Plasmas 101

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

?