Damping of the dust particle oscillations at very low neutral pressure M. Pustylnik, N. Ohno, S.Takamura, R. Smirnov

Introduction (Z d, m d – 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: 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, β is the damping rate and ω 0 is the eigenfrequency. If the dust particle is balanced against gravity by the electrostatic force only p – neutral gas pressure, ρ – is the density of the dust particle material, a – is the dust particle radius.

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:  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  m dust, supposing  β/p = 2.3 s -1 Pa -1 ZdZd x Z deq δZdδZd ZdZd

Collisionless sheath model with bi-Maxwellian electrons Energy and flux conservation for ions: Boltzman-distributed electrons Poisson equation z sheath presheath electrode φ0φ0 Dust particle U le

Generalized Bohm criterion at Φ=Φ 0 (Φ =  pl -  ; Φ 0 =  pl -  0 )

Charging of dust Equilibrium charge condition – total current equals zero. Electron and ion currents (bi-Maxwellian plasma): Charging time

Experimental setup U2U2 U1U1 R2R2 R3R3 R1R1 Amplifier 100 Hz, 100 sweeps UgUg Grid Anode Probe Filament N S UaUa UcUc Function generator, constant negative bias, iImpulse to excite vibration (10 ms), syncronized with videocamera Video imaging parameters: Frame rate 250 fps Exposure time 2 ms Spatial resolution ~13  m/pix Record duration – 6.55 s Laser sheet levitation electrode trench

Probe measurements in the bi- Maxwellian plasma Example of the measurements Probe characteristics 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 5 parameters

Dust dynamics Trajectory Amplitudes ~-βt

Pressure variation experiment instability Epstein law value Plasma parameters Damping rate

 variation experiment Plasma parameters Damping rate instability

Calculated map of  DCE

Non-uniformity of the plasma in the vicinity of the electrode Sheath is governed by several times smaller  than measured

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 Simulated ion VDFCurrents

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  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