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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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M. Pustylnik, N. Ohno, S.Takamura, R. Smirnov
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 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:
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
Energy and flux conservation for ions:
at Φ=Φ0 (Φ = fpl- f; Φ0 = fpl- f0)
Equilibrium charge condition – total current equals zero. Electron and ion currents
Video imaging parameters:
Frame rate 250 fps
Exposure time 2 ms
Spatial resolution ~13 mm/pix
Record duration – 6.55 s
constant negative bias,
iImpulse to excite vibration
(10 ms), syncronized with
Example of the measurements
Cathode current ~31 mA
Cathode voltage -80 V
Grid voltage 18 V
Anode voltage varied 0-18 V
Argon pressure 0.18 Pa
Sheath is governed
by several times
smaller a than measured
Simulated ion VDF