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• Laser-particle interaction (LPI) simulation.o Done with PIC-based solution of

Maxwell’s equations

• Two Temperature Model (TTM)o Electron and ions thermalize and

heat diffuses through targeto Computations done in Matlab

High-res LPI(fs)

Thermal Diffusion(ps)

• Pair Potential Model• Ions modeled as neutral particles

interacting through pair potential

Material Ablation(ns)

Russell and Schumacher, Physics of Plasmas 24, 080702 (2017). Russell, et al., https://arxiv.org/abs/1704.07482.

Experimental test: laser ablation

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• A key strength of the algorithm is the ability to produce a full morphological profile of the laser damage

• Copper was chosen as a test material: no ionization model needed, plenty of data on material properties

• Existing experimental data lacks uniformity – collaborated with Enam Chowdhury, Kyle Kafka at OSU for production of well characterized copper craters

Laser Setup Interferometer Depth Profile Lineout

-1.60E-01

-1.40E-01

-1.20E-01

-1.00E-01

-8.00E-02

-6.00E-02

-4.00E-02

-2.00E-02

0.00E+00

2.00E-02

0 1 2 3 4

Dept

h (u

m)

Distance (um)

Experiment and Simulation Comparison

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• Good agreement overall (within 25 nm), but better at lower fluences

• Extrapolating to zero depth to find ablation threshold fluence gives 0.7 J/cm2 , consistent with experimental data

SEM image of 4.8 J/cm2

experimental crater

More advanced approach implemented for Aluminum

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M. Dharma-Wardana, Phys. Rev. E, 86(3) (2012).

• Only two simulation phases: short pulse laser heating (fs), target evolution (ps, ns)

• Use of embedded atom model and DFT for potentials and pair-correlation function

Fwidth = 0.21 J/cm2

Fdepth = 1.47 J/cm2

Summary

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Funding:DE-NA0003878FA9550-14-1-0085 (development of PIC/MD)

• Use laser excited microexplosions and develop single shot diagnostics• Development at low energies and then scaling to higher energies• Novel modeling PIC tool employing atomic pair potentials• Bring them together and benchmark

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Pump probe

1.73 ps

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0 ps 0.133 ps 0.4 ps 0.533 ps 0.667 ps 0.8 ps

0.933 ps 1.067 ps 1.2 ps 1.33 ps 1.47 ps 1.6 ps

1.867 ps 2.0 ps 2.33 ps 2.67 ps 3 ps

Short delays

102 ps

142 ps

6.67 ps 8.67 ps

3.33 ps 3.67 ps 4.0 ps 4.67 ps

62 ps

5.33 ps 6.0 ps

7.33 ps 12.0 ps 15.3 ps 22.0 ps

35.3 ps 75.3 ps 208 ps

Long delays

678 ps 978 ps778 ps745 ps 1111 ps

1178 ps

1211 ps

1245 ps

1278 ps

1311 ps

1045 ps