Dusty Plasmas I

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

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

Plasma properties & diagnostics

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

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

?

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

Astrophysical dusty plasmas

Astrophysical phenomenahow do neutron stars, giant planet cores, gamma ray

bursters, dusty plasmas, jets work?

Fundamental physics questionsproperties of the matter, interactions with energy under

extreme conditions

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

generallya phenomenonin crystals butnot liquids

plasma basics – Debye Length

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 number electrons inside Debye sphere is typically large

ND= N/VD= VD VD= 4/3 D3

1/2

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

expect low viscosity in strongly coupled plasma S. Ichimaru, Univ. of Tokyo

in (colored) quark gluon plasma

Gelman, Shuryak, Zahed, nucl-th/0601029

Dusty Plasmas – part II

how are dusty plasmas prepared in the lab methods to study dusty plasma results, especially on viscosity

backup slides

density and opacity

via

transmission measurement

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

can we look at shock propagation through our plasma?

could be….

important question about

radiation, energy loss and

transport:

radiation vs. collisions

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

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

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

theoretical view of radiation vs. collisions(and charm vs. bottom)

Wicks, et al. nucl-th/0512076

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?

ideal gas or strongly coupled plasma?

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

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

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