skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Carbon ionization at gigabar pressures: An ab initio perspective on astrophysical high-density plasmas

Abstract

A realistic description of partially ionized matter in extreme thermodynamic states is critical to model the interior and evolution of the multiplicity of high-density astrophysical objects. Current predictions of its essential property, the ionization degree, rely widely on analytical approximations that have been challenged recently by a series of experiments. Here, we propose an ab initio approach to calculate the ionization degree directly from the dynamic electrical conductivity using the Thomas-Reiche-Kuhn sum rule. This density functional theory framework captures genuinely the condensed-matter nature and quantum effects typical for strongly correlated plasmas. We demonstrate this capability for carbon and hydrocarbon, which most notably serve as ablator materials in inertial confinement fusion experiments aiming at recreating stellar conditions. We find a significantly higher carbon ionization degree than predicted by commonly used models, yet validating the qualitative behavior of the average atom model purgatorio. Additionally, we find the carbon ionization state to remain unchanged in the environment of fully ionized hydrogen. Our results will not only serve as benchmark for traditional models, but more importantly provide an experimentally accessible quantity in the form of the electrical conductivity.

Authors:
ORCiD logo; ; ; ; ; ; ; ; ORCiD logo
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1631399
Alternate Identifier(s):
OSTI ID: 1635091
Report Number(s):
LLNL-JRNL-800319
Journal ID: ISSN 2643-1564; PPRHAI; 023260
Grant/Contract Number:  
100182; AC52-07NA27344; 18-ERD-033
Resource Type:
Published Article
Journal Name:
Physical Review Research
Additional Journal Information:
Journal Name: Physical Review Research Journal Volume: 2 Journal Issue: 2; Journal ID: ISSN 2643-1564
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; Density of states; Electrical conductivity; High-energy-density plasmas; Inertial confinement fusion; Plasma ionization; Plasma transport; Pressure effects; Space & astrophysical plasma; Temperature; Physical Systems; Warm-dense matter

Citation Formats

Bethkenhagen, Mandy, Witte, Bastian B. L., Schörner, Maximilian, Röpke, Gerd, Döppner, Tilo, Kraus, Dominik, Glenzer, Siegfried H., Sterne, Philip A., and Redmer, Ronald. Carbon ionization at gigabar pressures: An ab initio perspective on astrophysical high-density plasmas. United States: N. p., 2020. Web. doi:10.1103/PhysRevResearch.2.023260.
Bethkenhagen, Mandy, Witte, Bastian B. L., Schörner, Maximilian, Röpke, Gerd, Döppner, Tilo, Kraus, Dominik, Glenzer, Siegfried H., Sterne, Philip A., & Redmer, Ronald. Carbon ionization at gigabar pressures: An ab initio perspective on astrophysical high-density plasmas. United States. doi:https://doi.org/10.1103/PhysRevResearch.2.023260
Bethkenhagen, Mandy, Witte, Bastian B. L., Schörner, Maximilian, Röpke, Gerd, Döppner, Tilo, Kraus, Dominik, Glenzer, Siegfried H., Sterne, Philip A., and Redmer, Ronald. Mon . "Carbon ionization at gigabar pressures: An ab initio perspective on astrophysical high-density plasmas". United States. doi:https://doi.org/10.1103/PhysRevResearch.2.023260.
@article{osti_1631399,
title = {Carbon ionization at gigabar pressures: An ab initio perspective on astrophysical high-density plasmas},
author = {Bethkenhagen, Mandy and Witte, Bastian B. L. and Schörner, Maximilian and Röpke, Gerd and Döppner, Tilo and Kraus, Dominik and Glenzer, Siegfried H. and Sterne, Philip A. and Redmer, Ronald},
abstractNote = {A realistic description of partially ionized matter in extreme thermodynamic states is critical to model the interior and evolution of the multiplicity of high-density astrophysical objects. Current predictions of its essential property, the ionization degree, rely widely on analytical approximations that have been challenged recently by a series of experiments. Here, we propose an ab initio approach to calculate the ionization degree directly from the dynamic electrical conductivity using the Thomas-Reiche-Kuhn sum rule. This density functional theory framework captures genuinely the condensed-matter nature and quantum effects typical for strongly correlated plasmas. We demonstrate this capability for carbon and hydrocarbon, which most notably serve as ablator materials in inertial confinement fusion experiments aiming at recreating stellar conditions. We find a significantly higher carbon ionization degree than predicted by commonly used models, yet validating the qualitative behavior of the average atom model purgatorio. Additionally, we find the carbon ionization state to remain unchanged in the environment of fully ionized hydrogen. Our results will not only serve as benchmark for traditional models, but more importantly provide an experimentally accessible quantity in the form of the electrical conductivity.},
doi = {10.1103/PhysRevResearch.2.023260},
journal = {Physical Review Research},
number = 2,
volume = 2,
place = {United States},
year = {2020},
month = {6}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: https://doi.org/10.1103/PhysRevResearch.2.023260

Figures / Tables:

FIG. 1 FIG. 1: Electrical conductivity (solid lines) and TRK sum rule values (dashed lines) for a carbon simulation snapshot at 50 g/cm3 and T = 100 eV. The different colors indicate the total value and the individual components of both quantities according to Eq. (3) and Eq. (4). The final TRKmore » sum rule values are given as colored numbers.« less

Save / Share:

Works referenced in this record:

Generalized Gradient Approximation Made Simple
journal, October 1996

  • Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
  • Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868
  • DOI: 10.1103/PhysRevLett.77.3865

Material Properties for the Interiors of Massive Giant Planets and Brown Dwarfs
journal, September 2018

  • Becker, Andreas; Bethkenhagen, Mandy; Kellermann, Clemens
  • The Astronomical Journal, Vol. 156, Issue 4
  • DOI: 10.3847/1538-3881/aad735

Quantum-Mechanical Calculation of Ionization-Potential Lowering in Dense Plasmas
journal, July 2014


Ab initio determination of electrical and thermal conductivity of liquid aluminum
journal, September 2005


The transition to the metallic state
journal, February 1961


Equation of state, occupation probabilities and conductivities in the average atom Purgatorio code
journal, May 2007


Resonant K α Spectroscopy of Solid-Density Aluminum Plasmas
journal, December 2012


Ionization potential depression and optical spectra in a Debye plasma model
journal, November 2017

  • Lin, Chengliang; Röpke, Gerd; Reinholz, Heidi
  • Contributions to Plasma Physics, Vol. 57, Issue 10
  • DOI: 10.1002/ctpp.201700114

Observations of the Effect of Ionization-Potential Depression in Hot Dense Plasma
journal, June 2013


Path integral Monte Carlo simulations of warm dense aluminum
journal, June 2018


Lowering of Ionization Potentials in Plasmas
journal, April 1966

  • Stewart, John C.; Pyatt, Kedar D. , Jr.
  • The Astrophysical Journal, Vol. 144
  • DOI: 10.1086/148714

Electrical conductivity for warm, dense aluminum plasmas and liquids
journal, August 2002


Characterizing the ionization potential depression in dense carbon plasmas with high-precision spectrally resolved x-ray scattering
journal, November 2018

  • Kraus, D.; Bachmann, B.; Barbrel, B.
  • Plasma Physics and Controlled Fusion, Vol. 61, Issue 1
  • DOI: 10.1088/1361-6587/aadd6c

Validating Continuum Lowering Models via Multi-Wavelength Measurements of Integrated X-ray Emission
journal, April 2018


Comment on “Continuum Lowering and Fermi-Surface Rising in Strongly Coupled and Degenerate Plasmas”
journal, March 2018


�ber die Gesamtst�rke der von einem Zustande ausgehenden Absorptionslinien
journal, December 1925


Hu Replies:
journal, March 2018


Cryogenic thermonuclear fuel implosions on the National Ignition Facility
journal, May 2012

  • Glenzer, S. H.; Callahan, D. A.; MacKinnon, A. J.
  • Physics of Plasmas, Vol. 19, Issue 5
  • DOI: 10.1063/1.4719686

Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set
journal, October 1996


The new Los Alamos opacity code ATOMIC
journal, May 2006

  • Hakel, P.; Sherrill, M. E.; Mazevet, S.
  • Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 99, Issue 1-3
  • DOI: 10.1016/j.jqsrt.2005.04.007

Ab initio molecular-dynamics simulation of the liquid-metal–amorphous-semiconductor transition in germanium
journal, May 1994


X-ray scattering measurements on imploding CH spheres at the National Ignition Facility
journal, July 2016


Platform for spectrally resolved x-ray scattering from imploding capsules at the National Ignition Facility
journal, May 2016


Dense plasmas, screened interactions, and atomic ionization
journal, August 1998


Creation and diagnosis of a solid-density plasma with an X-ray free-electron laser
journal, January 2012

  • Vinko, S. M.; Ciricosta, O.; Cho, B. I.
  • Nature, Vol. 482, Issue 7383
  • DOI: 10.1038/nature10746

Electronic transport coefficients from ab initio simulations and application to dense liquid hydrogen
journal, June 2011


Mean-Value Point in the Brillouin Zone
journal, June 1973


Ab initiomolecular dynamics for liquid metals
journal, January 1993


Warm Dense Matter Demonstrating Non-Drude Conductivity from Observations of Nonlinear Plasmon Damping
journal, May 2017


Lowering of the Ionization Energy for a Plasma in Thermodynamic Equilibrium
journal, January 1963


�ber die Zahl der Dispersionselektronen, die einem station�ren Zustand zugeordnet sind
journal, December 1925

  • Reiche, F.; Thomas, W.
  • Zeitschrift f�r Physik, Vol. 34, Issue 1
  • DOI: 10.1007/BF01328494

Continuum Lowering and Fermi-Surface Rising in Strongly Coupled and Degenerate Plasmas
journal, August 2017


A plea for a reexamination of ionization potential depression measurements
journal, September 2014


Ionization potential depression and Pauli blocking in degenerate plasmas at extreme densities
journal, March 2019


Ionization potential depression in an atomic-solid-plasma picture
journal, April 2018

  • Rosmej, F. B.
  • Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 51, Issue 9
  • DOI: 10.1088/1361-6455/aab80f

A unified formulation of the constant temperature molecular dynamics methods
journal, July 1984

  • Nosé, Shuichi
  • The Journal of Chemical Physics, Vol. 81, Issue 1
  • DOI: 10.1063/1.447334

OPAL Equation-of-State Tables for Astrophysical Applications
journal, January 1996

  • Rogers, Forrest J.; Swenson, Fritz J.; Iglesias, Carlos A.
  • The Astrophysical Journal, Vol. 456
  • DOI: 10.1086/176705

Continuum lowering – A new perspective
journal, December 2014


Density functional theory calculations of continuum lowering in strongly coupled plasmas
journal, March 2014

  • Vinko, S. M.; Ciricosta, O.; Wark, J. S.
  • Nature Communications, Vol. 5, Issue 1
  • DOI: 10.1038/ncomms4533

Observations of Continuum Depression in Warm Dense Matter with X-Ray Thomson Scattering
journal, April 2014


Dynamical screening and self-energy of excitons in the electron–hole plasma
journal, November 1978

  • Zimmermann, R.; Kilimann, K.; Kraeft, W. D.
  • Physica Status Solidi (b), Vol. 90, Issue 1
  • DOI: 10.1002/pssb.2220900119

The Boltzmann Equation in the Theory of Electrical Conduction in Metals
journal, April 1958


Strongly Constrained and Appropriately Normed Semilocal Density Functional
journal, July 2015


Direct Measurements of the Ionization Potential Depression in a Dense Plasma
journal, August 2012


    Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.