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Particle’s Dynamics in Dusty Plasma with Gradients of Dust Charges Institute for High Energy Densities, Russian Academy of Sciences, Moscow, Russia, O. S. Vaulina, O. F. Petrov, V. E. Fortov School of Physics, University of Sydney, NSW 2006, Australia, A. A. Samarian, B.W.James2 Dust Vortices in Gas Discharge Plasma Stochastic Dust Motion Self-exited Dust Motion in Rf- Discharge Laboratory Dusty Plasma – weakly ionized gas with micron-sized dust particles (macroparticles) Typical conditions of experiments in gas discharge plasma Parameters of gas discharge plasma: Temperature of ions and electrons: Ti << Te~1-7eV Gas pressure: Р ~ 0.03-3 Тorr Plasma concentration: ~ 108-109 см-3 Neutral’s concentration : ~ 1014-1016 см-3 dc- discharge rf- discharge Laboratory Dusty Plasma – weakly ionized gas with micron-sized dust particles (macroparticles) Typical conditions of experiments Parameters of dust particles: Radius: ap ~ 1-10 м Charge: Z p ~ 102 - 105 Concentration: np ~ 103 - 105 см –3 Kinetic TEMPERATURE: Тp ~ 0.03-100 eV («Abnormal dust heating») Dust Vortices Crystal Fluid Oscillations of separate particles Instability of the system with the dust charge gradients orthogonal to the non-electrostatic force =Z(l)/l – due to inhomogeneity of plasma surrounding the dust cloud ne(i),Te(i) ),Ve(i) Electron Temperature Gradients (Te/r) Variations in regular ion’s velocity (Vi/r) Gradients of plasma densities ((ni - ne)/r) /<Z> ~ (1-100)% см-1 /<Z> ~ (1- 50)% см-1 /<Z> ~ (1- 50)% см-1 Equations of motions for particles with Zр(,y) in an electric field Eext of cylindrically symmetric trap: d lk dl k mp m p v fr F Fnon Fbr 2 dt dt 2 F Fint Fext, Fext = e Zр(,y) E(,y), Fint eZ ( , y ) l j l l k l j lk l j lk l j For typical conditions of ground-based experiments in gas discharge plasma Non-electrostatic forces Fnon - gravity force mpg, ion drag force Fi (0.1-0.5) mpg, thermothoretic force Fт < 0.1 mpg Conditions for occurrence of dust instabilities Disperse Instability when the frictional force does not damp the dust oscillations (regular vibrations or random dust fluctuations similar to the Brownian motion) Conditions of Occurrence for Z >> Z fr 2< c 2 < o / fr = rot V (y) Fnony() / {mpZofr}, o - shift parameter, c – resonance frequency Dissipative Instability when a restoring force is absent (dust vortexes) c 4 < ofr Dust vortices under ground-based conditions in dc- discharge in rf - discharge argon, Р ~ 0.02-0.2 Тorr, (aр ~ 1.4 м) argon, Р ~ 0.02-0.2 Тоrr, iron particles (aр ~ 3.5 м) Formation of combined dust oscillations due to variation of plasma parameters 1. Direction of dust rotation is in accordance to theoretical estimation of dust charge gradients 2. Small variations of dust charge < 1-5% см-1 need for formation of these dust rotations in field of gravity Dust vortices in microgravity conditions (International Space Station, PKE - Nefedov) Scheme of gas discharge camera Argon P = 36-98 Pa W=0.14-1 W Te = 1-3eV ni ~ 109 см -3 aр = 1.7 м Experiment Numerical Simulation o~ 0.04 -0.16 c-1 «void» 2o Fi /mpZpfr, Fi 0.3 mpg, /Zp ~ 5 - 20% cм-1 Random fluctuation of dust charge Two basic reasons: random nature of currents charging dust particles stochastic dust motions in spatially inhomogeneous plasma (in presence of dust charge gradients) Random fluctuations of dust charges fluctuation of interparticles potential ~ Zp(t)2; fluctuation of electric force ~ Zp(t)E in external electric field Е It leads to stochastic motions of dust particles additionally to their thermal Brownian motions Influence of discrete charging currents on kinetic dust temperature Additional kinetic energy: fT = e2Zp2E2/(frmp) Zp = <Zp>1/2 – amplitude and с=1/ - time of correlations for charge fluctuations in plasma fT, эВ In gas discharge plasma kinetic energy of macroparticles with radius ар > 10 м can reach fT ~ 1 eV , c-1 fT < 0.1 eV для ар < 2 м, Р > 0.02 Тоrr Influence of spatial variation of dust charge on kinetic dust temperature Taking into account of spatial inhomogeneity of bulk plasma in region of stochastic dust motions Additional kinetic energy: s T (Tn f T ) /(1 1 ) Stochastic dust oscillations near the electrode of rf- discharge Тр ~ 3 - 30 эВ y=dZp/dy Dependence of oscillation amplitude on pressure for particles : 1– 1 м; 2 – 2.1 м. 100 Ay (P i)/Ay(P o) y 1 2 Z v l р fr p 2 1 10 2 1 10 30 50 70 90 pressure, [мТоrr] Dust charge gradients y can lead to formation of stochastic dust motions with big kinetic energy CONCLUSIONS The small dust charge gradients due to inhomogeneity of plasma surrounding macroparticles can lead to the dust vortex formation, and can influence on the stochastic dust motions in plasma of gas discharges. Experimental Setup for Vertical Vortex Motion Dust vortex in discharge plasma (superposition of 4 frames) Melamine formaldehyde –2.67 μm (Side view) Experimental Setup for Horizontal Vortex Motion Grounded electrode Grounded electrode Pin electrode Dust Vortex Grounded Grounded electrode electrode Dust Vortex Dust Vortex Dust Vortex Powered electrode Side View electrode PinPin electrode Top View Video Images of Dust Vortices in Plasma Discharge -Dependency on Pressure wс = /2= F /{2mpZofr} Dependency of the rotation frequency on pressure for vertical (a) and horizontal (b) vortices a) 10 U=40 V b) 60 9 8 50 7 pg/{Zov fr } 6 =12 mm-1 5 40 Ftp/{2mdZov fr } 30 =320 mm-1 4 20 3 2 10 1 0 0 0 20 40 60 80 100 120 Pressure, mTorr 140 160 180 200 0 20 40 60 80 100 120 Pressure, mTorr 140 160 180 200 Self-excited oscillation in extreme region Grounded Electrode 4cm Powered Electrode 8cm 11cm Equation of Motion Side Observation Window Top View Top Observation Window Particle Dispenser Top Ground Electrode a v1 DC Power AC Power s1 Particle Driving Pad ZD mas F (v1 ) s1 F (v2 )s2 Zd (2f 0 ) 2 m E' Where f 0 is the resonant frequency ' And E is the electric field gradient where 4 F mnn vTn a 2 v 3 Gas Inlet RF Supply 15MHz f (r ) v Radial potential distribution potencial, [V] 50 /<Z>~(divE) 40 30 20 1,2 10 1,0 0 0,8 0 1 2 3 distance, [cm] 4 5 r 0,6 0,4 0,2 r/R 0,0 0,0 0,2 0,4 0,6 0,8 1,0 Dependences of critical amplitude and charge gradient 140 critical amplitude critical charge gradient ~ 20 mm-1 120 Input power, W 100 80 60 40 20 0 3.5 3.75 4 4.25 radial distance, mm 4.5 4.75 5 Summary The overview of experimental and theoretical investigations of charged gradient induced instabilities were presented. We attribute the observed instabilities to inhomogenaties in the plasma, and show that greater instability of dust structures can be explained by larger space charge gradient. The authors have clearly been developing and promoting this idea for the few years and are making some progress on the experimental and theoretical side. Thanks Everybody!