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Glasma instabilities

Glasma instabilities. Kazunori Itakura KEK, Japan In collaboration with Hirotsugu Fujii (Tokyo) and Aiichi Iwazaki (Nishogakusha). Goa, September 4 th , 2008. Dona Paula Beach Goa, photo from http://www.goa-holidays-advisor.com/. Contents. Introduction: Early thermalization problem

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Glasma instabilities

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  1. Glasma instabilities Kazunori Itakura KEK, Japan In collaboration with Hirotsugu Fujii (Tokyo) and Aiichi Iwazaki (Nishogakusha) Goa, September 4th, 2008 Dona Paula Beach Goa, photo from http://www.goa-holidays-advisor.com/

  2. Contents • Introduction: Early thermalization problem • Stable dynamics of the Glasma Boost-invariant color flux tubes • Unstable dynamics of the Glasma Instability a la Nielsen-Olesen Instability induced by enhanced fluctuation (w/o expansion) • Summary

  3. Introduction (1/3) High-Energy Heavy-ion Collision 5. Individual hadrons freeze out 4. Hadron gas cooling with expansion 3. Quark Gluon Plasma (QGP) thermalization, expansion 2. Non-equilibrium state (Glasma) collision 1. High energy nuclei (CGC) Big unsolved question in heavy-ion physics Q: How is thermal equilibrium (QGP) is achieved after the collision? What is the dominant mechanism for thermalization?

  4. Introduction (2/3) “Early thermalization problem” in HIC Hydrodynamical simulation of the RHIC data suggests QGP may be formed within a VERY short time t ~ 0.6 fm/c. Hardest problem! 1. Non-equilibrium physics by definition 2. Difficult to know the information before the formation of QGP 3. Cannot be explained within perturbative scattering process  Need a new mechanism for rapid equilibration Possible candidate: “Plasma instability” scenario Interaction btw hard particles (pt ~ Qs) having anisotropic distribution and soft field (pt << Qs) induces instability of the soft field  isotropization Weibel instability Arnold, Moore, and Yaffe, PRD72 (05) 054003

  5. Introduction (3/3) Problems of “Plasma instability” scenario 1. Only “isotropization” (of energy momentum tensor) is achieved. The true thermalization (probably, due to collision terms) is far away.  Faster scenario ? Another instability ?? 2. Kinetic description valid only after particles are formed out of fields: * At first : * Later : Formation time of a particle with Qs is t ~ 1/Qs  Have to wait until t ~ 1/Qs for the kinetic description available (For Qs < 1 GeV, 1/Qs > 0.2 fm/c) POSSIBLE SOLUTION : INSTABILITIES OF STRONG GAUGE FIELDS (before kinetic description available)  “GLASMA INSTABILITY” Qs only strong gauge fields (given by the CGC) pt soft fields Am particles f(x,p)

  6. Glasma Glasma (/Glahs-maa/): 2006~ Noun: non-equilibrium matter between Color Glass Condensate (CGC) and Quark Gluon Plasma (QGP). Created in heavy-ion collisions. solve Yang Mills eq. [Dm , Fmn]=0 in expanding geometry with the CGC initial condition CGC Randomly distributed

  7. Stable dynamics of the Glasma

  8. Boost-invariant Glasma High energy limit  infinitely thin nuclei  CGC (initial condition) is purely “transverse”.  (Ideal) Glasma has no rapidity dependence “Boost-invariant Glasma” At t = 0+(just after collision) Only Ez and Bz are nonzero (ET and BT are zero) [Fries, Kapusta, Li, McLerran, Lappi] Time evolution (t >0) Ez and Bz decay rapidly ET and BT increase [McLerran, Lappi]  new!

  9. 1/Qs random Typical configuration of a single event just after the collision Boost-invariant Glasma H.Fujii, KI, NPA809 (2008) 88 Just after the collision: only Ez and Bz are nonzero (Initial CGC is transversely random)  Glasma = electric and magnetic flux tubes extending in the longitudinal direction

  10. Bz2, Ez2 = BT2, ET2= ~1/t Single flux tube contribution averaged over transverse space (finite due to Qs = IR regulator) Boost-invariant Glasma An isolated flux tube with a Gaussian profile oriented to a certain color direction Qst=0 Qst =0 0.5 1.0 1.5 2.0 Qst=2.0

  11. Boost-invariant Glasma A single expanding flux tube at fixed time 1/Qs

  12. Glasma instabilities

  13. P.Romatschke & R. Venugopalan, 2006 Small rapidity dependent fluctuation can grow exponentially and generate longitudinal pressure . 3+1D numerical simulation PL ~ Very much similar to Weibel Instability in expanding plasma [Romatschke, Rebhan] Isotropization mechanism starts at very early time Qs t < 1 longitudinal pressure g2mt ~ Qst Unstable Glasma: Numerical results Boost invariant Glasma (without rapidity dependence) cannot thermalize  Need to violate the boost invariance !!!

  14. Unstable Glasma: Numerical results nmax(t) : Largest n participating instability increases linearly in t n : conjugate to rapidity h ~ Qst

  15. Unstable Glasma: Analytic results H.Fujii, KI, NPA809 (2008) 88 Investigate the effects of fluctuation on a single flux tube Rapidity dependent fluctuation Background field = boost invariant Glasma  constant magnetic/electric field in a flux tube * Linearize the equations of motion wrt fluctuations  magnetic / electric flux tubes * For simplicity, consider SU(2)

  16. 1/Qs Unstable Glasma: Analytic results H.Fujii, KI, NPA809 (2008) 88 Magnetic background Yang-Mills equation linearized with respect to fluctuations DOES have unstable solution for ‘charged’ matter Nielesen-Olesen ’78 Chang-Weiss ’79 • : conjugate to rapidity h Sign of w2 determines the late time behavior Lowest Landau level ( n=0, w2 = -gB < 0for minus sign) In(z) : modified Bessel function Growth time ~ 1/(gB)1/2 ~1/Qs instability grows rapidly Transverse size ~ 1/(gB)1/2 ~1/ Qs for gB~ Qs2

  17. Unstable Glasma: Analytic results • : conjugate to rapidity h n=8, 12 Modified Bessel function controls the instability f ~ Stable oscillation Unstable oscillate grow The time for instability to become manifest Modes with small n grow fast ! For large n

  18. E 1/Qs Unstable Glasma: Analytic results Electric background No amplification of the fluctuation = Schwinger mechanism infinite acceleration of the charged fluctuation always positive or zero No mass gap for massless gluons  pair creation always possible

  19. x (current) z (force) y (magnetic field) Nielsen-Olesen vs Weibel instabilities Weibel instability • Two step process • Motion of hard particles in the soft field additively generates soft gauge fields • Impossible for homogeneous field • Independent of statistics of charged particles Nielsen-Olesen instability * One step process * Lowest Landau level in a strong magnetic field becomes unstable due to anomalous magnetic moment w2 = 2(n+1/2)gB– 2gB < 0 for n=0 * Only in non-Abelian gauge field vector field  spin 1 non-Abelian  coupling btw field and matter * Possible even for homogeneous field Bz

  20. Glasma instability without expansion with H.Fujii and A. Iwazaki (in preparation) * What is the characteristics of the N-O instability? * What is the consequence of the N-O instability? (Effects of backreaction)

  21. Glasma instability without expansion • Color SU(2) pure Yang-Mills • Background field( “boost invariant glasma”) Constant magnetic field in 3rd color direction and in z direction. only (inside a magnetic flux tube) • Fluctuations other color components of the gauge field: charged matter field Anomalous magnetic coupling induces mixing of fi mass term with a wrong sign

  22. Glasma instability without expansion Linearized with respect to fluctuations for m = 0 Lowest Landau level (n = 0) of f(-) becomes unstable finite at pz= 0 g Growth rate Qs For inhomogeneous magnetic field, gB g <B> pz Qs For gB ~ Qs2

  23. Glasma instability without expansion Consequence of Nielsen-Olesen instability?? • Instability stabilized due to nonlinear term (double well potential for f ) • Screen the original magnetic field Bz • Large current in the z direction induced • Induced current Jz generates (rotating) magnetic field Bq Jz Jz ~ igf*Dzf ~ g2(B/g)(Qs/g) Bq~ Qs2/g for one flux tube Bz

  24. Glasma instability without expansion z Bq Consider fluctuation around Bq q r Centrifugal force Anomalous magnetic term Approximate solution Negative for sufficiently large pz Unstable mode exists for large pz !

  25. Glasma instability without expansion Numerical solution of the lowest eigenvalue Growth rate  unstable  stable

  26. Glasma instability without expansion Growth rate of the glasma w/o expansion Nielsen-Olesen instability with a constant Bzis followed by Nielsen-Olesen instability with a constant Bq • pz dependence of growth rate has the information of the profile • of the background field • In the presence of both field (Bz and Bq) the largest pz for the primary • instability increases

  27. Glasma instability without expansion Numerical simulation Berges et al. PRD77 (2008) 034504 t-z version of Romatschke-Venugopalan, SU(2) Initial condition Instability exists!! Can be naturally understood Two different instabilities ! In the Nielsen-Olesen instability

  28. Summary CGC and glasma are important pictures for the understanding of heavy-ion collisions Initial Glasma = electric and magnetic flux tubes. Field strength decay fast and expand outwards. Rapidity dependent fluctuation is unstable in the magnetic background. A simple analytic calculation suggests that Glasma (Classical YM with stochastic initial condition) decays due to the Nielsen-Olesen (N-O) instability. Moreover, numerically found instability in the t-z coordinates can also be understood by N-O including the existence of the secondary instability.

  29. In Region (3), and att =0+, the gauge field is determined bya1anda2 CGC as the initial condition for H.I.C. HIC = Collision of two sheets [Kovner, Weigert, McLerran, et al.] r1 r2 Each source creates the gluon field for each nucleus. Initial condition a1 , a2 : gluon fields of nuclei

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