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Relativistic and Strongly-Coupled Plasmas - Extreme Matter in Plasma-, Astro-, and Nuclear Physics

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

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Relativistic and Strongly-Coupled Plasmas - Extreme Matter in Plasma-, Astro-, and Nuclear Physics

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

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

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

  4. Quantum Plasmas Supernova W. dwarfs 106 Sun 103 Flames Lightening Tubes Pressure “Neon” 1 Relativistic Plasmas Fusion 10-3 Discharges Aurora Corona 10-6 Comets 100 103 106 Kelvin Temperature bar Complex Plasmas Strongly coupled Plasmas

  5. 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 gkT = 30 MeV >> 2mec2 • Magnetars: Neutron Stars with strong magnetic fieldsB > 1014 G • Accretion disks around Black Holes • High-intensity lasers (I > 1018 W/cm2) • g 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.

  6. Equationofstate • 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: Photon distribution function: Ultrarelativistic particles: E = p Particle number density:

  7. Example: T = 10 MeV g 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 g 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 Ultrarelativistic plasmas: scales T (hard momenta), eT (soft momenta) Relativistic interactions between electrons gQED

  9. Perturbation theory: Expansion in a = e2/4p =1/137 (e = 0.3) using Feynman diagrams, e.g. electron-electron scattering Evaluation of diagrams by Feynman rules g 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 g • propagation of collective plasma modes • dispersion relations Plasma frequency Debye screening length Plasmon wpl

  12. Relativistic plasmas gFermionic 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 g equilibrium electron-positron number density • Prediction: • 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 • rexp< reqg non-equilibrium plasma • Assumption: thermal equilibrium but no chemical equilibrium • electron distribution function fF = l nFwith fugacity l < 1

  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 >> lD Electron density > positron density g finite chemical potential m

  16. Temperature high enough g 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

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

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

  19. 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 g good chances for an equilibrated QGP in relativistic heavy-ion collisions Problem: QGP cannot be observed directly g discovery of QGP by comparison of theoretical predictions for signatures with experimental data (circumstantial evidence)

  20. 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.)

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

  22. Collisional energy loss of a quark with energy E in a QGP 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 • g collisional energy loss important • Mustafa, Thoma, Acta Phys. Hung. • A 22 (2005) 93

  23. Quark Matter and Neutron Stars 1. possibility: central density of neutron star > critical baryon density ghybrid star Quark matter?

  24. 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

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

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

  27. 4. Strongly-Coupled Plasmas 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, complex plasmas, quark-gluon plasma Ichimaru, Rev. Mod. Phys. 54 (1982) 1017

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

  29. Example: White Dwarf • Ions (C,O) in degenerated electron background g OCP good • approximation • Density: 109 kg/m3 , T=106-108 K gG=5-500 • Diamond core? • Asteroseismological observations • approximately 90% of the mass of BPM 37093 has crystallized (5×1029 kg).

  30. 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: • (higher mobility of electrons than ions) • strong Coulomb interaction between particles (G > 1) Fortov et al., Phys. Rep. 421 (2005) 1

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

  32. 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

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

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

  35. Nanofluidics:

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

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

  38. Plasma crystal Strong interaction between microparticles: G ~ Q2, d ~ 100 mmg 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

  39. Melting of the crystal by pressure reduction

  40. 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) gquasi 3D crystals, complicated plasma conditions • Gravity comparable to force between particles • g structure and dynamics of complex plasmas changed, weak forces • (attraction, ion drag) are covered • Some experiments (in particular with larger particles) impossible

  41. Microgravityg particles in field free bulk plasma Laboratory Microgravity

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

  43. Parabolic Flights (PK-4)

  44. ISS

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