1 / 25

Quantum Field Theoretic Description of Electron-Positron Plasmas

Quantum Field Theoretic Description of Electron-Positron Plasmas. Markus H. Thoma Max-Planck-Institute for Extraterrestrial Physics, Univ. Giessen, MAP, EMMI, Berner & Mattner Systemtechnik. Ultrastrong laser, supernovae g electron-positron plasma g prediction of properties necessary

bteresa
Download Presentation

Quantum Field Theoretic Description of Electron-Positron Plasmas

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Quantum Field Theoretic Description of Electron-Positron Plasmas Markus H. Thoma Max-Planck-Institute for Extraterrestrial Physics, Univ. Giessen, MAP, EMMI, Berner & Mattner Systemtechnik • Ultrastrong laser, supernovae • g electron-positron plasma • g prediction of properties necessary • g quantum field theoretic methods developed mainly for quark-gluon plasma • 1. Introduction • 2. Field Theoretic Description of Electron-Positron Plasmas • Summary M.H. Thoma, arXiv:0801.0956, Rev. Mod. Phys. 81 (2009) 959

  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: (WDM, Dusty Plasmas, QGP) GC: 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. What is an electron-positron plasma? • Strong electric or magnetic fields, high temperatures • massive pair production (E > 2mec2 = 1.022 MeV) • electron-positron plasma • Astrophysical examples: • Supernovae: Tmax = 3 x 1011 K g kT = 30 MeV >> 2mec2 • Magnetars: Neutron Stars with strong magnetic fields B > 1014 G • Accretion disks around Black Holes

  6. High-intensity lasers (I > 1024 W/cm2) • ELI: The Extreme Light Infrastructure European Project • Recent developments in laser technology • ultrashort pulses (10-18 s), ultrahigh intensities (> 1023 W/cm2) • g observation of ultra-fast processes (molecules), particle acceleration, • ultradense matter, electron-positron plasma

  7. Possibilities for electron-positron • plasma formation: • Thin gold foil (~1 mm) hit by two • laser pulses from opposite sides • (B. Shen, J. Meyer-ter-Vehn, • Phys. Rev. E 65 (2001) 016405) • g target electrons heated up to multi- • MeV temperatures g e- - e+ plasma • Colliding laser pulses g pair creation at about 1/100 of critical field • strength, i.e. 1014 V/cm corresponding to 5 x 1025 W/cm2 (ELI, XFEL) • g electromagnetic cascade, depletion of laser energy • (A.M. Fedotov et al., PRL 105 (2010) 080402) • Laser-electron beam interaction (ELI-NP: two 10 PW lasers plus • 600 MeV electron beam) (D. Habs, private communication) Habs et al.

  8. 2. Field Theoretic description of Electron-Positron Plasmas • Here: Properties of a thermalized electron-positron plasma, not production • and equlibration • Equation of state • Assumptions: • ultrarelativistic gas: T >> me (h= c = k =1) • thermal and chemical equilibrium • electron density = positron density g zero chemical potential • ideal gas (no interactions) • infinitely extended, homogeneous and isotropic Electron and positron distribution function: Photon distribution function: Ultrarelativistic particles: E = p Particle number density:

  9. Example: T = 10 MeVg Conversion: Photon density: Photons in equilibrium with electrons and positrons g electron-positron-photon gas Energy density: Stefan-Boltzmann law T = 10 MeV: Photons contribute 36% to energy density

  10. Volume of neutron star (10 km diameter) gE ~ 1041 J corresponding • to about 10% of entire Supernova energy (without neutrinos) • Volume 1 mm3g E = 3.8 x 1011 J = 0.1 kto TNT • Energy of a laser pulse about 100 J at I > 1024 W/cm2 ! • Is the ideal gas approximation reliable? • Coulomb coupling parameter: GC = e2/(dT) • Interparticle distance: d ~ (reqe)-1/3 = 2.7 x 10-14 m at T = 10 MeV • GC = 5.3 x 10-3 • weakly coupled QED plasma • equation of state of an ideal gas is a good approximation; interactions can be treated by perturbation theory Quark-gluon plasma: GC = 1 – 5 gquark-gluon plasma liquid?

  11. Collective phenomena • Interactions between electrons and positrons g collective phenomena, • e.g. Debye screening, plasma waves, transport properties, e.g. viscosity • 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) Collective phenomena: soft momenta Transport properties: hard momenta

  12. Relativistic interactions between electrons gQED 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), calculations more complicated than at T=0 Application: quark-gluon plasma (thermal QCD)

  13. Example: Photon self-energy or polarization tensor (K=(w,k)) Isotropic medium g 2 independent components depending on frequency w and momentum k=|k| High-temperature or hard thermal loop limit (T >> w, k ~ eT): Effective photon mass:

  14. Dielectric tensor: Momentum space: Isotropic medium: Relation to polarization tensor: Alternative derivation using transport theory (Vlasov + Maxwell equations) Same result for quark-gluon plasma (apart from color factors)

  15. Maxwell equations g • propagation of collective plasma modes • dispersion relations Plasma frequency: Yukawa potential: with Debye screening length Plasmon Landau damping wpl

  16. Relativistic plasmas gFermionic plasma modes: • dispersion relation of electrons and positrons in plasma • Electron self-energy: • electron dispersion relation (pole of effective electron propagator containing electron self-energy) • Plasmino branch • Note: minimum in plasmino dispersion • van Hove singularity • unique opportunity to detect fermionic modes in laser produced plasmas

  17. Transport properties • Transport properties of particles with hard (thermal) momenta (p ~ T)using perturbative QED at finite temperature • p ~ T • For example electron-electron scattering • g electron damping (interaction) rate, • electon energy loss, shear viscosity k • Problem: IR divergence • HTL perturbation theory (Braaten, Pisarski, Nucl. Phys. B337 (1990) 569) Resummed photon propagator for soft photon momenta, i.e. k ~ eT g IR improved (Debye screening), gauge independent results complete to leading order

  18. Electron damping rates and energy loss • Transport coefficients of e--e+ plasma, e.g. shear viscosity • Photon damping • Mean free path 1/gph = 0.3 nm for T=10 MeV for a thermal photon

  19. Photon Production • Thermal distribution of electrons and positrons, expansion of plasma • droplet (hydrodynamical model) • g Gamma ray flash from plasma droplet shows continuous spectrum • (not only 511 keV line) • M.G. Mustafa, B. Kämpfer, • Phys. Rev. A 79 (2009) 020103

  20. EoS Collective Transport

  21. Chemical non-equilibrium • T= 10 MeVg equilibrium electron-positron number density • Experiment: colliding laser pulses g electromagn. cascade, laser depletion • max. electron-positron number about 1013 in a volume of about 0.1 mm3 (diffractive limit of laser focus) at I = 2.7 x 1026 W/cm2 (A.M. Fedotov et al., PRL 105 (2010) 080402) • rexp< reqg non-equilibrium plasma • Assumption: thermal equilibrium but no chemical equilibrium • electron distribution function fF = l nFwith fugacity l < 1 2

  22. Non-equilibrium QED: M.E. Carrington, H. Defu, M.H. Thoma, Eur. Phys. C7 (1999) 347 Electron plasma frequency in sun (center): Debye screening length: Collective effects important since extension of plasma L ~ 1 mm >> lD Electron density > positron density g finite chemical potential m

  23. Particle production • Temperature high enough g new particles are produced • Example: Muon production via • Equilibrium production rate: • Invariant photon mass: • Muon production exponentially suppressed at low temperatures • T < mm= 106 MeV • Very high temperatures (T > 100 MeV): • Hadronproduction (pions etc.) and Quark-Gluon Plasma • I. Kuznetsova, D. Habs, J. Rafelski, Phys. Rev. D 78 (2008) 014027

  24. 3. Summary • Aim: prediction of properties of ultrarelativistic electron-positron • plasmas produced in laser fields and supernovae • Ultrarelativistic electron-positron plasma: weakly coupled system • g ideal gas equation of state (in contrast to QGP) • Interactions in plasma g perturbative QED at finite temperature • g collective phenomena (plasma waves, Debye screening) and • transport properties (damping rates, mean free paths, relaxation times, • production rates, viscosity, energy loss) using HTL resummation • New phenomenon: Fermionic collective plasma modes (plasmino), • van Hove singularities? • Deviation from chemical equilibrium g perturbative QED in • non-equilibrium

More Related