1. Dusty Plasmas I

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

3. Energy density of matter high energy density:  > 10 11 J/m 3 P > 1 Mbar I > 3 X 10 15 W/cm 2 Fields > 500 Tesla QGP energy density  > 1 GeV/fm 3 i.e. > 10 30 J/cm 3

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

5.  magnetic measurements: T, p, E, B  plasma particle flux probes: f, n, T, E  refraction & transmission of EM waves: n   emission from free electrons: f, n, T cyclotron, bremsstrahlung, Cherenkov  line radiation from atoms: n, T  scattering of EM waves: f, n, T, B, particle correlations Plasma diagnostics ?

6. What’s a dusty plasma? l 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 l 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

7. Astrophysical dusty plasmas l Astrophysical phenomena how do neutron stars, giant planet cores, gamma ray bursters, dusty plasmas, jets work? l Fundamental physics questions properties of the matter, interactions with energy under extreme conditions

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

9. generally a phenomenon in crystals but not liquids

10. plasma basics – Debye Length l 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 D D =  0 kT ------- n e e 2 l Debye sphere = sphere with radius l number electrons inside Debye sphere is typically large N D = N/V D =  V D V D = 4/3  D 3 1/2

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

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

13. Dusty Plasmas – part II l how are dusty plasmas prepared in the lab l methods to study dusty plasma l results, especially on viscosity

14. l backup slides

15. density and opacity via transmission measurement

16. x-ray transmission → Shock and interface trajectories l Slope of shock front yields U s l Slope of pusher interface gives U p streak camera record R. Lee, S. Libby, LLNL P-P 0 =  0 U s U p

17. can we look at shock propagation through our plasma? could be….

18. important question about radiation, energy loss and transport: radiation vs. collisions

19. consider leptons in matter l electrons vs. muons electrons radiate  and stop very quickly the radiation is bremsstrahlung l muons have large range because they DON’T radiate! radiation is suppressed by the large mass dominant energy loss mechanism is via collisions l 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

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

21. what’s diffusion, anyway? l diffusion = brownian motion of particles definition: flux density of particles J = -D grad n l integrating over forward hemisphere: D = diffusivity = 1/3 l so D = / 3n  D  collision time determines relaxation time for the system particle concentration l = mean free path

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

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

24. theoretical view of radiation vs. collisions (and charm vs. bottom) Wicks, et al. nucl-th/0512076

25. now, how about the viscosity?

26. relation of viscosity to diffusivity? D = 1/3 l and  = 1/3  l so D =  nice implication: measure D get  !  from T, or maybe transmission

27. how do the plasma physicists measure  ? l mostly they don’t l but for strongly coupled plasmas they are starting to dusty plasmas (suspension of highly charged  -scale particles in plasma) strongly coupled – liquid or even crystalline can image the dust particles make 2D and now 3D in the lab l 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  mass < particle mass coherent scattering off electrons → correlations

28. they find broad minimum in kinematic viscosity  for 70 <   d < 700 l low Reynolds number for shear flow R= L/(  = 0.7-17 L is characteristic length of fluid l can describe flow by Navier-Stokes equation Nosenko & Goree, PRL 93(2004) 155004

29. why is correlation among particles interesting? S(p) = 1/N  (p) is Fourier transformed particle density  (r) plasma physicists hope to measure by Thomson scattering (at small angle) is there an analogous measure for us?

30. ideal gas or strongly coupled plasma? estimate  = / using QCD coupling strength g =g 2 /d d ~1/(4 1/3 T) ~ 3T  ~ g 2 (4 1/3 T) / 3T g 2 ~ 4-6 (value runs with T) for T=200 MeV plasma parameter   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!  > 1: strongly coupled, few particles inside Debye radius see M. Thoma, J.Phys. G31(2005)L7

31. A little more on coupling potential V   s /r  T r=interparticle distance QCD matter:    /r 3    3 and so we see that r  1/T  = /  (  s /r)/T   s T/T   s T cancels, but does affect  s D = {T/(4   e 2  } 1/2 so D  {T/(  s T 3  } 1/2  1/(T  s 1/2 )  s We know 1/   #particles inside Debye volume N D N D = N/V D =  V D V D = 4/3  D 3  1/(  s 3/2 T 3 ) so N D =  1/  s 3/2 T cancels again for  s large, N D is small ( D fairly small, but included in N D ) for  s small, N D is large ( D largish)

32. putting in some numbers both  and N D depend on  s l at RHIC dN g /dy ~ 800 so  = 800/(1 fm *  R 2 fm 2 ) = 800/100 = 8 /fm 3 r = 0.5 from lattice at T~200 MeV  s = 0.5-1 for quarks for gluons multiply by 3/(4/3) = 9/4. It’s big! from pQCD  s = 0.3 for quarks and ~0.7 for gluons