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Dusty Plasmas I
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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
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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
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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
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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
?
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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
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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
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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
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generallya phenomenonin crystals butnot liquids
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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
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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
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expect low viscosity in strongly coupled plasma S. Ichimaru, Univ. of Tokyo
in (colored) quark gluon plasma
Gelman, Shuryak, Zahed, nucl-th/0601029
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Dusty Plasmas – part II
how are dusty plasmas prepared in the lab methods to study dusty plasma results, especially on viscosity
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backup slides
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density and opacity
via
transmission measurement
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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
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can we look at shock propagation through our plasma?
could be….
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important question about
radiation, energy loss and
transport:
radiation vs. collisions
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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
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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?
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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
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can we measure the diffusion coefficient?
PHENIX preliminaryAu+Au
Moore & TeaneyPRC71, 064904, ‘05
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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
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theoretical view of radiation vs. collisions(and charm vs. bottom)
Wicks, et al. nucl-th/0512076
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now,
how about the viscosity?
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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
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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
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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
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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?
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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
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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)
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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