Plasmas 101

1. Plasmas 101 Barbara Jacak PHENIX Focus May 16, 2006

2. outline • What is a plasma? • some characteristic features of plasmas • Why should we care? • Several interesting kinds of plasmas • experiments done to study them • Strong coupling in plasmas • properties • tools for study • why should we (QGP folks) care?

3. what is a plasma? • 4th state of matter (after solid, liquid and gas) • a plasma is: • ionized gas which is macroscopically neutral • exhibits collective effects • interactions among charges of multiple particles • spreads charge out into characteristic (Debye) length, lD • multiple particles inside this length • they screen each other • plasma size > lD • “normal” plasmas are electromagnetic (e + ions) • quark-gluon plasma interacts via strong interaction • color forces rather than EM • exchanged particles: g instead of g

4. asymptotic freedom At high temperature and density: force is screened by produced color-charges expect transition to gas of “free” quarks and gluons + +… QCD as compared to QED gluons carry color charge  gluons interact among themselves • theory is non-abelian trickier than QED at large distance: confinement of quarks in hadrons

5. plasma basics – Debye screening • distance over which the influence of an individual charged particle is felt by the other particles in the plasma • charged particles arrange themselves so as to effectively shield any electrostatic fields within a distance of order lD • lD = e0kT • ------- • nee2 • Debye sphere = sphere with radius lD • number electrons inside Debye sphere is large • ND= N/VD= rVD VD= 4/3 plD3 1/2 ne = number density e = charge

6. collective effects a basic feature distinguishing plasmas from ordinary matter • simultaneous interaction of each charged particle with a considerable number of others • due to long range of electromagnetic forces • both charge-charge and charge-neutral interactions • charge-neutral dominates in weakly ionized plasmas • neutrals interact via distortion of e cloud by charges • magnetic fields generated by moving charges give rise to magnetic interactions

7. Plasma Coulomb coupling parameter G • ratio of mean potential energy to mean kinetic energy • a = interparticle distance • e = charge • T = temperature • typically a small number in a normal, fully shielded plasma • when G > 1 have a strongly coupled, or non-Debye plasma • many-body spatial correlations exist • behave like liquids, or even crystals when G > 150 • lD  a

8. interlude why should we care about all this?

9. QGP energy density • > 1 GeV/fm3 i.e. > 1030 J/cm3 Energy density of matter high energy density: e > 1011 J/m3 P > 1 Mbar I > 3 X 1015W/cm2 Fields > 500 Tesla

10. Debye screening in QCD: a tricky concept • in leading order QCD (O. Philipsen, hep-ph/0010327) • vv

11. give up on the concept? Of course not!!! • Two options proposed by Philipsen: • 1) assume a pole in the propagator and attempt to measure its value from the exponential fall-off in some fixed gauge (done with lattice QCD) • 2) seek a manifestly gauge invariant definition • Lattice says: “interactions weak @ l =1/T, but screening function is not exponential until 1/2T” • a different idea: calculate lD for strongly coupled plasma & convert e inside to particle density

12. screening and thermal masses Screening mass, mD, defines inverse length scale Inside this distance, an equilibrated plasma is sensitive to insertion of a static source Outside it’s not. Thermal mass is ~ gT magnetic mass is ~ g2T Nakamura, Saito & Sakai, hep-lat/0311024 T dependence of electric & magnetic screening masses Quenched lattice study of gluon propagator figure shows: mD,m= 3Tc, mD,e= 6Tc at 2Tc lD ~ 0.4 & 0.2 fm magnetic screening mass significant not very gauge-dependent, but DOES grow w/ lattice size (long range is important)

13. let’s get a “feel” by oversimplifying • estimate G = <PE>/<KE> • using QCD coupling strength g • <PE>=g2/d d ~1/(41/3T) • <KE> ~ 3T • G ~ g2 (41/3T)/ 3T • g2 ~ 4-6 (value runs with T) for T=200 MeV plasma parameter G ~ 3 use l=0.2 fm and e=15 GeV/fm3 get 0.5 GeV inside Debye sphere FEW particles!  quark gluon plasma should be a strongly coupled plasma • As in warm, dense plasma at lower (but still high) T • dusty plasmas, cold atom systems • such EM plasmas are known to behave as liquids! G > 1: strongly coupled, few particles inside Debye radius see M. Thoma, J.Phys. G31(2005)L7

14. OK, now back to our scheduled program

15. nee2 wp =------ mee0 1/2 plasma frequency and oscillations • instantaneous disturbance of a plasma → collective motions • plasma wants to restore the original charge neutrality • electrons oscillate collectively around the (heavy) ions • characterized by natural oscillation frequency • plasma frequency • it’s typically high • restoring force: • ion-electron coulomb attraction • damping happens via collisions • if e-ion collision frequency < electron plasma frequency wpe/2p • then oscillations are only slightly damped • a plasma condition: electron collision time large vs. oscillation

16. particle velocity phase velocity of electric field wave Plasma instabilities • a mode with growing amplitude • transfer energy from the plasma particles to wave field • e.g. Weibel instability causes beam filamentation

17. from S. Mrowczynski, QM05

18. Plasma properties to be investigated • moments of the distribution function of particles f(x,v) • 0th moment → particle density (n) • 1st moment → <velocity> • 2nd moment → pressure tensor, temperature • 3rd moment → heat flux tensor • Transport (e.g. diffusion, viscosity) • hydrodynamic expansion velocity, shock propagation • radiation • bremsstrahlung, blackbody, collisional and recombination • Screening • Plasma oscillations, instabilities • Wave propagation

19. and now for some interesting kinds of plasmas

20. Inertial Confinement Fusion

21. Warm Dense Matter from Dick Lee, LLNL

22. what kinds of experiments can be done? LCLS = Linac Coherent Light Source (SLAC)

23. Method using 3 lasers: 1) create shock, 2) x-rays, and 3) probe sample 1) Shock generating laser 3) Probe laser 2) x-ray generating laser R. Lee, S. Libby, LLNL; RBRC workshop

24. x-ray transmission→ Shock and interface trajectories • Slope of shock front yields Us • Slope of pusher interface gives Up streak camera record R. Lee, S. Libby, LLNL P-P0=r0UsUp

25. an interesting aside • laser-driven plasmas have some parallels to our case • system expands and is short-lived • does it thermalize? does hydro work? • but those lucky plasma folks can time resolve…! • probe with particles with deBroglie wavelength short compared to thermal wavelength of plasma • hard x-rays compared to hard scattered partons • study transmission, scattering, correlations • aim to measure bulk properties, e.g. • equation of state • response to shocks

26. Dusty plasmas • Astrophysical phenomena • how do neutron stars, giant planet cores, gamma ray bursters, dusty plasmas, jets work? • laboratory dusty plasmas • liquid and crystalline properties • viscosity and wakes • wave modes

27. What’s a dusty plasma? • A plasma with admixture of dust particulates • size up to 1 micron • large and heavy compared to ions & electrons • dust gets charged up • either positive or negative • by collisions with ions or sticking of electrons • many examples in nature • space (comets, planetary rings, earth’s atmosphere) • in the lab (in discharges, plasma processing reactors) • from dirt in fusion devices • prepared in the lab on purpose

28. why should we care about dusty plasmas? • They are strongly coupled • i.e. G = <PE>/<KE> > 1 • number of particles inside sphere of Debye radius  1 • form liquids and even crystals when G > 150 • The dust particles are heavy and charged • diffuse through the plasma • sort of like heavy quarks in QGP • Plasma physicists can image the dust • opportunity to “see” phenomena also of interest for QGP

29. highly charged dust → strong coupling → crystalline structure preparing a dusty plasma in the lab Goree, et al. 1) create a weakly ionized Ar glow discharge (rf power to one electrode) 2) ring shape of electrodes makes a ring of plasma 3) dump in some dust 7 micron melamine here 4) illuminate with laser 5) look for 90° scattering off of the dust

30. how do the plasma physicists measure h? • mostly they don’t • dusty plasmas (suspension of highly charged m-scale particles in plasma) give a chance to try • strongly coupled – liquid or even crystalline • can image the dust particles • make 2D and now 3D in the lab • techniques to get at viscosity: • look at flow past an object that creates a shear • apply shear stress using ion drag forces • apply shear stress using radiation pressure from laser * • use Thomson scattering of photons of electron charges ** • where g mass < particle mass • coherent scattering off electrons → correlations

31. now, zap with 2 counter- propagating laser beams to induce a shear stress (but still planar) generally a phenomenon in crystals but not liquids

32. use this technique to measure viscosity melt crystal with laser light induce a shear flow (laminar) image the dust to get velocity study: spatial profiles vx(y) moments, fluctuations → T(x,y) curvature of velocity profile → drag forces viscous transport of drag in  direction from laser compare to viscous hydro. extract h/r shear viscosity/mass density PE vs. KE competition governs coupling & phase of matter Csernai,Kapusta,McLerran nucl-th/0604032

33. calculate G using molecular dynamics MD: solve the equations of motion for massive particles subject to (screened) interaction potential follow evolution of particle distribution function (&correlations) solve coupled diff.eq’s over nearby space density-density correlations →h B. Liu and J. Goree, cond-mat/0502009 minimum arises because kinetic part of h decreases with G & potential part increases

34. collisions → transport in the plasma • transport of particles → diffusion • transport of energy by particles → thermal conductivity • transport of momentum by particles → viscosity • transport of charge by particles → electrical conductivity • is transport of color charge an analogous question for us?

35. what’s diffusion, anyway? • diffusion = brownian motion of particles definition: flux density of particles J = -D grad n • integrating over forward hemisphere: D = diffusivity = 1/3 <v> l so D = <v>/ 3ns D  collision time determines relaxation time for the system particle concentration l = mean free path note: h = 1/3 r <v> l so D = h/r nice implication: measure D get h! r from T, or maybe transmission

37. PHENIX preliminary can we measure the diffusion coefficient? Au+Au Moore & Teaney PRC71, 064904, ‘05

38. collisional energy loss also implies flow from Derek Teaney D ~ 3/(2pT) strongly interacting! larger D would mean less charm e loss fewer collisions with plasma, smaller v2

39. competition: radiation vs. collisions Wicks, et al. nucl-th/0512076 bottom line: need to reduce the error bars separate c from b!

40. backup slides

41. Gelman, Shuryak, Zahed, nucl-th/0601029 in (classical) quark gluon plasma expect low viscosity in strongly coupled plasma S. Ichimaru, Univ. of Tokyo

42. from Csernai, Kapusta, McLerran nucl-th/0604032

43. A little more on coupling • potential V as/r <KE>  T r=interparticle distance • QCD matter:r1/r3 rT3 and so we see that r  1/T • G = <PE>/<KE>  (as/r)/T asT/T as T cancels, but does affect as • lD = {T/(4pe0e2r)}1/2 so lD {T/(asT3)}1/2  1/(Tas1/2) • as • We know 1/G #particles inside Debye volume ND • ND= N/VD= rVD VD= 4/3 plD3 1/(as3/2T3) • so ND=  1/as3/2 T cancels again • for as large, ND is small (lD fairly small, but included in ND) • for as small, ND is large (lD largish)

44. putting in some numbers • both G and ND depend on as • at RHIC dNg/dy ~ 800 • so r = 800/(1 fm * pR2 fm2) = 800/100 = 8 /fm3 • r = 0.5 • from lattice at T~200 MeV as= 0.5-1 for quarks • for gluons multiply by 3/(4/3) = 9/4. It’s big! • from pQCD as= 0.3 for quarks and ~0.7 for gluons

45. consider leptons in matter • electrons vs. muons • electrons radiate g and stop very quickly • the radiation is bremsstrahlung • muons have large range because they DON’T radiate! • radiation is suppressed by the large mass • dominant energy loss mechanism is via collisions • 2 questions for QGP: • should we expect collisional energy loss for heavy quarks? • is it reasonable to expect ONLY radiative energy loss for light quarks? EM plasmas suggest answer = no

47. now, how about the viscosity?

48. relation of viscosity to diffusivity? D = 1/3 <v> l and h = 1/3 r <v> l so D = h/r nice implication: measure D get h! r from T, or maybe transmission

49. how do the plasma physicists measure h? • mostly they don’t • but for strongly coupled plasmas they are starting to • dusty plasmas (suspension of highly charged m-scale particles in plasma) • strongly coupled – liquid or even crystalline • can image the dust particles • make 2D and now 3D in the lab • techniques to get at viscosity: • look at flow past an object that creates a shear • apply shear stress using ion drag forces • apply shear stress using radiation pressure from laser * • use Thomson scattering of photons of electron charges ** • where g mass < particle mass • coherent scattering off electrons → correlations

50. they find Nosenko & Goree, PRL 93(2004) 155004 • broad minimum in kinematic viscosity h/p • for 70 < G2d < 700 • low Reynolds number for shear flow • R=<v>L/(h/r) = 0.7-17 • L is characteristic length of fluid • can describe flow by Navier-Stokes equation