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Damping of the dust particle oscillations at very low neutral pressure. M. Pustylnik, N. Ohno, S.Takamura, R. Smirnov. Introduction. In the linear approximation the motion of a dust particle trapped in a sheath is described by the harmonic oscillator equation:.

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damping of the dust particle oscillations at very low neutral pressure

Damping of the dust particle oscillations at very low neutral pressure

M. Pustylnik, N. Ohno, S.Takamura, R. Smirnov

introduction
Introduction

In the linear approximation the motion of a dust particle trapped in a sheath

is described by the harmonic oscillator equation:

where z is the vertical coordinate, βis the damping rate and ω0 is the eigenfrequency. If the dust particle is balanced against gravity by the electrostatic force only

(Zd, md – dust particle charge and mass, E – local electric field). Usually it is accepted

that oscillations of the dust particles are damped by the neutral drag. Damping rate

is given by the Epstein formula:

p – neutral gas pressure, ρ – is the density of the dust particle material, a – is the

dust particle radius.

delayed charging
Delayed charging

Delayed charging is the effect, associated with the finite charging time of a dust particle. It has been shown that this effect leads to the modification of the damping factor:

Zd

Zdeq

Zd

δZd

x

ch – is the characteristic charging, i.e. time, required to compensate small deviation of the dust particle charge from its equilibrium value.

Convinient representation of damping factor – β/p. β/p is constant if only Epstein drag

works. For 2.5 mm dust, supposing d=1.44,β/p = 2.3 s-1Pa-1

collisionless sheath model with bi maxwellian electrons
Collisionless sheath model with bi-Maxwellian electrons

Energy and flux conservation for ions:

Boltzman-distributed electrons

z

presheath

φ0

Poisson equation

Dust

particle

sheath

Ule

electrode

generalized bohm criterion
Generalized Bohm criterion

at Φ=Φ0 (Φ = fpl- f; Φ0 = fpl- f0)

charging of dust
Charging of dust

Equilibrium charge condition – total current equals zero. Electron and ion currents

(bi-Maxwellian plasma):

Charging time

experimental setup
Experimental setup

Video imaging parameters:

Frame rate 250 fps

Exposure time 2 ms

Spatial resolution ~13 mm/pix

Record duration – 6.55 s

S

Laser sheet

Ua

Anode

N

U1

R1

Probe

Filament

R2

Amplifier

100 Hz,

100 sweeps

U2

R3

levitation

electrode

Uc

Function

generator,

constant negative bias,

iImpulse to excite vibration

(10 ms), syncronized with

videocamera

trench

Grid

Ug

probe measurements in the bi maxwellian plasma
Probe measurements in the bi-Maxwellian plasma

Example of the measurements

Probe characteristics

5 parameters

Discharge parameters

Cathode current ~31 mA

Cathode voltage -80 V

Grid voltage 18 V

Anode voltage varied 0-18 V

Argon pressure 0.18 Pa

pressure variation experiment
Pressure variation experiment

Plasma parameters

Damping rate

Epstein

law value

instability

a variation experiment
a variation experiment

Plasma parameters

Damping rate

instability

non uniformity of the plasma in the vicinity of the electrode
Non-uniformity of the plasma in the vicinity of the electrode

Sheath is governed

by several times

smaller a than measured

pic simulation of the sheath
PIC simulation of the sheath
  • Bi-Maxwellian electrons
  • Ions are injected as Maxwellian with the room temperature
  • Elastic and charge-exchange collisions for ions are taken into account
  • Plasma particles penetrate through the electrode with the probability 0.88
  • Length of the simulated domain 2 cm
effect of the shape of the ion vdf on the equilibrium potential of a dust grain
Effect of the shape of the ion VDF on the equilibrium potential of a dust grain

Simulated ion VDF

Currents

conclusions
Conclusions
  • Large deviations of the damping rate from the value, predicted by the Epstein neutral drag formula are observed
  • The deviation appears at low pressure and is larger at lower values of a
  • At comparatively lower plasma density the damping rate is smaller than the Epstein value and transition to instability is clearly observed.
  • At higher plasma density damping rate is higher than the Epstein value
  • Qualitative agreement between the theoretical calculations and experimental measurements is acieved