## This content will become publicly available on June 17, 2020

# Plasma kinetic effects on interfacial mix and burn rates in multispatial dimensions

## Abstract

The physics of mixing in plasmas is of great significance to inertial confinement fusion and high energy density laboratory experiments. Two- and three-dimensional (2D and 3D) particle-in-cell simulations with a binary collision model are used to explore kinetic effects arising during the mixing of plasma media. The applicability of the one-dimensional (1D) ambipolarity condition is evaluated in 2D and 3D simulations of a plasma interface with a sinusoidal perturbation. The 1D ambipolarity condition is found to remain valid in 2D and 3D, as electrons and ions flow together required for $J$ = 0. Simulations of perturbed interfaces show that diffusion-induced total pressure imbalance and hydroflows flatten fine interface structures and drive rapid atomic mix. The atomic mix rate from a structured interface is faster than the ~$$\sqrt{\bar{t}}$$ scaling obtained from 1D theory in the small-Knudsen-number limit. Plasma kinetic effects inhibit the growth of the Rayleigh-Taylor instability at small wavelengths and result in a nonmonotonic growth rate scaling with wavenumber *k* with a maximum at a low *k* value, much different from $$\sqrt{Agk}$$ (where *A* is the Atwood number and *g* is the gravitational constant) as expected in the absence of plasma kinetic effects. Simulations under plasma conditions relevant to MARBLE separated-reactant experiments on Omega and the NIF show kinetic modification of DT fusion reaction rates. With non-Maxwellian distributions and relative drifts between D and T ions, DT reactivity is higher than that inferred from rates using stationary Maxwellian distributions. Reactivity is additionally revealed to be reduced in the presence of finite-Knudsen-layer losses.

- Authors:

- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1544744

- Report Number(s):
- LA-UR-19-24145

Journal ID: ISSN 1070-664X

- Grant/Contract Number:
- 89233218CNA000001

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 26; Journal Issue: 6; Journal ID: ISSN 1070-664X

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 97 MATHEMATICS AND COMPUTING

### Citation Formats

```
Yin, Lin, Albright, Brian James, Vold, Erik Lehman, Nystrom, William David, Bird, Robert Francis, and Bowers, Kevin J. Plasma kinetic effects on interfacial mix and burn rates in multispatial dimensions. United States: N. p., 2019.
Web. doi:10.1063/1.5109257.
```

```
Yin, Lin, Albright, Brian James, Vold, Erik Lehman, Nystrom, William David, Bird, Robert Francis, & Bowers, Kevin J. Plasma kinetic effects on interfacial mix and burn rates in multispatial dimensions. United States. doi:10.1063/1.5109257.
```

```
Yin, Lin, Albright, Brian James, Vold, Erik Lehman, Nystrom, William David, Bird, Robert Francis, and Bowers, Kevin J. Mon .
"Plasma kinetic effects on interfacial mix and burn rates in multispatial dimensions". United States. doi:10.1063/1.5109257.
```

```
@article{osti_1544744,
```

title = {Plasma kinetic effects on interfacial mix and burn rates in multispatial dimensions},

author = {Yin, Lin and Albright, Brian James and Vold, Erik Lehman and Nystrom, William David and Bird, Robert Francis and Bowers, Kevin J.},

abstractNote = {The physics of mixing in plasmas is of great significance to inertial confinement fusion and high energy density laboratory experiments. Two- and three-dimensional (2D and 3D) particle-in-cell simulations with a binary collision model are used to explore kinetic effects arising during the mixing of plasma media. The applicability of the one-dimensional (1D) ambipolarity condition is evaluated in 2D and 3D simulations of a plasma interface with a sinusoidal perturbation. The 1D ambipolarity condition is found to remain valid in 2D and 3D, as electrons and ions flow together required for $J$ = 0. Simulations of perturbed interfaces show that diffusion-induced total pressure imbalance and hydroflows flatten fine interface structures and drive rapid atomic mix. The atomic mix rate from a structured interface is faster than the ~$\sqrt{\bar{t}}$ scaling obtained from 1D theory in the small-Knudsen-number limit. Plasma kinetic effects inhibit the growth of the Rayleigh-Taylor instability at small wavelengths and result in a nonmonotonic growth rate scaling with wavenumber k with a maximum at a low k value, much different from $\sqrt{Agk}$ (where A is the Atwood number and g is the gravitational constant) as expected in the absence of plasma kinetic effects. Simulations under plasma conditions relevant to MARBLE separated-reactant experiments on Omega and the NIF show kinetic modification of DT fusion reaction rates. With non-Maxwellian distributions and relative drifts between D and T ions, DT reactivity is higher than that inferred from rates using stationary Maxwellian distributions. Reactivity is additionally revealed to be reduced in the presence of finite-Knudsen-layer losses.},

doi = {10.1063/1.5109257},

journal = {Physics of Plasmas},

number = 6,

volume = 26,

place = {United States},

year = {2019},

month = {6}

}

Works referenced in this record:

##
Thermo-diffusion in inertially confined plasmas

journal, April 2014

- Kagan, Grigory; Tang, Xian-Zhu
- Physics Letters A, Vol. 378, Issue 21

##
Inhibition of turbulence in inertial-confinement-fusion hot spots by viscous dissipation

journal, May 2014

- Weber, C. R.; Clark, D. S.; Cook, A. W.
- Physical Review E, Vol. 89, Issue 5

##
Plasma kinetic effects on interfacial mix

journal, November 2016

- Yin, L.; Albright, B. J.; Taitano, W.
- Physics of Plasmas, Vol. 23, Issue 11

##
Progress in the development of the MARBLE platform for studying thermonuclear burn in the presence of heterogeneous mix on OMEGA and the National Ignition Facility

journal, May 2016

- Murphy, T. J.; Douglas, M. R.; Fincke, J. R.
- Journal of Physics: Conference Series, Vol. 717

##
Assessment of ion kinetic effects in shock-driven inertial confinement fusion implosions using fusion burn imaging

journal, June 2015

- Rosenberg, M. J.; Séguin, F. H.; Amendt, P. A.
- Physics of Plasmas, Vol. 22, Issue 6

##
Development and validation of a turbulent-mix model for variable-density and compressible flows

journal, October 2010

- Banerjee, Arindam; Gore, Robert A.; Andrews, Malcolm J.
- Physical Review E, Vol. 82, Issue 4

##
An adaptive, conservative 0D-2V multispecies Rosenbluth–Fokker–Planck solver for arbitrarily disparate mass and temperature regimes

journal, August 2016

- Taitano, W. T.; Chacón, L.; Simakov, A. N.
- Journal of Computational Physics, Vol. 318

##
Multi-species plasma transport in 1D direct-drive ICF simulations

journal, March 2019

- Vold, E.; Rauenzahn, R.; Simakov, A. N.
- Physics of Plasmas, Vol. 26, Issue 3

##
Influence of Coulomb collisions on the structure of reconnection layers

journal, July 2009

- Daughton, W.; Roytershteyn, V.; Albright, B. J.
- Physics of Plasmas, Vol. 16, Issue 7

##
A mass, momentum, and energy conserving, fully implicit, scalable algorithm for the multi-dimensional, multi-species Rosenbluth–Fokker–Planck equation

journal, September 2015

- Taitano, W. T.; Chacón, L.; Simakov, A. N.
- Journal of Computational Physics, Vol. 297

##
Viscous effects in Rayleigh-Taylor instability

journal, January 1974

- Plesset, Milton S.
- Physics of Fluids, Vol. 17, Issue 1

##
Visualization of expanding warm dense gold and diamond heated rapidly by laser-generated ion beams

journal, September 2015

- Bang, W.; Albright, B. J.; Bradley, P. A.
- Scientific Reports, Vol. 5, Issue 1

##
Effects of Diffusion on Interface Instability between Gases

journal, January 1962

- Duff, R. E.; Harlow, F. H.; Hirt, C. W.
- Physics of Fluids, Vol. 5, Issue 4

##
A binary collision model for plasma simulation with a particle code

journal, November 1977

- Takizuka, Tomonor; Abe, Hirotada
- Journal of Computational Physics, Vol. 25, Issue 3

##
Observation of early shell-dopant mix in OMEGA direct-drive implosions and comparisons with radiation-hydrodynamic simulations

journal, May 2014

- Baumgaertel, J. A.; Bradley, P. A.; Hsu, S. C.
- Physics of Plasmas, Vol. 21, Issue 5

##
Ultrahigh performance three-dimensional electromagnetic relativistic kinetic plasma simulation

journal, May 2008

- Bowers, K. J.; Albright, B. J.; Yin, L.
- Physics of Plasmas, Vol. 15, Issue 5

##
Hydrodynamic description of an unmagnetized plasma with multiple ion species. I. General formulation

journal, March 2016

- Simakov, Andrei N.; Molvig, Kim
- Physics of Plasmas, Vol. 23, Issue 3

##
Self-similar solutions for multi-species plasma mixing by gradient driven transport

journal, March 2018

- Vold, E.; Kagan, G.; Simakov, A. N.
- Plasma Physics and Controlled Fusion, Vol. 60, Issue 5

##
Hydrodynamic description of an unmagnetized plasma with multiple ion species. II. Two and three ion species plasmas

journal, March 2016

- Simakov, Andrei N.; Molvig, Kim
- Physics of Plasmas, Vol. 23, Issue 3

##
Effective Potential Theory for Transport Coefficients across Coupling Regimes

journal, June 2013

- Baalrud, Scott D.; Daligault, Jérôme
- Physical Review Letters, Vol. 110, Issue 23

##
Nonlinear Structure of the Diffusing Gas-Metal Interface in a Thermonuclear Plasma

journal, October 2014

- Molvig, Kim; Vold, Erik L.; Dodd, Evan S.
- Physical Review Letters, Vol. 113, Issue 14

##
The character of the equilibrium of an incompressible heavy viscous fluid of variable density

journal, January 1955

- Chandrasekhar, S.
- Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 51, Issue 1

##
Advances in petascale kinetic plasma simulation with VPIC and Roadrunner

journal, July 2009

- Bowers, K. J.; Albright, B. J.; Yin, L.
- Journal of Physics: Conference Series, Vol. 180

##
The effects of plasma diffusion and viscosity on turbulent instability growth

journal, September 2014

- Haines, Brian M.; Vold, Erik L.; Molvig, Kim
- Physics of Plasmas, Vol. 21, Issue 9

##
Diffusion-driven fluid dynamics in ideal gases and plasmas

journal, June 2018

- Vold, E. L.; Yin, L.; Taitano, W.
- Physics of Plasmas, Vol. 25, Issue 6

##
Improved formulas for fusion cross-sections and thermal reactivities

journal, April 1992

- Bosch, H. -S; Hale, G. M.
- Nuclear Fusion, Vol. 32, Issue 4

##
Classical transport equations for burning gas-metal plasmas

journal, September 2014

- Molvig, Kim; Simakov, Andrei N.; Vold, Erik L.
- Physics of Plasmas, Vol. 21, Issue 9

##
Influence of coupling on thermal forces and dynamic friction in plasmas with multiple ion species

journal, July 2017

- Kagan, Grigory; Baalrud, Scott D.; Daligault, Jérôme
- Physics of Plasmas, Vol. 24, Issue 7

##
Knudsen Layer Reduction of Fusion Reactivity

journal, August 2012

- Molvig, Kim; Hoffman, Nelson M.; Albright, B. J.
- Physical Review Letters, Vol. 109, Issue 9

##
Revised Knudsen-layer reduction of fusion reactivity

journal, December 2013

- Albright, B. J.; Molvig, Kim; Huang, C. -K.
- Physics of Plasmas, Vol. 20, Issue 12

##
Observation of amplification of light by Langmuir waves and its saturation on the electron kinetic timescale

journal, December 2010

- Kirkwood, R. K.; Ping, Y.; Wilks, S. C.
- Journal of Plasma Physics, Vol. 77, Issue 4

##
The RAGE radiation-hydrodynamic code

journal, October 2008

- Gittings, Michael; Weaver, Robert; Clover, Michael
- Computational Science & Discovery, Vol. 1, Issue 1

##
Inference of ICF implosion core mix using experimental dataand theoretical mix modeling

journal, December 2009

- Welser-Sherrill, L.; Haynes, D. A.; Mancini, R. C.
- High Energy Density Physics, Vol. 5, Issue 4

##
Plasma transport in an Eulerian AMR code

journal, April 2017

- Vold, E. L.; Rauenzahn, R. M.; Aldrich, C. H.
- Physics of Plasmas, Vol. 24, Issue 4