plasmas 101. outline l what is a plasma? some characteristic features of plasmas l why should we...
TRANSCRIPT
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
propertiestools for studywhy should we (QGP folks) care?
what is a plasma?
4th state of matter (after solid, liquid and gas) a plasma is:
ionized gas which is macroscopically neutralexhibits collective effects
interactions among charges of multiple particlesspreads charge out into characteristic (Debye) length, D
multiple particles inside this lengththey screen each other
plasma size > D
“normal” plasmas are electromagnetic (e + ions)quark-gluon plasma interacts via strong interaction
color forces rather than EMexchanged particles: g instead of
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
+ +…
At high temperature and density: force is screened by produced color-charges expect transition to gas of “free” quarks and gluons
asymptotic freedom
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 D
D = 0kT
-------
nee2
Debye sphere = sphere with radius D
number electrons inside Debye sphere is largeND= N/VD= VD VD= 4/3 D
3
1/2 ne = number densitye = charge
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 forcesboth charge-charge and charge-neutral interactions
charge-neutral dominates in weakly ionized plasmasneutrals interact via distortion of e cloud by charges
magnetic fields generated by moving charges give rise to magnetic interactions
Plasma Coulomb coupling parameter
ratio of mean potential energy to mean kinetic energy
a = interparticle distancee = chargeT = temperature
typically a small number in a normal, fully shielded plasma when > 1 have a strongly coupled, or non-Debye plasma
many-body spatial correlations existbehave like liquids, or even crystals when > 150 D a
interlude
why should we care about all this?
Energy density of matter
high energy density: > 1011 J/m3
P > 1 MbarI > 3 X 1015W/cm2 Fields > 500 Tesla
QGP energy density > 1 GeV/fm3
i.e. > 1030 J/cm3
Debye screening in QCD: a tricky concept
in leading order QCD (O. Philipsen, hep-ph/0010327)
vv
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 D for strongly coupled plasma & convert inside to particle density
screening and thermal masses
Screening mass, mD, defines inverse length scaleInside this distance, an equilibrated plasma is sensitive to
insertion of a static sourceOutside it’s not.
Thermal mass is ~ gTmagnetic mass is ~ g2T
T dependence of electric &magnetic screening massesQuenched lattice studyof gluon propagator figure shows: mD,m= 3Tc, mD,e= 6Tc at 2Tc D ~ 0.4 & 0.2 fm
magnetic screening mass significantnot very gauge-dependent, but DOESgrow w/ lattice size (long range is important)
Nakamura, Saito & Sakai, hep-lat/0311024
let’s get a “feel” by oversimplifying
estimate = <PE>/<KE> using QCD coupling strength g
<PE>=g2/d d ~1/(41/3T)
<KE> ~ 3T ~ g2 (41/3T) / 3Tg2 ~ 4-6 (value runs with T)
for T=200 MeV plasma parameter
use =0.2 fm and =15 GeV/fm3 get 0.5 GeV inside Debye sphere
FEW particles!
quark gluon plasma should be a strongly coupled plasmaAs in warm, dense plasma at lower (but still high) Tdusty 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
OK,
now back to our scheduled program
plasma frequency and oscillations
instantaneous disturbance of a plasma → collective motionsplasma wants to restore the original charge neutralityelectrons oscillate collectively around the (heavy) ionscharacterized by natural oscillation frequency
plasma frequencyit’s typically high
restoring force: ion-electron coulomb attraction
damping happens via collisionsif e-ion collision frequency < electron plasma frequency pe/2 then oscillations are only slightly dampeda plasma condition: electron collision time large vs. oscillation
nee2
p = ------me0
1/2
Plasma instabilities
a mode with growing amplitudetransfer energy from the plasma particles to wave field
e.g. Weibel instability causes beam filamentation
particle velocity
phase velocity of electric field wave
from S. Mrowczynski, QM05
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, temperature3rd moment → heat flux tensor
Transport (e.g. diffusion, viscosity)hydrodynamic expansion velocity, shock propagation
radiationbremsstrahlung, blackbody, collisional and recombination
Screening Plasma oscillations, instabilities Wave propagation
and
now for
some interesting kinds of plasmas
Inertial Confinement Fusion
Warm Dense Matterfrom Dick Lee, LLNL
what kinds of experiments can be done?LCLS = Linac Coherent Light Source (SLAC)
Method using 3 lasers: 1) create shock, 2) x-rays, and 3) probe sample
Sapphire window
Beryllium foil
Metal pusher
Copper
D2
Shock
Radiograph x-rays
X-ray µscope
and streak
camera
Iron foil
1) Shock generating laser
3) Probe laser2) x-ray generating laser
R. Lee, S. Libby, LLNL; RBRC workshop
x-ray transmission→ Shock and interface trajectories
Slope of shock front yields Us
Slope of pusher interface gives Up
.
Al
D2
time (ns)
shock front
Al pusher
dista
nce (µ
m)
0.0 5.01.0 2.0 3.0 4.0 6.0 7.0 8.0
0
100
200
300
x
L
Lx
=o
=
Us
Us-U
p
streak camera record
R. Lee, S. Libby, LLNL
P-P0=0UsUp
an interesting aside
laser-driven plasmas have some parallels to our casesystem 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 plasmahard x-rays compared to hard scattered partonsstudy transmission, scattering, correlations
aim to measure bulk properties, e.g.equation of stateresponse to shocks
Dusty plasmas
Astrophysical phenomenahow do neutron stars, giant planet cores, gamma ray
bursters, dusty plasmas, jets work?
laboratory dusty plasmasliquid and crystalline propertiesviscosity and wakeswave modes
What’s a dusty plasma?
A plasma with admixture of dust particulatessize up to 1 micron
large and heavy compared to ions & electronsdust gets charged up
either positive or negativeby collisions with ions or sticking of electrons
many examples in naturespace (comets, planetary rings, earth’s atmosphere)in the lab (in discharges, plasma processing reactors)from dirt in fusion devicesprepared in the lab on purpose
why should we care about dusty plasmas?
They are strongly coupledi.e. = <PE>/<KE> > 1number of particles inside sphere of Debye radius 1form liquids and even crystals when > 150
The dust particles are heavy and charged diffuse through the plasmasort of like heavy quarks in QGP
Plasma physicists can image the dustopportunity to “see” phenomena also of interest for
QGP
preparing a dusty plasma in the lab
1) create a weakly ionized Ar glow discharge (rf power to one electrode)2) ring shape of electrodes makes a ring of plasma3) dump in some dust 7 micron melamine here4) illuminate with laser5) look for 90° scattering off of the dust
highly charged dust → strong coupling → crystalline structure
Goree, et al.
how do the plasma physicists measure ?
mostly they don’t dusty plasmas (suspension of highly charged -scale
particles in plasma) give a chance to trystrongly coupled – liquid or even crystallinecan image the dust particlesmake 2D and now 3D in the lab
techniques to get at viscosity:look at flow past an object that creates a shearapply shear stress using ion drag forcesapply shear stress using radiation pressure from laser *use Thomson scattering of photons of electron charges **
where mass < particle masscoherent scattering off electrons → correlations
generallya phenomenonin crystals butnot liquids
now, zapwith 2counter-propagatinglaserbeams toinduce ashear stress(but stillplanar)
use this technique to measure viscosity
melt crystal with laser lightinduce a shear flow (laminar)image the dust to get velocitystudy: spatial profiles vx(y) moments, fluctuations → T(x,y) curvature of velocity profile → drag forces viscous transport of drag in direction from lasercompare to viscous hydro. extract shear viscosity/mass densityPE vs. KE competition governs coupling & phase of matterCsernai,Kapusta,McLerran nucl-th/0604032
calculate using molecular dynamics
B. Liu and J. Goree, cond-mat/0502009
minimum arises because kinetic part of decreases with & potential part increases
MD: solve theequations of motionfor massive particlessubject to (screened)interaction potential
follow evolution ofparticle distributionfunction (&correlations)
solve coupled diff.eq’sover nearby space
density-densitycorrelations →
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 conductivityis transport of color charge an analogous question for us?
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>/ 3nD collision time
determines relaxation time for the system
particle concentration
l = mean free path
note: = 1/3 <v> l so D = nice implication: measure D get ! from T, or maybe transmission
can we measure the diffusion coefficient?
PHENIX preliminaryAu+Au
Moore & TeaneyPRC71, 064904, ‘05
collisional energy loss also implies flow
from Derek Teaney
D ~ 3/(2T) strongly interacting!
larger D would mean less charm e loss fewer collisions with plasma, smaller v2
competition: radiation vs. collisions
Wicks, et al. nucl-th/0512076
bottom line: need to reduce the error barsseparate c from b!
backup slides
expect low viscosity in strongly coupled plasma S. Ichimaru, Univ. of Tokyo
in (classical) quark gluon plasma
Gelman, Shuryak, Zahed, nucl-th/0601029
from Csernai, Kapusta, McLerrannucl-th/0604032
A little more on coupling
potential V s/r <KE> T r=interparticle distanceQCD matter: /r3 3 and so we see that r 1/T
= <PE>/<KE> (s/r)/T sT/T s
T cancels, but does affect s
D = {T/(4e2}1/2 so D {T/(sT3}1/2 1/(Ts1/2)
s
We know 1/ #particles inside Debye volume ND
ND= N/VD= VD VD= 4/3 D3
1/(s3/2T3)
so ND= 1/s3/2 T cancels again
for s large, ND is small (D fairly small, but included in ND)
for s small, ND is large (D largish)
putting in some numbers
both and ND depend on s
at RHIC dNg/dy ~ 800
so = 800/(1 fm * R2 fm2) = 800/100 = 8 /fm3
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
consider leptons in matter
electrons vs. muons electrons radiate and stop very quickly
the radiation is bremsstrahlung muons have large range because they DON’T radiate!
radiation is suppressed by the large massdominant 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
now,
how about the viscosity?
relation of viscosity to diffusivity?
D = 1/3 <v> l and = 1/3 <v> l
so D = nice implication: measure D get !
from T, or maybe transmission
how do the plasma physicists measure ?
mostly they don’t but for strongly coupled plasmas they are starting to dusty plasmas (suspension of highly charged -scale
particles in plasma)strongly coupled – liquid or even crystallinecan image the dust particlesmake 2D and now 3D in the lab
techniques to get at viscosity:look at flow past an object that creates a shearapply shear stress using ion drag forcesapply shear stress using radiation pressure from laser *use Thomson scattering of photons of electron charges **
where mass < particle masscoherent scattering off electrons → correlations
they find
broad minimum in kinematic viscosity for 70 < d < 700
low Reynolds number for shear flowR=<v>L/( = 0.7-17
L is characteristic length of fluid
can describe flow by Navier-Stokes equation
Nosenko & Goree, PRL 93(2004) 155004
why is correlation among particles interesting?
S(p) = 1/N <(p)(-p)>
(p) is Fourier transformedparticle density (r)
plasma physicists hope to measure by Thomson scattering(at small angle)
is there an analogous measure for us?
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
?