Dusty plasmas in basic science, astronomy, industry & fusion John Goree
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Transcript Dusty plasmas in basic science, astronomy, industry & fusion John Goree
Dusty plasmas in basic science,
astronomy, industry & fusion
John Goree
The Univ. of Iowa
The growth of dusty plasmas as a field of research
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Outline
1. What is dust?
2. Formation of dust
• Fusion
• Industry
• Astronomy
3. Dust charge
4. Forces acting on dust
5. Some physics experiments:
• Voids under microgravity conditions
• Strongly-coupled vs. Weakly-coupled
Plasmas
• Waves & Instabilities
• Shear flow
• Wakes
What is dust?
“Dust” = small particles of solid matter, 10 nm – 1 mm, usually dielectric
Astronomy: “dust”
M16 pillar
Credit: NASA, HST, J. Hester & P. Scowen (ASU)
Semiconductor industry
“particulates” or “particles”
G.S. Selwyn, Plasma Sources Sci. Tehcnol. 3, 340 (1994)
What is dust?
Safety Issues for fusion
Radiological
Dust:
• activated
• retains tritium
• ITER safety limit: 350 kg Tungsten dust
Fire & chemical explosion
Hydrogen:
• stored in dust
• released during accidental exposure to:
• air
• steam
• ITER safety limit: 6 kg dust allowed on hot surfaces
Phil Sharpe
Fusion Safety Program, Idaho National Laboratory
Dust in Fusion Plasmas Workshop
2005
Formation of dust
1. What is dust?
2. Formation of dust
• Fusion
• Industry
• Astronomy
3. Dust charge
4. Forces acting on dust
5. Some physics experiments:
• Voids under microgravity conditions
• Strongly-coupled vs. Weakly-coupled
Plasmas
• Waves & Instabilities
• Shear flow
• Wakes
Formation
What’s the source of dust in a plasma?
Produced on surfaces
• Flaking of deposited films
• Bubbles & blistering of
surfaces
Produced in the gas phase
• Nucleation
• Coagulation
Purchased from vendor
Formation: tokamaks
Fusion: various shapes of dust collected from the Tore Supra tokamak
Composition is mainly:
• carbon
• constituents of stainless steel
Phil Sharpe
Fusion Safety Program, Idaho National Laboratory
Dust in Fusion Plasmas Workshop
2005
Formation: tokamaks
Tungsten dust formation: flaking from He bubbles
2 mm
Divertor Plasma Simulator NAGDIS-II
Surface Temp.:
Flux:
Ion Energy:
Time:
2200 K
8.3×1022 m-2s-1
15 eV
104 s
N. Ohno, S. Takamura, Dai. Nishijima
“Formation and Transport of Dust
in the Divertor Plasma Simulators”
Dust in Fusion Plasmas Workshop
2005
Formation: tokamaks
Observation of High Z Dust in TRIAM-1M
by Fast Framing Camera, 4500 fps
Dust
High Z dust is
emitted from the
Mo poloidal limiter.
N. Ohno, S. Takamura, Dai. Nishijima
“Formation and Transport of Dust
in the Divertor Plasma Simulators”
Poloidal Limiter
Dust in Fusion Plasmas Workshop
2005
A lesson from the semiconductor industry
Particles were always there,
but you didn’t know it until you used the right diagnostics:
camera
imaging
in-situ
G.S. Selwyn, Plasma Sources Sci. Tehcnol. 3, 340 (1994)
electron
microscopy
ex-situ
Formation: gas phase
Gas-phase formation in
astrophysics:
• Vapor flowing outward
from a carbon star cools
& nucleates dust
• Dust grains then grow by
“coagulation”
M16 pillar, Credit: NASA, HST, J. Hester & P. Scowen (ASU)
Formation: gas phase
Gas-phase
formation
G. Praburam and J. Goree
Astrophys. J 1995
Formation: gas phase
Cauliflower particles grow in the gas phase:
intact
Gary Selwyn, IBM, 1989
fractured
Ganguly et al., J. Vac. Sci. Technol. 1993
Formation: gas phase
Particles grown
by sputtering tungsten
Coagulated particles
consisting of 3+ cauliflowers
300 nm
D. Samsonov and J. Goree
J. Vac. Sci. Technol. A 1999
Formation: gas phase
Particles grown
by sputtering graphite
D. Samsonov and J. Goree
J. Vac. Sci. Technol. A 1999
Formation: gas phase
Particles grown
by sputtering aluminum
D. Samsonov and J. Goree
J. Vac. Sci. Technol. A 1999
Formation: purchased from vendor
Polymer microspheres:
• melamine-formaldehyde
• diameter 8.09 0.18 mm
• used in basic science experiments
• introduced into plasma with a “salt shaker”
Outline
1. What is dust?
2. Formation of dust
• Fusion
• Industry
• Astronomy
3. Dust charge
4. Forces acting on dust
5. Some physics experiments:
• Voids under microgravity conditions
• Strongly-coupled vs. Weakly-coupled
Plasmas
• Waves & Instabilities
• Shear flow
• Wakes
Charging: mechanisms
Ielectron collection
+ Iion collection
+ Ielectron emission
Ielectron collection
+ Iion collection
H+
H+
e-
e-
_
eCharging by collecting
electrons and ions only
negative charge
Goree, Plasma Sources Sci. Technol. 1994
+
Electron emission
• secondary emission due to e- impact
• photoemission
• thermionic
positive charge
Charging: mechanisms
Particles immersed in a plasma collect currents:
Itotal = Ielectron collection + Iion collection + Ielectron emission
Each of these currents depends on the potential V of the particle
H+
Equilibrium:
e-
Itotal = 0 at the “floating potential” V:
a
Q = CV
esurface
potential V
Goree, Plasma Sources Sci. Technol. 1994
C = 4 p e0 a
is capacitance of sphere of radius a
Charging: mechanisms
Charging by collecting electrons & ions
only
Ielectron collection
+ Iion collection
Consider a particle that is suddenly exposed
to plasma:
H+
e-
• Initially it collects electrons more rapidly
than ions, due to higher vte
• Eventually it reaches equilibrium “floating
potential”:
Hydrogen, Ti = Te
V = -2.5 kTe
• Example:
Parameters:
Te= 1 eV
a = 1 mm
Charge: Q = - 1737 e
Goree, Plasma Sources Sci. Technol. 1994
_
Forces
1. What is dust?
2. Formation of dust
• Fusion
• Industry
• Astronomy
• Pure physics
3. Dust charge
4. Forces acting on dust
5. Some pure physics experiments:
• Strongly-coupled vs. Weakly-coupled
Plasmas
• Waves & Instabilities
• Shear flow
• Wakes
Forces
Forces acting on a particle
Coulomb
QE
a
provides levitation
Lorentz
Q v B
a
tiny except in astronomy
Ion drag
a2
big for high-density plasmas
Radiation pressure
a2
if a laser beam hits particle
Gas drag
a2
requires gas
Thermophoretic force
a2
requires gas
Gravity
a3
tiny unless a > 0.1 mm
Ion drag force
Momentum is imparted to the dust particle
_
Orbit force:
Ion orbit is deflected
_
Collection force:
Ion strikes particle
Ion drag force
Dust (laser light
scattering from a
horizontal laser
sheet)
Void is due to
ion drag
Glow
Plasma:
• RF parallel-plate
• glow discharge
• argon gas
D. Samsonov and J. Goree
Instabilities in a Dusty Plasma with Ion Drag and Ionization
Physical Review E Vol. 59, 1047-1058, 1999
Dust:
• nm size
• carbon
• grown by sputtering
graphite target
Ion drag force
Dust (laser light
scattering from a
horizontal laser
sheet)
Void is due to
ion drag
Glow
Plasma:
• RF parallel-plate
• glow discharge
• argon gas
D. Samsonov and J. Goree
Instabilities in a Dusty Plasma with Ion Drag and Ionization
Physical Review E Vol. 59, 1047-1058, 1999
Dust:
• nm size
• carbon
• grown by sputtering
graphite target
Ion drag force
How ion drag produces a void:
dust
void
Ionization source
Positive plasma potl
Outward ion flow
J. Goree, G. E. Morfill, V. N. Tsytovich and S. V. Vladimirov,
Theory of Dust Voids in Plasmas,
Physical Review E Vol. 59, 7055-7067, 1999
Ion drag force
Ion drag force
• Orbit force (this is the
usual drag force for
Coulomb collisions,
except that lnL is
problematic)
• Collection force (ions
actually strike the
particle)
ion drag force, normalized
Two contributions:
V
V2
10
Depends on ion velocity ui
Force ni
J. Goree, G. E. Morfill, V. N. Tsytovich and S. V. Vladimirov,
Theory of Dust Voids in Plasmas,
Physical Review E Vol. 59, 7055-7067, 1999
E. C. Whipple, Rep. Prog. Phys. 44, 1198 (1981)
Collection force
from OML model
Orbit force
from Rosenbluth potential
V-2
1
0.01
0.1
1
10
100
ion velocity / ion thermal velocity
Te / Ti = 60, mi = 40 amu, lD = 130 mm
Ion drag is normalized by 4 p ni a2 Te / (Ti/Te)0.5
Ion drag force
Ion drag force
• Te = Ti, deuterium mass
ion drag force, normalized
• Fusion edge plasma
parameters:
1000
100
10
1
0.1
0.01
0.1
1
10
ion velocity / ion thermal velocity
Te / Ti = 1, mi = 2 amu, lD = 13 mm
Ion drag is normalized by 4 p ni a2 Te / (Ti/Te)0.5
Data computed March 2005 using the same code as in
J. Goree, G. E. Morfill, V. N. Tsytovich and S. V. Vladimirov,
Theory of Dust Voids in Plasmas,
Physical Review E Vol. 59, 7055-7067, 1999
Gas drag force
Gas drag
Stokes-flow regime
molecular-flow regime
Epstein:
•
•
•
•
•
Ngas
mgas
cgas
V
d
F d
4p
N gasmgasc gasa 2V
3
gas atom:
number density
mass
mean thermal speed
velocity of particle with respect to the gas
dimensionless, ranges from 1.0 to 1.442
P. Epstein, Phys. Rev. 23, 710 (1924).
M. J. Baines, I. P. Williams, and A. S. Asebiomo, Mon. Not. R. Astron. Soc. 130,
63 (1965).
Radiation pressure force
Radiation pressure
F
q
transparent
2microsphere
laser
pa I
momentum
laserimparted
to microsphere
Fradiation
incident
laser
c
pa 2 I laser
c
B. Liu, V. Nosenko, J. Goree and L. Boufendi, Phys. Plasmas (2003).
Physics experiments
1. What is dust?
2. Formation of dust
• Fusion
• Industry
• Astronomy
• Pure physics
3. Dust charge
4. Forces acting on dust
5. Some physics experiments:
• Microgravity conditions
• Strongly-coupled vs. Weakly-coupled
Plasmas
• Waves & Instabilities
• Shear flow
• Wakes
Physics experiments
Remainder of this talk:
All experiments performed with polymer
microspheres
Microgravity conditions
electrode
electrode
positive
Equipotential
Contours (RF glow
discharge)
Without gravity,
particles fill
3-D volume
potential
QE
mg
electrode
electrode
With gravity,
particles
sediment to highfield region
2-D layer
Microgravity conditions
To obtain a 3D dust suspension, use zero g conditions:
Parabolic flights, NASA KC-135
Microgravity conditions
Parabolic flights, NASA KC-135
Microgravity conditions
Parabolic flights, NASA KC-135
video
Strongly-coupled vs. weakly-coupled plasmas
Coulomb coupling parameter:
G
interparti cle potential energy
particle kinetic energy
G>1
G << 1
Q 2 / 4pe0 r
k BT
plasma is like a solid or a liquid
plasma is like a gas
“strongly coupled”
dusty plasma:
Q big
star interior:
r small
pure-ion plasma: T small
Physics experiments
Next:
Waves in a weakly-coupled dusty plasma
Dust acoustic wave experiment: Kiel Univ.
camera
plasma column
probes
dust tray
anodic plasma
particles
anode
3 cm
RF-discharge
Parameter:
gas: Argon
p = 1.0 .. 2.5 Pa
ni = 1015 m-3
B = 20 .. 80 mT
Anode:
UA = 50 .. 100 V
IA = 3 .. 12 mA
dust:
MF-spheres
d = 1 µm
nd = 0.5 .. 3 x 1011 m-3
Courtesy Alexander Piel, Kiel University, Germany, 2005
Dusty Plasma Research, A. Piel, 2005
41
Dust acoustic wave experiment: Kiel Univ.
15 mm
Time lapse 1:10
p = 2.5 Pa
IA = 10 mA
B = 20 mT
Courtesy Alexander Piel, Kiel University, Germany, 2005
Dusty Plasma Research, A. Piel, 2005
42
Physics experiments
Next:
Shear flow in a strongly-coupled dusty plasma (plasma crystal).
Shear flow in a 2D dusty plasma
VCR
video camera
(top view)
scanning
mirrors
microspheres
lower electrode
scanning
mirrors
y
x
mod ulator
modulator 1
RF
Ar laser
beam 2
video camera
(side view)
two Ar+ laser beams:
• 0.61 mm width
• rastered into vertical sheets
Ar laser
beam 1
Shear flow in a strongly-coupled dusty plasma
+ laser pushes
monolayer
Arundisturbed
particles
Transport: radiation pressure
medium
power:
power:
plastic
melting
deformation,
the lattice
flow
low high
power:
slow
deformation,
rotation
Shear flow in a strongly-coupled dusty plasma
Zoom-in view
A 2D liquid, observed at an atomistic level
Shear flow in a strongly-coupled dusty plasma
Video data:
particle’s x,y position
measured in each video frame
Data recorded:
x & v for each particle
i.e., a kinetic approach
Next step in analysis:
convert to a continuum approach, by spatial averaging
Shear flow in a strongly-coupled dusty plasma
Velocity profiles
Plaser = 3.41 W
6
4
1.44 W
2
x
particle velocity v (mm/s)
2.00 W
0
1.04 W
0.82 W
-2
-4
-6
-5
0
distance y (mm)
5
Navier-Stokes equation
v
1
v v p 2 v (/ /3) ( v) E v
t
v
fluid velocity
areal mass density (2D)
p
pressure (2D)
h/ kinematic viscosity (2D)
second viscosity (2D)
E
gas drag
Navier-Stokes equation
Our experiment:
Navier-Stokes equation reduces to:
2D
/t = 0
/x = 0
vy = 0
d 2 v x ( y) E
v x ( y) 0
2
dy
kinematic viscosity
E gas drag coefficient
Velocity profiles fit to Navier-Stokes
Plaser = 3.41 W
6
4
1.44 W
2
x
particle velocity v (mm/s)
2.00 W
0
1.04 W
0.82 W
-2
-4
-6
-5
0
distance y (mm)
5
Results: viscosity vs. inverse temperature
viscosity has
a minimum
3
kinematic viscosity
h
2
(mm /s)
4
2
1
water at STP (3D)
0
high temperature
100
G
couplingGparameter
y 1/Ty
y
rw / lD
0.36
0.42
0.53
1000
low temperature
Physics experiments
Next:
Waves in a strongly-coupled dusty plasma
Waves: two modes in a lattice
S & P waves in seismology
Only the P wave
passes through
the core of Earth
– because the
core is liquid
Frequency ww0
Wave dispersion relation – 2D triangular lattice
3
2
1
acoustic limit
0
0
2
wavenumber ka/p
Theory for a triangular lattice, q 0°
Wang, Bhattacharjee, Hu , PRL (2000)
4
Longitudinal wave
k
Laser incident here
f = 1.8 Hz
4mm
Nunomura, Goree, Hu, Wang, Bhattacharjee
Phys. Rev. E 2002
Random particle motion
No Laser!
4mm
S. Nunomura, Goree, Hu, Wang, Bhattacharjee, Avinash
PRL 2002
ka/p
-1.5
-1.0
0.5
0.0
1.5
15
2.0
4.0
3.0
4.0
2.0
2.0
1.0
0.0
0.0
4.0
Transverse mode
6.0
w/w0
f (Hz)
1.0
Longitudinal mode
6.0
f (Hz)
0.5
3.0
4.0
2.0
2.0
1.0
0.0
0.0
-6.0
-4.0
-2.0
0.0
k (mm-1)
S. Nunomura, Goree, Hu, Wang, Bhattacharjee, Avinash
PRL 2002
2.0
4.0
6.0
10
5
w/w0
-2.0
Energy density / kBT (10-3mm2s)
Wave spectrum & sinusoidally-excited waves
q= 0°
k
a
Mach Cones
Courtesy of Dan Dubin, UCSD
Mach cone angle
C = U Sin m
U
m
wk
Supersonic
disturbance
Courtesy of Dan Dubin, UCSD
Acoustic
wavefronts
Ship’s wake
Transverse Wake
w k
Courtesy of Dan Dubin, UCSD
Lateral wake
Wakes in a dusty plasma
Wake pattern is
determined by
dispersion relation
plasma crystal
air
m
wk
Mach cone
water
wk
Has both features:
• Mach Cone
• Lateral & transverse wakes
Dan Dubin, Phys. Plasmas 2000
Lateral & transverse wakes
Mach cone excitation
Nosenko et al. PRL 2002
V/CL = 1.17
Speed map
for compressional Mach cone
particle
speed v
(mm/s)
The Early History of Dusty Plasmas
• The first observations of a dusty plasma in the laboratory
were made by Langmuir.
• He reported these observations on September 18, 1924
at an address at the Centenary of the Franklin Institute in
Philadelphia.
• “. . . we have observed some phenomena of remarkable
beauty which may prove to be of theoretical interest.”
Langmuir, Found and Dittmer, Science, vol. 60, No.
1557, p 392 (1924)
Langmuir’s Streamer Discharge
A
negative
particles
tungsten
globules
0.01 -0.1 mm
C
S
2 – 4 Torr Argon
Langmuir’s Observations
• small tungsten ‘globules’ were sputtered into the
discharge from the filament
• these globules could be made to move upward
and their motions could easily be followed
visually
• by concentrating a beam of sunlight into the
tube, he could see a ‘very intense scattering’
from the particles
Langmuir’s conclusions
• Langmuir concluded that since the walls of the
tube are negatively charged, the particles must
also be negatively charged because they do not
deposit on the walls
• the negatively charged particles is surrounded by
a positive ion shielding cloud
• the negative particles can lose their charge when
moving through an ion sheath, and the resulting
neutral particles can condense into larger solid
particles
Formation: gas phase
Gas-phase
formation
resulting from
graphite
sputtering:
• Graphite targets
were sputtered by
Ar+ in a glow
discharge
• Particles grew in
the gas phase
• Particles (white)
are imaged here
resting on the
graphite lower
electrode
G. Praburam and J. Goree
Cosmic Dust Synthesis by Accretion and Coagulation
Astrophysical Journal Vol. 441, pp. 830-838, 1995
Formation: gas phase
Gas-phase
formation
resulting from
graphite
sputtering:
• Graphite targets
were sputtered by
Ar+ in a glow
discharge
• Particles grew in
the gas phase
• Particles (white)
are imaged here
resting on the
graphite lower
electrode
G. Praburam and J. Goree
Cosmic Dust Synthesis by Accretion and Coagulation
Astrophysical Journal Vol. 441, pp. 830-838, 1995
Formation: gas phase
Gas-phase
formation
resulting from
graphite
sputtering:
• Graphite targets
were sputtered by
Ar+ in a glow
discharge
• Particles grew in
the gas phase
• Particles (white)
are imaged here
resting on the
graphite lower
electrode
G. Praburam and J. Goree
Cosmic Dust Synthesis by Accretion and Coagulation
Astrophysical Journal Vol. 441, pp. 830-838, 1995
Formation: gas phase
D. Samsonov and J. Goree
Particle growth in a sputtering discharge
J. Vac. Sci. Technol. A 1999
Log lambda used in code
log_lambda = max([3.,alog(debye_length / max([b_c,b_pi]))]) ; John's ad-hoc Coulomb logarithm
; corresponds to impact parameters ranging from
; the one that causes pi/2 scattering or collection on grain
; whichever is bigger, to the Debye length
; the outermost max function assures a nearly zero log lambda if the
; Debye length is shorter than the other length
; minimum value of 3 is suggested by Tsytovich (private communication)
Formation: gas phase
Explanation
proposed for
cauliflower shape:
The origin of the
bumpy shape has
been attributed to
columnar growth.
If true, column size will
depend on
temperature
J.A. Thornton, J. Vac. Sci. Technol. A 11, 666 (1974).
columnar growth, for thin films on a planar surface, using sputter
deposition
Formation: gas phase
Gas-phase formation resulting from sputtering:
• Targets were sputtered by Ar+ in a glow discharge
• Particles grew in the gas phase
vacuum vessel
inside wall
gas inlet
ground
shield
laser sheet
l= 488 nm
upper elec trode
powered
electrode
grounded
electrode
lower electrode
grounded plate
4 cm
turbopump
D. Samsonov and J. Goree
Particle growth in a sputtering discharge
J. Vac. Sci. Technol. A 1999
400
10 10
300
10 9
200
10 8
100
10 7
0
10 6
0
50
100
150
time (sec)
200
250
300
Growth of carbon particles, from sputtering
graphite in an rf discharge
D. Samsonov and J. Goree
Particle growth in a sputtering discharge
J. Vac. Sci. Technol. A 1999
dust number densitycm
( -3 )
Gas-phase
formation
resulting from
sputtering:
dust particle diameter (nm)
Formation: gas phase
Formation: gas phase
Particles grown
by sputtering titanium
Spherical-shaped primary
particles that have coagulated
into aggregates consisting of a
few spheres.
The surface of the
particles appears smoother
than that of the graphite.
D. Samsonov and J. Goree
Particle growth in a sputtering discharge
J. Vac. Sci. Technol. A 1999
Formation: gas phase
Particles grown
by sputtering stainless steel
D. Samsonov and J. Goree
Particle growth in a sputtering discharge
J. Vac. Sci. Technol. A 1999
Formation: gas phase
Particles grown
by sputtering copper
D. Samsonov and J. Goree
Particle growth in a sputtering discharge
J. Vac. Sci. Technol. A 1999
Formation: gas phase
Particles grown
by sputtering
Growth rate varies
tremendously,
depending on the
material
D. Samsonov and J. Goree
Particle growth in a sputtering discharge
J. Vac. Sci. Technol. A 1999
Electron
depletion
When the density
N of negativelycharged dust is
high:
• Dust potential
is reduced
• Dust charge is
reduced
• Plasma
potential is
altered
potential (normalized by electron temperature)
Charging: electron depletion
-
10
-
-
-
1
0.1
0.01
0.01
plasma potential
0.1
1
floating potential
of particle
10
100
normalized particle number density P
Goree, Plasma Sources Sci. Technol. 1994
P 695 TeV amm N cm 3 / ncm 3
1000
Charging: secondary emission
Secondary electron
emission (electron impact)
For mono-energetic electrons:
d ( E ) 7.4 d m ( E / Em ) exp( 2 E / Em )
Yield d
1.2
For small particles, yield is bigger
than for bulk, because of bigger
solid angles for secondary
electrons to escape particle
1
yield d / dm
Graphite in bulk:
dm = 1
Em = 400 eV
0.8
0.6
0.4
0.2
0
Goree, Plasma Sources Sci. Technol. 1994
0
2
4
6
E / Em
8
10
Charging : secondary emission
Secondary electron emission (electron
impact)
For Maxwellian electrons:
Meyer-Vernet* provides formulae for electron
current, result:
• Polarity of particle’s charge switches from
negative to positive
• Occurs for Te in range 1 – 10 eV, depending
on dm
Other electron emission processes:
• photoemission due to UV (very common in
space)
• thermionic emission (uncommon?)
*Meyer-Vernet, Astron. Astrophys. 105,98 (1982)
Ielectron collection
+ Iion collection
+ Ielectron emission
H+
e-
e-
+
Charging: charging time
Charging time
A particle’s charge:
• Can change at a finite rate, as plasma conditions change
• Fluctuates randomly as individual electrons & ions are collected
Characteristic time scale is called “charging time, can be defined as:
• charge / current of one of the two incident species“floating potential V
TeV
t Kt
amm ncm 3
Kt = -1510 sec
for hydrogen, Te = Ti
Typically t 1 msec for a 1 micron grain in a glow discharge
Goree, Plasma Sources Sci. Technol. 1994
Charging: stochastic fluctuations
Charge
fluctuations
0
Stochastic, due to
collection of
individual
electrons and ions
at random times
-5
dQ 0.5 (Q/e)1/2
charge number N
charging time t
discrete
continuous
-10
-15
-20
0
0.5
1.0
1.5
t (msec)
Goree, Plasma Sources Sci. Technol. 1994
2.0
2.5
3.0
Navier-Stokes equation
v
1
v v p 2 v (/ /3) ( v) E v
t
v
fluid velocity
areal mass density (2D)
p
pressure (2D)
h/ kinematic viscosity (2D)
second viscosity (2D)
E
gas drag
● equilibrium
simulation
▲ non-equilibrium
experiment
this talk
normalized by
normalized kinematic viscosity h
Comparison: experiment & MD simulation
1
0.1
Q2
2pe 0 a
1
10
100
coupling
parameter
inverse
temperature
GG
1/T
1000
ka/p
-1.5
-1.0
0.5
0.0
1.5
15
2.0
4.0
3.0
4.0
2.0
2.0
1.0
0.0
0.0
4.0
Transverse mode
6.0
w/w0
f (Hz)
1.0
Longitudinal mode
6.0
f (Hz)
0.5
3.0
4.0
2.0
2.0
1.0
0.0
0.0
-6.0
-4.0
-2.0
0.0
k (mm-1)
S. Nunomura, Goree, Hu, Wang, Bhattacharjee, Avinash
PRL 2002
2.0
4.0
6.0
10
5
w/w0
-2.0
Energy density / kBT (10-3mm2s)
Wave spectrum & theory
q= 0°
k
a
Formation: tokamaks
Dust formation: flaking
J. Winter, Phys. Plasmas 7, 3862 (2000)