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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 1. Introduction What is a plasma? Plasma = (partly) ionized gas (4. state of matter) 99% of the visible matter in universe Plasmas emit light Plasmas can be produced by high temperatures electric fields kT mc 2 Relativistic plasmas: Quantum plasmas: B Strongly coupled plasmas: h d m v th Q2 G 1 d kT radiation (Supernovae) (White Dwarfs) (Quark-Gluon Plasma) G: Coulomb coupling parameter = Coulomb energy / thermal energy W. dwarfs Supernova Quantum Plasmas bar 106 Pressure 103 Relativistic Plasmas Complex Plasmas Sun Strongly coupled Plasmas Flames 1 Lightening “Neon” Tubes Fusion 10-3 Discharges 10-6 Aurora Corona Comets 100 103 Temperature 106 Kelvin 2. Electron-Positron Plasma What is an electron-positron plasma? Strong electric or magnetic fields, high temperatures massive pair production (E > 2mec2 = 1.022 MeV) electron-positron plasma Examples: • Supernovae: Tmax = 3 x 1011 K kT = 30 MeV >> 2mec2 • Magnetars: Neutron Stars with strong magnetic fields B > 1014 G • Accretion disks around Black Holes • High-intensity lasers (I > 1018 W/cm2) target electrons heated up to multi-MeV temperatures Example: Thin gold foil (~1 mm) hit by two laser pulses from opposite sides Habs et al. Equation of state Notation: h = c = k =1 Assumptions: • ultrarelativistic gas: T >> me • thermal and chemical equilibrium • electron density = positron density • ideal gas (no interactions) • infinite extension, isotropic system Electron and positron distribution function: nF Photon distribution function: nB 1 eE / T 1 1 eE / T 1 Ultrarelativistic particles: E = p Particle number density: eq e d3p 3 gF n ( p) 0 . 37 T , gF 4 F 3 ( 2 ) Example: T = 10 MeV 34 3 eq 4 . 9 10 cm e Photon density: Photons in equilibrium with electrons and positrons eq d3p 3 gB n ( p) 0 . 24 T , gB 2 B 3 ( 2 ) Energy density: Stefan-Boltzmann law eq d3p d3p 4 gF p n ( p) g p n ( p) 1 . 81 T F B B ( 2 )3 ( 2 )3 T = 10 MeV: eq 3.8 1023 J cm 3 Photons contribute 36% to energy density Interactions between electrons and positrons collective phenomena, e.g. Debye screening, plasma waves Non-relativistic plasmas (ion-electron): classical transport theory with scales: T, me Debye screening length Plasma frequency kT D 4 e2 e 4 e2 e pl me Ultrarelativistic plasmas: scales T (hard momenta), eT (soft momenta) Relativistic interactions between electrons QED Perturbation theory: Expansion in a = e2/4 =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) Polarization tensor: Relation to dielectric tensor (high-temperature approximation): 3m L ( ,k ) L ( ,k ) 1 1 2 2 k k k 1 2k ln k 3m T ( ,k ) T ( ,k ) 1 1 2 2k 2 k2 k ln 1 1 2 2 k k Effective photon mass: m eT 3 T 10 MeV m 1MeV 2 2 Alternative derivation using transport theory (Vlasov + Maxwell equations) k2 Maxwell equations L ( ,k ) 0, T ( ,k ) 2 propagation of collective plasma modes dispersion relations Plasma frequency pl L,T ( k 0 ) m Plasmon 1.5 1021 Hz (T 10 MeV ) Debye screening length pl 1 D 3m 1.1 1013 m (T 10 MeV ) Relativistic plasmas Fermionic plasma modes: dispersion relation of electrons and positrons in plasma Electron self-energy: electron dispersion relation Plasmino branch 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. Applications to laser induced electron-positron plasmas T= 10 MeV equilibrium electron-positron number density eq 5 1034 cm3 Prediction: exp 5 1022 cm3 2 laser pulses of 330 fs and intensity of 7 x 1021 W/cm2 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 fF = nF with fugacity < 1 exp d3p 12 gF n ( p) 10 F eq ( 2 )3 Non-equilibrium QED: 2 4 e m2 2 dp pfF ( p) 3 0 M.E. Carrington, H. Defu, M.H. Thoma, Eur. Phys. C7 (1999) 347 m meq 1eV pl 1.5 1015 Hz Debye screening length: D 0.1mm Collective effects important if extension of plasma L >> D Electron density > positron density finite chemical potential m Temperature high enough new particles are produced Example: Muon production via Muon production exponentially suppressed at low temperatures T < mm= 106 MeV Very high temperatures (T > 100 MeV): Hadronproduction (pions etc.) and Quark-Gluon Plasma 3. Weakly-Coupled Quark-Gluon Plasma (QGP) 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 Critical baryon density: c 10 0 0 0.125 GeV / fm3 2.2 1017 kg / m3 Critical temperature: Tc 150 200 MeV (1.8 2.4) 1012 K Heavy-ion (nucleus-nucleus) collisions: RHIC: Au+Au at 200 GeV/N hot, dense, expanding fireball quark-gluon plasma for 10-22 s? Space-time evolution of the fireball Maximum volume (U-U): 3000 fm3 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) Theoretical description of QGP: 1. Perturbative QCD (finite temperature): Valid only for small coupling, i.e. at high temperatures (T>>Tc) 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.) Example: Strong quenching of hadron spectra at high momenta (jet quenching) large energy loss of quarks in QGP Collisional energy loss of a quark with energy E in a QGP dE 4 dx 3 Nf 2 2 E 1 a s T ln 6 a sT Thoma, Gyulassy, Nucl. Phys. B 351 (1990) 491, Braaten, Thoma, Phys. Rev. D 44 (1991) 2625 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 Quark Matter and Neutron Stars 1. possibility: central density of neutron star > critical baryon density hybrid star Quark matter? 2. possibility: strange quark stars Speculation: strange quark matter containing up, down, and strange quarks more stable than atomic nuclei (Fe) Witten (1984) Self-bound star made of strange quark matter Stöcker Quark matter: Fermi gas (free quarks) High-density approximation to quark self-energy (T=0, m large) effective quark mass m*f mf 2 m 2f 2 g 2 m 2f 6 2 Quasiparticle approximation 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 4. Strongly-Coupled Plasmas Coulomb coupling parameter Q2 G d kT Q: charge of plasma particles d: inter particle distance T: plasma temperature Ideal plasmas: G << 1 (most plasmas: G < 103) Strongly coupled plasmas: G > O (1) Examples: ion component in white dwarfs, high-density plasmas at GSI, complex plasmas, quark-gluon plasma Ichimaru, Rev. Mod. Phys. 54 (1982) 1017 Numerical simulations of stongly coupled plasmas, e.g. molecular dynamics One-component plasma (OCP), pure Coulomb-interaction (repulsive): G > 172 Coulomb crystal Debye screening Yukawa system Q r / D V(r) e r Example: White Dwarf Ions (C,O) in degenerated electron background OCP good approximation Density: 109 kg/m3 , T=106-108 K G=5-500 Diamond core? Asteroseismological observations approximately 90% of the mass of BPM 37093 has crystallized (5×1029 kg). 5. Complex Plasma Complex plasmas = multi component plasmas containing in addition to electrons, ions and neutral gas microparticles, e.g. dust Example: microparticles (1-10 mm) in a low-temperature discharge plasma Dust particles get highly charged by electron collection: Q 103...105 e (higher mobility of electrons than ions) strong Coulomb interaction between particles (G > 1) Fortov et al., Phys. Rep. 421 (2005) 1 RF- or DC-discharge in plasma chamber Noble gases at 300 K and 0.1 – 1.0 mbar Injection of monodisperse plastic spheres 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 Excitation of plasma waves Direct observation of microparticle system on the microscopic and kinetic level in real time Turbulence in particle flow How many particles are needed for collectivity? How do macroscopic quantities (e.g. viscosity) develop? Nanofluidics: 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, … Astrophysics: comets, planetary rings, interstellar clouds, planet formation, noctilucent clouds, … Plasma crystal Strong interaction between microparticles: G ~ Q2, d ~ 100 mm 1 < G < 105, 1 < k <5 Complex plasmas may exist in gaseous, liquid or solid phase (new states of „soft matter“) 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 Melting of the crystal by pressure reduction Plasma experiments under microgravity 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 Microgravity particles in field free bulk plasma Laboratory Microgravity MPE experiments under microgravity PK-3 Plus PlasmaLab BEC PK-4 2008 ISS PKE-Nefedov 2006 2004 2002 Texus 2000 1998 1994 1996 Parabolic flights Parabolic Flights (PK-4) ISS 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) Agglomeration starting phase of planet formation? 6. Strongly-coupled Quark-Gluon Plasma Estimate of interaction parameter Ca S G2 dT Thoma, J. Phys. G 31 (2005) L7 and 539 C = 4/3 (quarks), C = 3 (gluons) T 200 MeV aS = 0.3 - 0.5 d = 0.5 fm Ultrarelativistic plasma: magnetic interaction as important as electric G 1.5 – 6 QGP Liquid? 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 Example: Static structure function experimental and theoretical analysis of liquids Hard Thermal Loop approximation (T >> Tc): S ( p) 2N f T 3 n p2 , m D 1 / D 2 2 p mD interacting gas QCD lattice simulations Thoma, Phys. Rev. D 72 (2005) 094030 QGP liquid? Example: String theory prediction (AdS/CFT): Lower limit for ratio of viscosity to entropy density 6.08 10 13 Ks s 4k B Strongly-coupled OCP: Minimum value at G = 12 4.89 s 4kB M.H. Thoma and G.E. Morfill, Europhys. Lett. 82 (2008) 65001 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 Thank you very much for your attention! 35. ESA parabolic flight campaign (Bordeaux, October 2003) PKE-Nefedov on board of the ISS