**Challenges in High Energy Density Physics:**

**Plasma Physics in the 21^st^ Century**

**April 19, 2006**

**Introduction**

The purpose of this white paper is to provide a framework for
understanding the role plasma physics issues are expected to play in
successful ASC Predictive Science Academic Alliance Program (PSAAP), and
to identify areas of particular interest and relevance to the NNSA
Laboratories. The ASC Predictive Science Academic Alliance Program seeks
large scale projects that require the successful integration of these
plasma physics areas in a "multi-physics"' framework.

Matter in the plasma state spans a wide range of physical regimes and
phenomena including metals, the core of the sun, brown dwarfs, space
plasmas, magnetic and inertial fusion. Specifically, high energy density
plasmas, which are of critical importance to the NNSA National Labs, are
a subset of plasmas that require an understanding of matter at extreme
conditions. High energy density plasmas typically involve complex
processes that take place over a wide range of length and time scales.
Depending on the specific application, accurate descriptions require
detailed understanding of processes that include dynamic screening,
particle correlations, external fields, radiative transfer, and
thermonuclear reactions. Due to the complexity of the plasma state and
the desire to make large multi-physics simulations tractable,
computational physicists at the National Laboratories have had to make a
number of assumptions to model these and other aspects of high energy
density plasmas in the ASC radiation-hydrodynamic codes. Sometimes,
these assumptions are based on good physical judgment. In other cases,
however, there exists a lack of theoretical and/or experimental
information to help guide approximations. It is hoped that the science
developed at successful ASC PSAAP Centers will elucidate these
approximations.

This white paper is closely coupled to the Particle Transport white
paper, and both white papers should be read as a pair.

**Plasmas and High Energy Density** **Physics**

The working definition of high energy density (HED) that will be used in
this paper is taken from the report "Frontiers for Discovery in High
Energy Density Physics" prepared by the National Task Force on High
Energy Density Physics \[1\]. High energy density refers to energy
densities exceeding$\text{10}^{\text{11}}\frac{J}{m^{3}}$, or
equivalently to pressures in excess of 1Mbar. Alternative
characterizations of HED include electromagnetic wave intensities
exceeding$3 \times \text{10}^{\text{15}}\frac{W}{\text{cm}^{2}}$, or
static magnetic fields exceeding 500 Tesla.

The ratio of potential energy to kinetic energy is also a useful
parameter for categorizing plasmas. The so-called ion-ion plasma
coupling parameter is defined by

$$G = \frac{Z^{2}e^{2}}{\text{kT}}(4\frac{pn}{3})^{\frac{1}{3}}$$

representing the ratio of average potential energy (Z^2^e^2^/a) to
average kinetic energy (kT) for charge Z particles separated by an ion
sphere radius a. Weakly coupled, near ideal plasmas correspond to
$\Gamma\text{<<}1$ . Plasmas in this regime have weak particle-particle
correlations and are dominated by thermal properties. This is the regime
populated by magnetic fusion studies and by portions of the laser-plasma
target phase space.

Moderately coupled to moderately-strongly coupled plasmas are
characterized by
$\text{\textasciitilde}\text{.}1 < \Gamma < \text{\textasciitilde}\text{10}$
and$\Gamma > \text{\textasciitilde}\text{10}$. These so called nonideal
plasmas exhibit behavior very different from the weakly coupled plasmas
discussed above. In this regime, particle-particle correlations are
important. Moderately and strongly-coupled plasmas are a difficult to
treat theoretically because standard approximations and expansion
methods breakdown. These regimes are populated by high intensity
laser-matter or pulsed power targets at higher densities or if high Z
dopants present, as well as in the cores of giant planets.

Moderate to strong coupling, as well as high densities drive far ranging
effects in plasmas because strong ion-ion and electron-ion correlations
cause dynamical structures that can affect important atomic, radiative,
and nuclear processes in the medium \[2\]. Equations governing radiative
and collisional rates, energy exchange and reaction rates are all
altered in this environment.

Figure 1 shows the density-temperature space of some representative
plasmas along with iso-contours of ion-ion coupling for a hydrogen
plasma (Z=1). Also shown are iso-contours of number density multiplied
by the electron or proton thermal deBroglie volume. These help
distinguish electron and proton degeneracy regimes. Shown in figure 1 is
the density-temperature phase space spanned by hot and warm dense
matter. Each of these plasma types will be discussed next.

**Hot Dense** **Matter**

Applications as widely varying in scale from laboratory, transient,
dense laser-plasma experiments to the cores of stars involve
understanding the complex processes present in hot dense radiative
plasmas (HDR). The temperatures in HDR plasmas range from a few hundred
eV to tens of keV. This extreme state of matter combines atomic,
radiative, and even thermonuclear processes where relevant, in highly
nonlinear ways. The interaction of these aspects can greatly magnify
uncertainties in understanding and predicting the behaviors of hot dense
matter.

HDR plasmas of interest to the NNSA National Laboratories typically have
the following complicating properties:

-   Multiple species of disparate elements.

    -   Low Z ions (e.g. p, D, T, He3\...)

    -   High Z ions (e.g. C, N, O, Cl, Xe, and higher Z)

-   Separate temperatures for ion species, electrons, and radiation

-   Thermonuclear burn

    -   Low Z reactants with or without the presence of high Z dopants

    -   High Z reactants (stellar cores)

-   Atomic processes (listed below is a sample)

    -   Inverse bremsstrahlung

    -   Photoionization

    -   Line absorption

    -   Electron impact ionization

    -   Continuum lowering

    -   Many body effects on spectral line profiles

-   Radiation field propagation in the presence of emission, absorption,
    and scattering

-   Partially degenerate electrons

An important aspect of HDR plasmas is that the photons interact strongly
with the medium. The plasma itself will emit, absorb and scatter
photons. The radiation field contributes to the overall hydrodynamic
motion of the plasma through a large radiation pressure. For
temperatures of the order of a keV or greater, which is expected in some
laboratory plasmas and at the core of stars, the radiation field becomes
the dominant transport mechanism for energy and momentum in hot dense
plasmas. Hence, accurate treatment of plasma behaviors depends
critically on the photon transport algorithm.

What are some of the issues facing HDR plasmas? An otherwise weakly
coupled plasma doped with high Z material can exhibit all the behaviors
of a moderately to strongly coupled plasma because the ion-ion plasma
coupling parameter depends on the square of the effective ionization.
The effects of a nonideal environment on plasma thermalization
properties and thermonuclear reaction rates continues to be studied
theoretically \[2\] and is beginning to be studied computationally. In
order to improve predictive capability, the National Laboratories will
require a detailed understanding of thermonuclear reactions, charged
particle slowing down, energy and momentum exchange processes in dynamic
nonideal HDR plasmas, through theory and simulation. One avenue is to
use molecular dynamic simulations to validate existing approximate
models of thermalization.

**Warm Dense** **Matter (WDM)**

Warm dense matter physics has received a lot of attention in recent
years \[2,5\] due to the challenges it poses for both experimentalists
and theorists. Plasmas in this regime tend to be strongly coupled and
therefore have all the properties described above. Cold dense plasmas
such as the cores of giant planets are warm dense matter prototypes.
Other examples include the behaviors of targets under irradiation by
short pulse lasers at intensities under 10^13^ watts/cm^2^ Many of the
issues relevant to WDM focus on equations of state and transport
(conductivity).

**Dusty Plasmas**

Simply put, dusty plasmas are a many-body collection of charged
particles that contains charged microscopic particulates. The presence
of these charged "dust grains\" can have important effects on the nature
of the plasma by introducing new types of instabilities and waves. What
role the existence of charged micro sized grains might have in HDR
plasmas is relatively unexplored. The presence of small particulates
(\"dust\") in a plasma can change the physical environment in
significant ways. For example, if the plasma is cold and only weakly
ionized, it is considerably easier to knock electrons off the dust
particles than it is to ionize a background neutral atom and thus
significantly increase the ionization state of the plasma. Generally in
the presence of a plasma, the particulates collect background ions and
electrons, become charged, like small Langmuir probes, and modify the
charge balance in the plasma. The charged dust particles interact with
the background plasma species, with each other and with walls and other
conductors. The principal issues in these so called dusty plasmas are
related to the various mechanisms by which the dust grains charge, the
resultant forces on the grains and their transport through the plasma
\[6\]. The grains can charge to very large values (e.g., a one micron
radius particle in a one eV plasma can acquire a net charge of several
thousand electrons) and if the density of such grains is large enough,
their Coulomb coupling parameter
![](media/image1.wmf){width="0.1527777777777778in"
height="0.16666666666666666in"}can easily exceed 100. Indeed, for
![](media/image2.wmf){width="0.6527777777777778in" height="0.19375in"},
grains can form into a crystalline state, as has been often observed
experimentally. Most of the experimental studies, and related theory of
dusty plasmas, have dealt with low temperature, low density rf
discharges and extensions to astrophysical systems. There has been some
recent interest in particulates in higher density and hotter plasmas,
e.g., for magnetic fusion applications \[7\]. The Laboratories are
interested in understanding how the physics of dusty plasmas is modified
in these higher energy density regimes and how such processes could be
studied theoretically, experimentally and computationally.

: ![](media/image3.png){width="3.8346456692913384in"
height="3.8751968503937007in"}

**Figure 1: Density temperature diagram for various common plasmas. The
gamma curves are for a pure hydrogen plasma. \[2\]**

.

**References**

1)  National Task Force on HED Physics "Frontiers for Discovery in High
    Energy Density Physics", July 2004.

2)  D. Kremp et al., "Quantum Statistics of Non-ideal Plasmas",
    **Springer-Verlag** (2005).

3)  Salpeter, Aust. J. Phys. 7, 373 (1954); Brown and Sawyer, Rev. Mod.
    Phys. **69**, 411 (1997).

4)  Pollock and Militzer, Phys. Rev. Lett. **92**, 021101 (2004).

5)  M. Koenig et al, Plasma Phys. Control. Fusion **47**, B441 (2005).

6)  V. E. Fortov et al., Phys. Uspekhi, 47, 447 (2004).

7)  A. Yu. Pigarov et al., Phys. Plasmas, 12, 122505 (2005).

**Points of Contact**

Frank Graziani

Lawrence Livermore National Laboratory

<graziani1@llnl.gov>

Len Margolin

Los Alamos National Laboratory

<len@lanl.gov>

Thomas Mehlhorn

Sandia National laboratories

<tamehlh@sandia.gov>

**Acknowledgements**

The authors wish to thank the help and contributions of many colleagues.
In particular, Brian Albright, Denise Hinkel, Dana Knoll, Bruce Langdon,
and Dan Winske deserve special thanks for their contributions.

This work was, in part, performed by the Lawrence Livermore National
Laboratory, Los Alamos National Laboratory, and Sandia National
Laboratories under auspices of the U.S. Department of Energy.

This document was prepared as an account of work sponsored by an agency
of the United States Government. Neither the United States Government
nor the University of California nor any of their employees, makes any
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This work was performed under the auspices of the U.S. Department of
Energy by University of California, Lawrence Livermore National
Laboratory under Contract W-7405-Eng-48.