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Dusty Plasmas I
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
Energy density of matter
high energy density:
e > 1011 J/m3
P > 1 Mbar
I > 3 X 1015W/cm2
Fields > 500 Tesla
QGP energy density
e > 1 GeV/fm3
i.e. > 1030 J/cm3
Plasma properties & diagnostics
 moments of the distribution function of particles f(x,v)
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
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
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
Plasma diagnostics
 magnetic measurements: T, p, E, B
 plasma particle flux probes: f, n, T, E
 refraction & transmission of EM waves: n
 g 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
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
Astrophysical dusty plasmas
 Astrophysical phenomena
how do neutron stars, giant planet cores, gamma ray
bursters, dusty plasmas, jets work?
 Fundamental physics questions
properties of the matter, interactions with energy under
extreme conditions
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
generally
a phenomenon
in crystals but
not 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 lD
lD = e0kT 1/2
------nee2
Debye sphere = sphere with radius
number electrons inside Debye sphere is typically large
ND= N/VD= rVD VD= 4/3 p lD3
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
expect low viscosity in strongly coupled plasma
Gelman, Shuryak,
Zahed,
nucl-th/0601029
S. Ichimaru,
Univ.
of Tokyo
in (colored) quark gluon plasma
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
Al
Al pusher
D2
L
0
x
200
shock front
distance (µm)
100
300
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
time (ns)
Us
r
L
ro = x = U -U
s
p
 Slope of shock front yields Us
 Slope of pusher interface gives Up
streak camera record
R. Lee, S. Libby, LLNL
P-P0=r0UsUp
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 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
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?
what’s diffusion, anyway?
 diffusion = brownian motion of particles
definition: flux density of particles J = -D grad n
particle concentration
 integrating over forward hemisphere:
D = diffusivity = 1/3 <v> l
l = mean free path
so D = <v>/ 3ns
D  collision time
determines relaxation time for the system
can we measure the diffusion coefficient?
PHENIX preliminary
Au+Au
Moore & Teaney
PRC71, 064904, ‘05
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
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 h = 1/3 r <v> l
so D = h/r
nice implication: measure D get h!
r from T, or maybe transmission
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
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
why is correlation among particles interesting?
S(p) = 1/N <r(p)r(-p)>
r(p) is Fourier transformed
particle density r(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 G = <PE>/<KE>
using QCD coupling strength g
<PE>=g2/d d ~1/(41/3T)
<KE> ~ 3T
G > 1: strongly coupled, few
G ~ g2 (41/3T) / 3T
particles inside Debye radius
g2 ~ 4-6 (value runs with T)
for T=200 MeV plasma parameter G ~ 3
see M. Thoma, J.Phys. G31(2005)L7
 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!
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 p lD3  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)
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