1. Complex Plasmas as a Model for the Quark-Gluon-Plasma Liquid
Markus H. Thoma*
Max-Planck-Institute for Extraterrestrial Physics
Strongly Coupled Plasmas
Complex Plasmas
Applications to the Quark-Gluon Plasma
* Supported by DLR (BMBF)

2. Strongly Coupled Plasmas
Plasma = ionized gas, 99% of visible matter in Universe
Plasmas generated by high temperatures, electric fields, or radiation
Classifications:
Non-relativistic – relativistic plasmas (pair plasmas, QGP)
Classical – quantum plasmas (white dwarfs, QGP)
Ideal – strongly coupled plasmas (complex plasmas, QGP)

4. Coulomb coupling parameter
Q: charge of plasma particles
d: inter particle distance
T: plasma temperature
Ideal plasmas: G << 1 (most plasmas: G < 10-3)
Strongly coupled plasmas: G > O (1)
Examples: ion component in white dwarfs, high-density plasmas at GSI
Non-perturbative description, e.g., molecular dynamics
One-component plasma, pure Coulomb interaction (repulsive):
G > 172 g Coulomb crystal

5. Debye screening g Yukawa systems
Additional parameter: k = d/lD
Liquid phase: G > O (1)
Purely repulsive interaction
g no gas-liquid transition,
only supercritical fluid

6. 2. Complex Plasmas
Dusty or complex plasmas = multi component plasmas containing
ions, electrons, neutral gas, and microparticles, e.g., dust
Example: low temperature neon plasma in a dc- or rf discharge

7. Injection of microparticles with diameter
1 – 10 mm
High electron mobility g microparticles
collect electrons on surface g large
negative charge: Q = 103 – 105 e
Inter particle distance about 200 mm
g G >> 1 g plasma crystal (predicted 1986, discovered 1994 at MPE)
Observation: illumination by laser sheet and recorded by CCD camera

8. Melting of plasma crystal by
pressure reduction
less neutral gas friction
gtemperature increase
gdecrease of Coulomb
coupling parameter G = Q2/(dT)

9. Quantitive analysis of equation of state and determination of G:
pair correlation function
Crystal: long range order
sharp peaks at the nearest
neighbors, next to nearest
neighbors and so on
Liquid: short range order (incompressibility)
gonly one clear peak corresponding to inter particle distance plus one or
two broad and small peaks
Gas: no order gno clear peaks

10. Gravity has strong influence on microparticles gmicrogravity experiments

11. Applications of complex plasmas:
1. Model system for phase transitions, crystallization, dynamical behavior
of liquids and plasmas on the microscopic level
2. Astrophysics: comets, interstellar plasmas, star and planet formation,
planetary rings, …
3. Technology: plasma coating and etching, e.g. microchip production,
problem: dust contamination

12. 3. Applications to the Quark-Gluon Plasma
Estimate of interaction parameter
C = 4/3 (quarks), C = 3 (gluons)
T = 200 MeV g aS =
d = 0.5 fm
Ultrarelativistic plasma: magnetic interaction as important as electric
G = 1.5 – 6 g QGP Liquid?
RHIC data (hydrodynamical description
with small viscosity, fast thermalization)
indicate QGP Liquid
Attractive and repulsive interaction g
gas-liquid transition at a temperature
of a few hundred MeV

13. Static structure function (Fourier transform of pair correlation function)
g experimental and theoretical analysis of liquids
Hard Thermal Loop approximation (T >> Tc):
interacting gas
QCD lattice simulations g QGP liquid?

14. Strongly coupled plasmas g cross section enhancement
Reason: Coulomb radius, rC = Q2/E, larger than Debye screening length
lD = 1/mD g modification of Coulomb scattering theory
g enhancement of ion-microparticle interaction (ion drag force)
QGP: rC /lD = 1 – 5 g parton cross section enhancement by factor 2 – 9
small mean free path l (corresponding to small viscostity h ~ l) and fast
thermalization.
Additional cross section enhancement by non-linear and non-perturbative
effects
Implication: enhancement of collisional
energy loss,
suppression of radiative energy loss by
LPM effect (formation time)
g jet quenching

15. Conclusions Strongly coupled plasmas are of increasing importance in
fundamental research as well as technology
QGP and complex plasmas are important examples of strongly
coupled plasmas
QGP is the most challenging strongly coupled plasma
Complex plasmas can easily be studied and used as a model
for the QGP (phase transitions, correlation functions, cross sections, …)
RHIC and ISS provide very important information on strongly coupled
plasmas