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