1. Relativistic and Strongly-Coupled Plasmas - Extreme Matter in Plasma-, Astro-, and Nuclear Physics Markus H. Thoma Max-Planck-Institut für extraterrestrische Physik 1.Introduction 2. Electron-Positron Plasma 3. Weakly-Coupled Quark-Gluon Plasma 4.Strongly-Coupled Plasma 5.Complex Plasma 6.Strongly-Coupled Quark-Gluon Plasma

2. 1.Introduction 1. Introduction Plasma = (partly) ionized gas (4. state of matter) 99% of the visible matter in universe Plasmas emit light What is a plasma?

3. Plasmas can be produced by high temperatures electric fields radiation Relativistic plasmas: (Supernovae) Quantum plasmas: (White Dwarfs) Strongly coupled plasmas: (Quark-Gluon Plasma)  : Coulomb coupling parameter = Coulomb energy / thermal energy

4. Lightening Aurora Flames Tubes Comets “Neon” Discharges Quantum Plasmas Relativistic Plasmas Sun Fusion Corona W. dwarfs Temperature Pressure 1 10 3 10 6 10 -3 10 -6 10 3 10 6 10 0 Kelvin Supernova bar Strongly coupled Plasmas ComplexPlasmas

5. What is an electron-positron plasma? Strong electric or magnetic fields, high temperatures  massive pair production (E > 2m e c 2 = 1.022 MeV)  electron-positron plasma Examples: Supernovae: T max = 3 x 10 11 K  kT = 30 MeV >> 2m e c 2 Magnetars: Neutron Stars with strong magnetic fields B > 10 14 G Accretion disks around Black Holes High-intensity lasers (I > 10 18 W/cm 2 )  target electrons heated up to multi-MeV temperatures Example: Thin gold foil (~1  m) hit by two laser pulses from opposite sides Habs et al. 2. Electron-Positron Plasma

6. Equation of state Notation:  = c = k =1 Assumptions: ultrarelativistic gas: T >> m e thermal and chemical equilibrium electron density = positron density ideal gas (no interactions) infinite extension, isotropic system Electron and positron distribution function: Photon distribution function: Ultrarelativistic particles: E = p Particle number density:

7. Example: T = 10 MeV  Photon density: Photons in equilibrium with electrons and positrons Energy density: Stefan-Boltzmann law T = 10 MeV: Photons contribute 36% to energy density

8. Interactions between electrons and positrons  collective phenomena, e.g. Debye screening, plasma waves Non-relativistic plasmas (ion-electron): classical transport theory with scales: T, m e  Debye screening length  Plasma frequency Ultrarelativistic plasmas: scales T (hard momenta), eT (soft momenta) Relativistic interactions between electrons  QED

9. Perturbation theory: Expansion in  = e 2 /4  =1/137 (e = 0.3) using Feynman diagrams, e.g. electron-electron scattering Evaluation of diagrams by Feynman rules  scattering cross sections, damping and production rates, life times etc. Interactions within plasma: QED at finite temperature Extension of Feynman rules to finite temperature (imaginary or real time formalism)

10. Polarization tensor: Relation to dielectric tensor (high-temperature approximation): Effective photon mass: Alternative derivation using transport theory (Vlasov + Maxwell equations)

11. Maxwell equations   propagation of collective plasma modes  dispersion relations Plasma frequency Debye screening length  pl Plasmon

12. Relativistic plasmas  Fermionic plasma modes: dispersion relation of electrons and positrons in plasma Electron self-energy:  electron dispersion relation  Plasmino branch

13. Examples for further quantities which can be calculated using perturbative QED at finite temperature (HTL resummed perturbation theory): Electron and photon damping rate Electron transport rate Electron and photon mean free path Electron and photon collision time Electron and photon viscosity Electron energy loss M.H. Thoma, arXiv:0801.0956, to be published in Rev. Mod. Phys.

14. Applications to laser induced electron-positron plasmas T= 10 MeV  equilibrium electron-positron number density Prediction: 2 laser pulses of 330 fs and intensity of 7 x 10 21 W/cm 2 on thin foil B. Shen, J. Meyer-ter-Vehn, Phys. Rev. E 65 (2001) 016405  exp <  eq  non-equilibrium plasma Assumption: thermal equilibrium but no chemical equilibrium  electron distribution function f F =  n F with fugacity 

15. Non-equilibrium QED: M.E. Carrington, H. Defu, M.H. Thoma, Eur. Phys. C7 (1999) 347 Debye screening length: Collective effects important if extension of plasma L >> D Electron density > positron density  finite chemical potential 

16. Temperature high enough  new particles are produced Example: Muon production via Muon production exponentially suppressed at low temperatures T < m  = 106 MeV Very high temperatures (T > 100 MeV): Hadronproduction (pions etc.) and Quark-Gluon Plasma

17. Deconfinement transition similar to Mott transition (insulator/conductor): Electron concentration low  weak screening of ion potential  electrons bound in atoms  insulator (nucleus) Electron concentration high  strong screening of ion potential  free electrons  conductor (QGP = color conductor) Example: metallic hydrogen in Jupiter 3. Weakly-Coupled Quark-Gluon Plasma (QGP)

18. Critical baryon density: Critical temperature: Heavy-ion (nucleus-nucleus) collisions: RHIC: Au+Au at 200 GeV/N  hot, dense, expanding fireball  quark-gluon plasma for 10 -22 s?

24. Space-time evolution of the fireball Maximum volume (U-U): 3000 fm 3 Quark and gluon number: ~ 10000 Pre-equilibrium time: ~1 fm/c = 3 x 10 -24 s Life time of QGP: ~ 5 – 10 fm/c  good chances for an equilibrated QGP in relativistic heavy-ion collisions Problem: QGP cannot be observed directly  discovery of QGP by comparison of theoretical predictions for signatures with experimental data (circumstantial evidence)

25. Theoretical description of QGP: 1. Perturbative QCD (finite temperature): Valid only for small coupling, i.e. at high temperatures (T>>T c ) Polarization tensor, quark self-energy, dispersion relations, damping and production rates, transport coefficients, energy loss, … Apart from color factors similar calculations and results as in the case of an electron-positron plasma 2. Lattice QCD: non-perturbative method Valid also for large coupling Only static quantities (critical temperature, order of phase transition, equation of state, …), no signatures 3. Classical methods from electromagnetic plasmas: Transport theory, strongly coupled plasmas (molecular dynamics etc.)

26. Example: Strong quenching of hadron spectra at high momenta (jet quenching)  large energy loss of quarks in QGP

27. Collisional energy loss of a quark with energy E in a QGP RHIC data (quenching of hadron spectra)  radiative energy loss (gluon bremsstrahlung) not sufficient  collisional energy loss important Mustafa, Thoma, Acta Phys. Hung. A 22 (2005) 93 Thoma, Gyulassy, Nucl. Phys. B 351 (1990) 491, Braaten, Thoma, Phys. Rev. D 44 (1991) 2625

28. Quark Matter and Neutron Stars 1. possibility: central density of neutron star > critical  baryon density  hybrid star Quark matter?

29. 2. possibility: strange quark stars Speculation: strange quark matter containing up, down, and strange quarks more stable than atomic nuclei (Fe) Witten (1984) Stöcker Self-bound star made of strange quark matter

30. Quark matter: Fermi gas (free quarks) High-density approximation to quark self-energy (T=0,  large)  effective quark mass Quasiparticle approximation

31. Quark stars have small radii Reason: quark matter has a larger compressibility than neutron matter Strange QS Hybrid star Schertler, C. Greiner, Schaffner-Bielich, Thoma (2000) XMM Newton, Chandra: X-ray observation of RXJ1856  R > 16 km

32. Coulomb coupling parameter Q: charge of plasma particles d: inter particle distance T: plasma temperature Ideal plasmas:  most plasmas:    Strongly coupled plasmas:  Examples: ion component in white dwarfs, high-density plasmas at GSI, complex plasmas, quark-gluon plasma Ichimaru, Rev. Mod. Phys. 54 (1982) 1017 4. Strongly-Coupled Plasmas

33. One-component plasma (OCP), pure Coulomb-interaction (repulsive):  > 172  Coulomb crystal Debye screening  Yukawa system Numerical simulations of stongly coupled plasmas, e.g. molecular dynamics

34. Example: White Dwarf Ions (C,O) in degenerated electron background  OCP good approximation Density: 10 9 kg/m 3, T=10 6 -10 8 K   =5-500 Diamond core? Asteroseismological observations  approximately 90% of the mass of BPM 37093 has crystallized (5×10 29 kg).

35. Complex plasmas = multi component plasmas containing in addition to electrons, ions and neutral gas microparticles, e.g. dust Example: microparticles (1-10  m) in a low-temperature discharge plasma Dust particles get highly charged by electron collection: (higher mobility of electrons than ions)  strong Coulomb interaction between particles (  > 1) 5. Complex Plasma Fortov et al., Phys. Rep. 421 (2005) 1

36. RF- or DC-discharge in plasma chamber Noble gases at 300 K and 0.1 – 1.0 mbar Injection of monodisperse plastic spheres

37. Electrostatic field above the lower electrode or the glass wall levitates particles against gravity Illumination of microparticles with a laser sheet, recording of scattered light by a CCD camera

38. Excitation of plasma waves Direct observation of microparticle system on the microscopic and kinetic level in real time

39. Turbulence in particle flow How many particles are needed for collectivity? How do macroscopic quantities (e.g. viscosity) develop?

40. Nanofluidics:

41. Applications of complex plasmas: Microscopic model for structure formation, dynamical processes and self-organisation in strongly interacting many-body systems in plasma, solid state, fluid, and nuclear physics Technology: dust contamination in microchip production by plasma etching, dust in tokamaks, …

42. Astrophysics: comets, planetary rings, interstellar clouds, planet formation, noctilucent clouds, …

44. Complex plasmas may exist in gaseous, liquid or solid phase (new states of „soft matter“) Plasma crystal 1986: theoretical prediction of the crystallization of dust particles in laboratory plasmas 1994: discovery of the plasma crystal at MPE, in Taiwan and Japan Thomas et al., Phys. Rev. Lett. 73 (1994) 652 Strong interaction between microparticles:  Q 2, d ~ 100  m  1 <  < 10 5, 1 <  <5

45. Melting of the crystal by pressure reduction

46. Disturbing effects of gravity on complex plasmas: Electrostatic field for levitation of particles neccessary Restriction to plasma sheath (electric field for levitation strong enough)  quasi 3D crystals, complicated plasma conditions Gravity comparable to force between particles  structure and dynamics of complex plasmas changed, weak forces (attraction, ion drag) are covered Some experiments (in particular with larger particles) impossible Plasma experiments under microgravity

47. Microgravity  particles in field free bulk plasma LaboratoryMicrogravity

48. 2000 1996 1998 2002 2004 2006 2008 1994 Parabolic flights Texus PK-4 ISS PKE-Nefedov PK-3 Plus PlasmaLab BEC MPE experiments under microgravity

49. Parabolic Flights (PK-4)

50. ISS

51. PKE-Nefedov Experiments on the space station from 2001 to 2005 (supported by DLR) First scientific experiment on board the ISS Collaboration with Institute for High Energy Densities (IHED, Moscow)

52. Agglomeration  starting phase of planet formation?

53. Estimate of interaction parameter C = 4/3 (quarks), C = 3 (gluons)  200  MeV   S = 0.3 - 0.5 d = 0.5 fm Ultrarelativistic plasma: magnetic interaction as important as electric   1.5 – 6  QGP Liquid? Thoma, J. Phys. G 31 (2005) L7 and 539 6. Strongly-coupled Quark-Gluon Plasma RHIC data (hydrodynamical description with small viscosity, fast thermalization) indicate QGP Liquid Attractive and repulsive interaction  gas-liquid transition at a temperature of a few hundred MeV Thoma, Nucl. Phys. A 774 (2006) 30

54. Example: Static structure function  experimental and theoretical analysis of liquids Hard Thermal Loop approximation (T >> T c ):  interacting gas QCD lattice simulations  QGP liquid? Thoma, Phys. Rev. D 72 (2005) 094030

55. Example: String theory prediction (AdS/CFT): Lower limit for ratio of viscosity to entropy density Strongly-coupled OCP: Minimum value at  = 12 M.H. Thoma and G.E. Morfill, Europhys. Lett. 82 (2008) 65001

56. Conclusions Laser produced electron-positron plasmas can be described by perturbative QED at finite temperature  PHELIX Perturbative QCD for the QGP  predictions of signatures, e.g. jet quenching, quark matter in neutron stars (no indication)  FAIR, LHC Strongly coupled plasmas  new phenomena, e.g. plasma crystal  PHELIX, FAIR Complex plasmas  model for strongly-interacting many-body systems, applications in technology and astrophysics, microgravity experiments  PHELIX, FAIR, LHC Properties of strongly coupled QGP (equation of state, transport phenomena, thermalization, etc. ) by comparison with strongly coupled electromagnetic plasmas  FAIR, LHC S. Mrowczynski, M.H. Thoma, Annu. Rev. Nucl. Part. Sci. 57 (2007) 61

57. Thank you very much for your attention!

58. 35. ESA parabolic flight campaign (Bordeaux, October 2003)

59. PKE-Nefedov on board of the ISS