Introduction to Dusty Plasmas - Sektion Physikbonitz/si08/talks/August_4th/Morning... ·...
Transcript of Introduction to Dusty Plasmas - Sektion Physikbonitz/si08/talks/August_4th/Morning... ·...
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Introduction to Dusty Plasmas
André Melzer
Institute of Physics,
Ernst-Moritz-Arndt-Universität Greifswald Germany
Extended Lecture Notes see: www5.physik.uni-greifswald.de
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Coulomb crystallizationof trapped particles
Dynamics and transport in plasmas
Dusty (Complex, Colloidal) Plasmas
Dusty Plasmas = Microscopic particles in a
Selwyn 1991
Astrophysics… Etching
Microscopic particles in a gaseous plasmaenvironment
Deposition and…
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Dusty Plasmas in Astrophysics
Comet Hale-Bopp
Saturn rings
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Dusty Plasmas in Astrophysics
Saturn rings 1981
2005
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Dusty Plasmas in the Atmosphere
Noctilucent clouds
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Dusty Plasmas in Technology
Plasma etching
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Dusty Plasmas in Technology
Selwyn 1991
„Killer particle“
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Dusty Plasmas in the Laboratory
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Dusty Plasmas under Microgravity
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Contents of Lecture
• Dust charging
• Forces
• Strongly coupled systems, particle-particle and
particle-plasma interaction
• Waves
• Finite systems and normal modes
For an extended introduction see:www5.physik.uni-greifswald.de
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Charging
plasma
Q<0
ions
electrons
Q<0
In typical discharges:Particle will be charges negatively due to higher mobility of electrons
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OML currents
ΦΦΦΦ−−−−====
ii
iii
kT
e
m
kTenaI 1
82
ππππππππ
Ion current
Probe theory of Langmuir and Mott-Smith 1929
ΦΦΦΦ====
ie
eee
kT
e
m
kTenaI exp
82
ππππππππ
Electron current
increased collectioncross section
thermal velocitiesgeometry
density reductionBoltzmann factor
electronand
ion currents
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Particles as floating probes
∑∑∑∑ ====ΦΦΦΦq
flqI 0)(
ΦΦΦΦ====
ΦΦΦΦ−−−−
e
fl
i
e
e
i
i
e
i
fl
kT
e
n
n
m
m
T
T
kT
eexp1 With OML collection
currents only
Te/Ti 1 10 20 100
H -2.50 -1.91 -1.70 -1.24
He -3.05 -2.39 -2.16 -1.65
Ar -3.99 -3.24 -2.99 -2.41
Values of eΦΦΦΦfl /kTe for ne=ni
ekTefl /2−−−−≈≈≈≈ΦΦΦΦ
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Limitations of OML description
Often: ion drift velocity ui (much) larger than ion thermal velocity vth,i SHEATH
exact
• collisionless (ion) trajectories
• Maxwellian velocity distribution
• isotropic
none of that ismet in „real“ discharges
ΦΦΦΦ−−−−====
2
2 21
ii
iiium
eeunaI ππππ
ΦΦΦΦ−−−−====
ii
iii
kT
e
m
kTenaI 1
82
ππππππππ
exact solution
approximation
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The capacitance model
aC 04πεπεπεπε====
flCQ ΦΦΦΦ==== Particle as a spherical capacitorof capacitance C
Capacitance in vacuum
For a particle of a=1µm: 700 e per Volt
With the rule-of-thumb approximation: ΦΦΦΦ=2kTe/e
eVe,m1400 TaQ µµµµ====
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Other charging currents
hνννν electrons
Photoelectron emission(UV radiation)
02 <<<<ΦΦΦΦΓΓΓΓ==== eaI µµµµππππ Secondary electron emission
Particle can become positively charged
electrons
0)/exp(
0
2
2
>>>>ΦΦΦΦΦΦΦΦ−−−−ΓΓΓΓ====
<<<<ΦΦΦΦΓΓΓΓ====
flpfl
fl
kTeeaI
eaI
νννννννν
νννννννν
µµµµππππ
µµµµππππ
−−−−====
m
e
m
eme
E
E
E
EE exp4.7)( δδδδδδδδ
Secondary electron emission
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Charging time scale
ithi
ii
venae
kTa
,20
14
πππππεπεπεπεττττ ==== RC====ττττ
Time constant for
charging of a capacitor
C U 1/I
ai1∝∝∝∝ττττ Smaller particles
are charged slower
Plasma
time
1 µs
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Summary Charging
• Micrometer sized particles carry 103 to 104 elementary charges
• Charging time: microseconds: Charge in dynamical equilibrium
• Charge to mass ratio Q/m extremely small: • Charge to mass ratio Q/m extremely small: slow timescales
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Forces on dust particles
• Gravity
• Electric field force
• Thermophoresis
• Ion Drag
• Neutral Drag
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Gravity
gagmFrvr
3
3
4πρπρπρπρ========
What else needs to be said ?
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Electric Force
EaEQFrrr
ΦΦΦΦ======== 04πεπεπεπε
Also for a charged particle with (symmetric) shielding cloud
dust
shieldingcloud
Q
EQFrr
=
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Drag Forces
„streaming“ species
dustparticle
A
Force = momentum transfer x ΑΑΑΑ x density x velocity
particle
vrel dt
# of incident particles
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Neutral Drag
„streaming“ species
dustparticle
A
v dt
p
p‘
∆∆∆∆p
v dt
relnnth,n2
3
4vnvmaFrr
ππππδδδδ−−−−≅≅≅≅
av
pxmF
nth,
8
ρρρρππππδδδδββββββββ −−−−====−−−−==== &
NB:
Stokes friction
F ~ a
(a>λλλλ)
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Ion Drag
2 components:
1. Collection Force
2. Coulomb Force
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1. Collection Force
e Φ2r
iiii
i
umunmu
eaF
Φ−=
2
2 21π
r
cross section as for charging
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2. Coulomb force
iiii umunF coulσ=r
ΛΛΛΛ==== ln22/coul ππππππππσσσσ b
p
p‘
∆∆∆∆p
Coulomb scattering cross section
20
2/4 iium
Qeb
πεπεπεπεππππ ====
====ΛΛΛΛ
min
maxlnlnb
b
p∆∆∆∆p
impact parameter for 90° collisions
Coulomb logarithm
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Thermophoresis
T∇T
v
kaF ∇∇∇∇−−−−====
rr
nth,
n2
15
16ππππ „hot“ „cold“
Force towards coldest point!
Force due to a temperature gradientin the neutral gas
F
Force towards coldest point!
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Comparison of forces
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Trapping (Laboratory)
Electrode
Plasma
Fth FgFE Fion
sheath
Electrode
Plasma
Fth FgFE Fion
sheath
Trapping in the plasma sheath
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Trapping (Microgravity and nanometric particles)
Electrode
Plasma
FEFionFth
Electrode
Plasma
FthFE Fion
Trapping in the plasma volume
sl. 9
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Particle trapping in the laboratory
E
E
V 0
sheathedge Plasma
m
EQ ′′′′==== 02
0ωωωω
QE
mg
(z ) E
z
electrode z
E
z
0
0
particle
V(z)
(z)
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Resonance method
mgzEzQ ====)()( 00Force balance
ext)()( FzEzQzmzm ====++++++++ &&& ββββ Equation of motion
0)( QzQ ====
)()()( zzEzEzE −−−−′′′′++++====
Assumption: constant charge
)()()( 00 zzEzEzE −−−−′′′′++++==== Linear electric field
200
20
20 )(
2
1)(
2
1zzEQzzm −−−−′′′′====−−−−ωωωω Potential well
m
EQ ′′′′==== 02
0ωωωω Resonance frequency
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Linear Resonances
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Charge measurement
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Summary Forces
• Laboratory: electric field force + gravity: Trapping in the sheath
• Microgravity: electric field force + ion drag:Trapping in the plasma volume (void)Trapping in the plasma volume (void)
• Weakly damped particle dynamics
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Strongly coupled systems
One Component Plasma:(Wigner 1938, Brush et al. 1966)
c
c 168
ΓΓΓΓ<<<<ΓΓΓΓ
====ΓΓΓΓ>>>>ΓΓΓΓ Solid Phase
Fluid Phase
Coulomb
energy
Thermal
energy
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Yukawa systems
−−−−====
D0
2
exp4
)(λλλλπεπεπεπε
φφφφr
r
Qr
λλλλκκκκ b====
Robbins et al. 1988
Dλλλλκκκκ b====
Screening strength
Crucial parameters
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Plasma crystals
cf: Chu et al. 1994, Thomas et al. 1994, Hayashi et al. 1994
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Interaction?
• Horizontal Interactionrepulsive Yukawa (Debye-Hückel) type
(Konopka 2000)
• Vertical Interactionattractive forcesorigin?
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Vertical Order
E0
sheathedge
Plasmaions
Attractive forces in the sheath?
QE
mg
(z ) E
z
E
electrode z
E0
0
0
particle (z)
ions
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Vertcal order: Simulations
1. Ion focus: Attraction2. supersonic ion flowtion:
Non-reciprocal forces, Only the lower particleexperiences attraction
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Vertical Order: Experiment
1. Particle: 3.47 µm
2. Particle: 4.18 µm
Vertical: force balance
Horizontal: free motion
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Vertical Order: Experiment (2)
The lower particleexperiencesattraction
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Vertical Order: Experiment (3)
The upper particledoes not
experienceattraction
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Summary Crystallization
• Strongly coupled systems with Yukawa interaction
• Attractive forces in the sheath due to ion flow (ion focus, ion wake field)
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Waves in strongly coupled dust: Dust lattice waves
Compressionaland Shear Waves in a 2D lattice
TransverseWave mode
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Dust lattice waves: theoretical treatment
n b(n-1) b (n+1) b (n+2) b
nx
1+nx
2+nx
1−nx
)2( ++++−−−−==== xxxkxm && linear chain with )2( 11 −−−−++++ ++++−−−−==== nnnn xxxkxm && linear chain with spring constant k
)exp( tiinqbAxn ω−=
2sin4
)1(cos2)2(
22
2
qb
m
k
qbkeekm iqbiqb
=
−=−+=− −
ω
ω
dispersion relation of a linear chain
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Dust lattice waves: theoretical treatment
n a(n-1) a (n+1) a (n+2) a
nx
1+nx
2+nx
1−nx
spring constant from
−==
rQrV
Vdk exp)(
22
spring constant fromYukawa potential
dispersion relation w.Yukawa potential
−==
= Dbr
r
r
QrV
dr
Vdk
λπεexp
4)(
0
2
2
2
( )( )2
30
2
22exp4
κκκπε
++−=b
Qk
( )( )
++−=
2sin22exp 22
30
22 qb
bm
Qκκκ
επω
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2D dust lattice waves
• many (infinite) neighbors
• 2D hexagonal structure• compressional and shear mode
qb qb
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Dust lattice waves: 1D
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Dust lattice waves : 1D
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)exp( tiiqx ωωωωξξξξ −−−−∝∝∝∝
Driven wave:
ω ω ω ω real
q complex
Re q
Dispersion ωωωω(q)
Dust lattice waves : 1D
q complex
Im q
====++++
2sin4 22 qb
m
kiβωβωβωβωωωωω
)22)(exp(4
)(
2
30
22
2
2
κκκκκκκκκκκκπεπεπεπε
++++++++−−−−
====∂∂∂∂
ΦΦΦΦ∂∂∂∂====
b
eZ
x
xk
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Variation of
the
screening
strength
Re q
Dust lattice waves : 1D
Im q
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Dust lattice waves: shear mode
Laser pulse
Nunomura 2001
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Dust lattice waves: shear modefr
eq
ue
nc
y
Nunomura 2002
wave number
fre
qu
en
cy
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Dust lattice waves: transverse mode
nz
1+nz
2+nz
1−nz
++++
−−−−====
rr
r
QrF
λλλλλλλλπεπεπεπε1exp
4)(
2
2
electrostatic force betweenparticles
DDr λλλλλλλλπεπεπεπε4 2
0
a
zazar
2
222 ∆∆∆∆
++++≈≈≈≈∆∆∆∆++++====
(((( )))) (((( )))) )(1exp4
.).(
)()(
130
2
nnz
z
zza
QnnF
r
zrFrF
−−−−++++−−−−====
∆∆∆∆====
++++κκκκκκκκπεπεπεπε
particles
vertical forcecomponent
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Waves in weakly coupled dust: Dust-acoustic waves
Complete analog to ion-acoustic waves:
Ions DustElectrons Electrons and ions
pepipd ωωωωωωωωωωωωωωωω ,<<<<<<<<<<<<
DA velocity
Dispersion for cold dust, ions
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Summary Waves
• Dust lattice waves (strongly coupled system)
• Longitudinal (compressional) waves• Shear (transverse) waves• Out-of-plane (transverse) waves• Out-of-plane (transverse) waves
• Determination of screening strength and interaction potential
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Dusty plasmas: unique properties!
• High Particle Charge Z: additional charge carrier in plasma
• High Particle Charge Z: strong coupling � crystallization
• High Particle Mass m: slow dynamics � video microscopy
• Particle surface a: novel type of forces for plasmas
• gravity
• ion drag
• thermophoresis
• novel type of waves: dust lattice waves
dust acoustic waves