# Presentation: 210369

## Strongly Coupled Plasmas at LLNL 

**Frank R. Graziani**
**Lawrence Livermore National Laboratory**
**February 9-10, 2006**
**Presentation to the Modeling the QCD Equation of State at RHIC **

**This work was performed under the auspices of the U.S. Department of Energy by the University of**
**California, Lawrence Livermore National Laboratory under Contract No. W-7405-Eng-48.**

**UCRL-PRES-218785**

## High energy density plasmas common to ICF and astrophysics are hot dense plasmas with complex properties    

- Ichimaru, *“Statistical Plasma Physics Vol. II”,* **Westview Press** (2004)
- Kremp et al., *“Quantum Statistics of Non-ideal Plasmas”,* **Springer-Verlag** (2005)

**Ichimaru plasma coupling**

**Thermal deBroglie **
**wavelength**

**Brueckner parameter**

**ICF**

## High energy density plasmas common to astrophysics and ICF are hot dense dynamic plasmas with complex properties

**    ****Hot dense radiative plasma characteristics**
**Multi-species**
- Low Z ions (p, D, T, He3..)
- High Z ions (C, N, O, Cl, Xe..)
- 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
**Atomic processes**
- Inverse bremsstrahlung
- Photoionization
- Line absorption
- Electron impact ionization
- Continuum lowering
**Radiation field undergoing emission, absorption, and scattering **

## High Z atoms in a weakly coupled plasma can have significant impact on the character of the plasma

**Weakly **
**coupled**

**DT Plasma Coupling**

**Strongly **
**coupled**

**DT + 10% Xe**

**Strongly **
**coupled**

**DT + 1% Xe**

**Strongly **
**coupled**

**Weakly **
**coupled**

**Weakly **
**coupled**

**The presence of high Z atoms in an otherwise**
**weakly coupled plasma pushes the strongly**
**coupled regime to lower densities**

- *Brown and Yaffe, *Phys. Rep.* **340**, (2001)

## Plasma properties can range from the usual low density ionized gas phase to a state almost solid like

**Weakly coupled plasma properties:**
** **Collisions are long range and many body
-  Mutual ion-ion and electron-ion interactions are weak
-  Debye sphere is densely populated
-  Charged particle scattering is the result of the cumulative effect of many
-    small angle weak collisions
-  Characteristic of plasmas that are low density and high temperature

**Moderately to strongly coupled plasma properties:**
** **Mutual ion-ion and electron-ion interactions are strong
-  Particle motions are strongly influenced by nearest neighbor interactions
-  Debye sphere is sparsely populated
-  Large angle scattering as the result of a single encounter becomes important
-  Characteristic of plasmas that are high density, high Z, and/or low temperature** **

## The temporal evolution of plasmas depends on the complex interaction of collisional, radiative, and reactive processes  

**Relaxation processes**
**Collisional relaxation due to Coulomb interactions**
**Presence of bound states**
**Radiative processes**
**Thermonuclear reactions**
**Beam matter interaction**
**Charge particle slowing down**
**Presence of bound states**
**Radiative processes**
**Thermonuclear reactions**

## The Landau kinetic equation assumes a classical statically screened weakly coupled plasma 

**Classical weakly coupled plasma properties:**
**Collisions are long range and many body**
**Mutual ion-ion and electron-ion interactions are weak**
**Fully ionized**
**Charged particle scattering is the result of the **
**   ****cumulative effect of many small angle weak collisions**

**Features:**
** ****Brownian motion analogy**
** ****Static Debye shielding **
** ****Particle, momentum and kinetic energy conservation**
** ****Markovian**
** ****H-Theorem (Maxwellian static solution)**
** ****Short and long distance divergence (Coulomb logarithm)**

- Boyd and Sanderson, *“Physics of Plasmas”,* **Cambridge Press** (2003)

## The Lenard - Balescu equation describes a classical but dynamically screened weakly coupled plasma

**Collisions are long range and many body**
**Mutual ion-ion and electron-ion interactions are weak**
**Fully ionized**
**Charged particle scattering is the result of the **
**   ****cumulative effect of many small angle weak collisions**

**The Lenard - Balescu equation describes a classical ****but dynamically screened weakly coupled plasma**

**Features:**
** ****Dynamic screening of the long range Coulomb forces**
** ****plasma dielectric function provides cutoff **
** ****Particle, momentum and kinetic energy conservation**
** ****Markovian**
** ****H-Theorem (Maxwellian static solution)**
** ****Short distance cutoff still needed**
** ****Landau equation recovered**

- Boyd and Sanderson, *“Physics of Plasmas”,* **Cambridge Press** (2003)

## The quantum kinetic equations of Kadanoff-Baym and Keldysh provide the basis for describing complex plasmas 

**Features:**
** ****Quantum diffraction, exchange and degeneracy effects **
** ****Interacting many body conservation laws obeyed (total energy) **
** ****Formation and decay of bound states included**
** ****Dynamical screening **
** ****Non-Markovian**

- RPA self energy with a statically
- screened potential (weakly coupled)

**Quantum Landau equation**

- RPA self energy (dynamic screening)

**Quantum Lenard-Balescu equation**

**Time diagonal K- B equation describes the Wigner distribution**** **

**Dense strongly coupled plasma properties:**
**Mutual ion-ion and electron-ion interactions are strong**

- Kremp et al., *“Quantum Statistics of Non-ideal Plasmas”,* **Springer-Verlag** (2005)

## The Landau-Spitzer model of collisional relaxation rests on the assumptions of a weakly coupled classical plasma 

**Many issues are ignored:**
** ****partial ionization (bound states)**
** ****collective behavior (dynamic screening)**
** ****strong binary collisions **
** ****strong coupling **
**quantum effects**
**non-Maxwellian distributions**
**degeneracy***

**Major source of uncertainty**

**Temperature (keV)**

- *H. Brysk, *Phys. Plasmas* **16**, 927 (1974)

## The quantum kinetic approach to collisional relaxation highlights the differences between Landau-Spitzer

**Weakly coupled**

- Ohde et al., *Phys. Plasmas* **3**, 1241 (1996)
- Gericke et al., *Phys. Rev. E* **65**, 036406 (2002)
- Dharma-Wardana and Perrot, *Phys. Rev. E* **58**, 3705 (1998)
- Hazak et al., *Phys. Rev. E * **64**, 066441 (2001)

**Energy transfer rate as computed from K-B equations**
** ****Non-degenerate plasma**
** ****Local equilibrium distributions for all species**

**Electron ion energy exchange rate **

**Spitzer under-predicts the energy transfer rate for the modified form of the Coulomb logarithm**

## Validation experiments show discrepancies for a Landau-Spitzer strongly coupled plasmas 

**Validation experiments show discrepancies for a Landau-Spitzer strongly coupled plasmas **

- Celliers et al., *PRL* **68**, 2305 (1992)

- Silicon

- shock front

**Optical emission from **
**shocked Si is measured**

**Observed shock emission**

**Spitzer**

**Lee-More**

**Study yielded first ever measurement**
**of electron-ion coupling in a strongly**
**coupled plasma**

- Al

- CH

- CH

- Riley et al., *PRL* **84**, 1704 (2000)

**Laser**

**Laser**

**Laser**

**X-ray scattering cross-section from a dense plasma**

## Beam matter interaction is one of the key tools for creating, heating, and diagnosing dense plasmas

**Beam matter interaction is one of the key tools for creating, heating, and diagnosing dense plasmas**

**A number applications require a quantitative understanding of the **
**energy loss of fast heavy particles passing through matter**
** ****The slowing down of 3.5 MeV alpha particles in a DT thermonuclear plasma**
** ****Heavy ion driven inertial fusion**
** ****Electron cooling of heavy ion beams**

## Stopping power formulas can be validated against both experiments and simulations  

- Belyaev et al., *Phys. Rev. E* **53**, 2701 (1996)

**Temporal behavior of the proton **
**energy loss in the plasma target**

**Experiment inferred a value for the Coulomb logarithm which was **
**consistent with theoretical predictions for weakly coupled plasmas**

**Coulomb energy loss by 1 MeV protons**

**Comparison of different approximation schemes for the stopping power with data from PIC (*) and MD (crosses) confirm the quantum kinetic approach in strongly coupled plasmas**** **

- Zwicknagel et al., *Phys. Rep. * **309**, 117 (1999)

## Ultra-short pulse lasers are being proposed as a tool to measure the properties of dense plasmas 

**Target**

**Laser**

**Ion beam**

**Laser for heating target**

**Attenuated ions**

**Foil**

**R. Shepard, S. Wilks, P. Beirersdorfer**

**Reduced Mass Targets Heated by Ultra-Intense Lasers **
**as a Means of Creating Kilovolt Plasmas at Solid Densities**
- S. C. Wilks, et. al, in preparation for Phys Rev. Lett. Dec. 2005.

**Energetic proton generation in ultra-intense laser-solid interactions , **S. C. Wilks, *et. al*., *Physics of Plasmas*, 8, 542 2001.)

- G. Gregori, et. Al., Contrib. Plasma Phys. **45**, No 3-4, 284-292 (2005).

**Direct Experimental Evidence of Back-Surface Ion Acceleration from Laser-Irradiated Foils** Matthew Allen, et. al., Phys Rev. Lett. **93**, 265004 (2004)

## The standard model of thermonuclear reaction rates rests on a Maxwellian distributed weakly coupled plasma 

**Y**

**X**

**a**

**b**

**DT cross section**

**Ion **
**distribution**

**Gamow peak**

**Velocity (cm/microsecond)**

**T=10.4 keV**

**Fusion reactivity**

**ion distribution**

**cross section**

**The Gamow Peak**

## Thermonuclear reaction rates can be a sensitive function of their plasma environment

**Dense plasma effects on nuclear reaction rates**
**Screening due to electrons and ions**
**Salpeter (’54): The potential shift increases**
**  ****the probability that the two charges interact**
**What is the effect of high Z non-reacting dopants **
** ****on the reaction rate (e.g. DT+10%Xe)  **

**Ion Distribution Functions**
**Non-thermal**
**Self-similar ion distributions in**
**  ****laser irradiated high Z plasmas**
**Kinetic treatment of a reacting plasma**

**Temperature (keV)**

**DT reaction rate for three **
**different ion distributions**

- Brown and Sawyer, *Rev. Mod. Phys.* **69**, 411 (1997)
- Bahcall et al., *A&A*, **383**, 291 (2002)
- Pollock and Militzer, *PRL* **92**, 021101 (2004)

## Are there common problems that the QGP and the hot dense radiative plasma communities face ?    

**ICF**

**Understanding hot dense radiative**
**plasmas is an immense undertaking**
**What are the parallels between**
**the Abelian and non-Abelian plasmas ?**

**QGP ?**