radiation pressure and gas drag forces on a single particle and wave excitation in a dusty plasma
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Radiation pressure and gas drag forces on a single particle and wave excitation in a dusty plasma
B. Liu, J. Goree, V. Nosenko, K. Avinash
plasma = electrons + ions Plasma
+
-
+
+
+
+
+
++
- -
-
-
--
-
+
-
What is a dusty plasma?
D
• Debye shielding
small particle of solid matter
• becomes negatively charged
• absorbs electrons and ions
& neutral gas
Forces Acting on a Particle
Coulomb
QE
Other forces:• Gas drag• Ion drag• Thermophoresis• Radiation Pressure
Gravitymg
polymer microspheres8 m diameter
Particles
separation a 0.5 mmcharge Q - 104 e
Confinement of 2D monolayer
– Interparticle interaction is repulsive Coulomb (Yukawa)
– External confinement by curved electric sheath above lower electrode
triangular lattice with hexagonal symmetry
2D lattice
Yukawa inter-particlepotential
incident laser intensity I
Radiation Pressure Force
transparent microsphere
momentum imparted to microsphere
Force = 0.97 I rp2
Setup
Argon laser pushes particles in the monolayer
H eN e laserho riz o nta ls he e t
v ideo cam e ra(to p v iew )
lo wer e lec tro deR F
two -axiss te e ring
m ic ro sphe res
m o d ula tio n
A r lase rbe a m
xy
f ram egra bb e r
Ar laser
mirror
scanning mirrorchopsthe beam
beam dump
chopped beamChopping
Single-particle laser acceleration
laser beamradiation pressure
• Accelerated by laser radiation pressure
Coulombdrag
• Restored by confining potential
• Damped by gas drag
2 mm
Ar lasersheet
Movie of particle accelerated by laser beam
Equation of motion
offlaseronlaserF
dxdUxRxm laser
0
Assumption:• The dominant forces are
Gravity Vertical sheath electric field Radiation pressure force Drag force Horizontal confining potential
• One dimensional motion
Calculation: radiation pressure, gas drag, confining potential
calculate potential energy
time3.3 sec
)),(( RtxU
time
laser on
1 seclaserFthx
Gas drag coefficient R is an adjustable parameter to minimize the discrepancy between and . x thx
R R
x
time4.3 sec
record movierecord particle’s orbit
Horizontal confining potential energy
-1 0 1 2 3 4 5 6 7 8 9 10
0
100
200
300
400
500
600
U(x) [eV] = 8.53 ( x - 0.23 )2 + 0.97
pote
ntia
l ene
rgy
U(x
) (eV
)
distance from equilibrium point x (mm)
Radiationpressureforce
104 105 106
10-4
10-3
10-2
rp = 2.42 m
rp = 4.05 m
rp = 6.37 m
Ilaser
scaling
F/r p2 (
N m
-2)
Ilaser
(W m-2)
Gas drag force
0.01 0.1
10-13
10-12
rp (m) laser resonance
----------------------------------- 2.42 4.05 6.37
pgas
1.0 scaling
R/r p2 (k
g s-1
m-2)
pgas (torr)
2
34
prcmN
R
Gas drag
laserp
laser
IrcnFq
21
Radiation pressure
Coefficients for radiation pressure and gas drag
q result: measurment 0.94 0.11 ray optic theory 0.97
result: measurment 1.26 0.13 Epstein theory 1 ~ 1.44
Epstein, Phys. Rev. 1924
Application of radiation pressure force Laser sheet
Dispersion relationsin 2D triangular lattice
Wang et al. PRL 2001
0 0.5 1 1.5 20
1
2
3
4
ka
/
0
Transverse mode
Longitudinal mode
=1.2, /0=0.39=0,
k
/
0
laser beam
y
xz
• Transverse (perpendicular to the chain) : opticalThe oscillation in
y direction ( horizontal confining potential) z direction ( potential well formed by gravity and sheath )
• Longitudinal (along the chain) : acoustic
Waves in one-dimensional dusty plasma chain
Optical mode in solid(two atom in primitive cell)
optical
acoustic
Assumptions:• One dimension, infinite in x direction• Parabolic confinement in y direction• Yukuwa interaction potential• Nearest neighbor interaction• No gas damping
2sin)1(4 222 qae
M pd Optical:
2sin])1(1[4 2222
qaepd Acoustic: 3mapd /
Optical mode in one-dimensional chain
Dispersionrelation
“Optical” branch
Acoustic branch
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.60
2
4
6
8
10
(/
0)2
qa
Ashtray electrode
22-particle chain
x
y
z
Formation of one-dimensional chain
• Potential gradient in x direction
• Minimum potential energy requirement• Particle-particle interaction energy
• Confining potential energy
y
x
Bifurcation of chain
)(21 2
022
1 ymxmU yi
ix Case 1
)(21 2
0,2
0 i
ix xmU Case 2
Uy
y
Ux
x
Bifurcation condition
12
nUUx
y 202
2
10
No bifurcation condition
0.0 1.0x10-3 2.0x10-3 3.0x10-3 4.0x10-30.0
2.0x10-19
4.0x10-19
6.0x10-19
pote
ntia
l ene
rgy
(J)
x position (m)
Resonance frequency: x
Single-particle laser acceleration
x = 0.07 Hz
laser-excited resonance vibration
Resonance frequency: y
0 1 2 3 4 5 6 70
5
10
15
2 Hz
Am
plitu
de
frequency (Hz)
laser sheet
Velocity autocorrelation function of random motion
0 1 2 3 4 5-2
0
2
4
6
0 2 4 6 8 10
VA
CF
(mm
2 s-2)
time (s)
1.66 Hz
frequency (Hz)
Resonance frequency: y
0
00 )()(VACFt
tVttV
Laser beam
Excitation of optical mode
Excitation of optical mode
Laser beam
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