Experimental observation of self excited co–rotating multiple vortices in a dusty plasma with inhomogeneous plasma background. Mangilal Choudhary,a) S. Mukherjee, and P. Bandyopadhyay Institute for Plasma Research, HBNI, Bhat, Gandhinagar, 382428, India We report an experimental observation of multiple co–rotating vortices in a extended dust column in the backgroundofnon–uniformdiffusedplasma. InductivelycoupledRFdischargeisinitiatedinthebackground ofargongasinthesourceregionwhichlaterfoundtodiffuseinthemainexperimentalchamber. Asecondary DC glow discharge plasma is produced to introduce the dust particles into the plasma. These micron sized poly-dispersedustparticlesgetchargedintheplasmaenvironmentandtransportedbytheambipolarelectric field of the diffused plasma and found to confine in the potential well, where the resultant electric field of the 7 diffused plasma (ambipolar E–field) and glass wall charging (sheath E–field) hold the micron sized particles 1 against the gravity. Multiple co–rotating (anti–clockwise) dust vortices are observed in the dust cloud for 0 2 a particular discharge condition. The transition from multiple to single dust vortex is observed when input RF power is lowered. Occurrence of these vortices are explained on the basis of the charge gradient of dust n particles which is orthogonal to the ion drag force. The charge gradient is a consequence of the plasma a J inhomogeneity along the dust cloud length. The detailed nature and the reason for multiple vortices are still underinvestigationthroughfurtherexperiments, however, preliminaryqualitativeunderstandingisdiscussed 2 1 based on characteristic scale length of dust vortex. There is a characteristic size of the vortex in the dusty plasmasothatmultiplevorticesispossibletoformintheextendeddustyplasmawithinhomogeneousplasma ] background. Theexperimentalresultsonthevortexmotionofparticlesarecomparedwithatheoreticalmodel h and found some agreement. p - m I. INTRODUCTION motion along with vortex motion18–20 are observed in s a unmagnetized plasmas world wide. The horizontal and pl Dusty plasma is a low-temperature plasma consists vertical vortex motion of dust grains in the presence of . of electrons, ions, neutrals, and sub–micron to micron anauxiliaryelectrodenearthelevitateddustcloudinca- s c sized particles of solid matter (dielectric or conducting). pacitive coupled plasma is also reported by Samarian et i When these dust particles are introduced into the con- al.21 and Law et al.22. The rotation or vortex motion of s y ventionalplasma,theyundergocollisionswiththehighly thedustparticulatesintheabsenceofmagneticfieldcan h mobile electrons more frequently than with the slower beinducedbyasymmetricionsfloworshearedflowalong p and heavier ions within the plasma. As a result, the with electric field11,23,24, charge gradient of the particles [ dustparticlescollectthenegativechargesupto103−105 alongwiththenon–electrostaticforces19,25–27,Rayleigh– 1 times of an electronic charge. The interaction of the- Taylor instability28 and transient shear instability29. v ses highly negatively charged particles leads to exhibit In the presence of magnetic field (< 500 G), flows of 3 the collective behavior because of the coulomb interac- electrons and ions influence the state of dusty medium 3 tion. The instabilities1–3 in the medium provides the en- and affect the dust cloud motion to rotate as a rigid 2 ergy to grow the local/infinitesimal perturbation in this body30–36. Application of strong magnetic field ((cid:62) 4 3 dissipative medium. Evolution of local perturbation ap- Tesla) can magnetized the micron sized dust particles, 0 . peares in the form of linear and non-linear dust acoustic which may gyrate in a plane perpendicular to the mag- 1 modes4? –8, dust lattice wave9,10, and dust vortices11–13. netic filed vector37? . Apart from the magnetic field, 0 The vortex structures in the dusty plasma, which is one neutral flow under some specific conditions can induce 7 1 of the examples of the dynamical structures, are results the dust mass rotation. The dust rotation under the : ofthecollectiveresponseofthemedium. Thesedynamic action of convective motion of background neutral gas, v structures are mainly established either by dust parti- is studied by Ivlev et al.38. In the case of gas convec- i X clesmotionordrivenmotionofplasmaspecies(electrons tion,dustrotationissetupbecauseoftheneutral–dragor r andions)inthedissipativemedium. Propertiesofthedy- thermophoretic force to dust grains39. All the previous a namicstructures,drivenbytheionsorelectrons,changes reported work suggests that dust dynamics is strongly while the external electric field or magnetic field is ap- affected by the motion of background species (electrons, plied. The vortex or rotational motion of dust particles ions and neutral) and can give different equilibrium dy- is widely studied in various dusty plasma systems. The namical structures. spontaneous rotation of dust grains14, two–dimensional Dynamics of the dusty plasma medium in inhomo- (2D) dust vortex flow15, cluster rotation16 poloidal rota- geneous plasma environment is still unexplored area tion of dust grains with toroidal symmetry17, and wave of research. Inhomogeneity in the plasma density and the electron temperature can triggers the various instabilities1,26,40 in the dusty plasma medium, which a)Electronicmail: [email protected] excites the various dust acoustic modes and dust vortex 2 motion. The dynamic structures (vortices) in the dusty respectively. X=0cmandY=0cmindicatethepoints plasmawithinhomogeneousplasmabackgroundhasbeen on the axis passes through the centre of the experimen- the subject matter of the present studies. tal tube. The centre of source tube is located at Z ∼ 12 Inthepaper, wereporttheonsetofmultipleco–rotating cm, whereas the dust reservoir (a stainless steel disk of dust vortices in a dusty plasma medium. Dust parti- 6 cm diameter with a step like structure of 5 mm width cles are found to transport and trap in a potential well and 2 mm height at its periphery) is located at Z ∼ 45 created by inductively coupled diffused plasma. Parti- cm. A rotary pump, attached to buffer chamber, is used cles are confined in a combined electric field of diffused to evacuate the experimental chamber at ∼ 10−3 mbar. plasma(ambipolarE–field)andwallcharging(sheathE– Afterwards the argon gas is fed into the chamber till the field). Various self–oscillatory motions of dust particles pressure attains the values of ∼ 4–5 mbar. Then the such as acoustic vibrations and vortex motion are ob- chamber is pumped down again to the base pressure. servedatdifferentdischargeparameters. Inaparametric This process is repeated three to four times to reduce regime, when acoustic vibrations are diminished, multi- the impurities from the vacuum chamber. Finally the ple co–rotating (in anti–clockwise direction) vortices are operating pressure is set to 0.04 mbar by adjusting the found to be appeared in the dusty plasma medium. Oc- gas dosing valve and pumping speed. A loop antenna (5 currenceofastabledynamicalstructure(vortex)industy turnsofcopperwire)iswoundedonthecylindricalsource plasmaexistsduetopotentialsourceswhichcompensates tube(Z∼12cmlongand8cmdiameter)asindicatedin the dissipative energy losses. The possible energy source Fig. 1(a). Plasma is produced in the source tube using to drive the vortex motion is charge gradient with elec- the 13.56 MHz RF generator, which later diffuses in the tric field and the ion drag force. The dust vortex has main experimental chamber. A snapshot of the diffused a characteristics size in the dusty plasma with inhomo- plasmaglowinX–Yplaneforagivenplasmaparameters geneous plasma environment which depends on various is shown in Fig.1(b). The boundary of glow region, as dusty plasma parameters such as dust–dust interactions, indicatedinFig.1(b), changeswithinputRFpowerand dustdensityetc.. Theexperimentalresultsshowstheap- gas pressure (not shown in the figure). pearance of multiple vortices when the dimension of the Thediffusedplasmainthemainexperimentalchamberis dustcloudbecomesmultipleofthisvortexsize.Thequal- characterizedthoroughlybydifferentelectrostaticprobes itative understanding is discussed in the light of a theo- namely, the single42 and double43 Langmuir probes and retical model19,25,26 based on characteristic scale length emissive probe44 in a working range of RF power (4–10 of dust vortex in the dusty plasma and it appears that W) at argon pressure p = 0.04 mbar. Plasma param- multiplevorticesispossibletoformintheextendeddusty eters traces along X and Y–axes for working discharge plasmawithinhomogeneousplasmabackground. Theex- parameters are depicted in the Sec.IV. perimental results on the vortex motion of particles are found in some agreement with the model. However, the detailed nature and the reason for multiple vortices are For injecting the kaolin dust particles (ρ ∼ 2.6 still under investigation through further experiments, as d gm/cm3 and r ∼ 0.5 to 5 µm) into the confining po- expanding Helical trajectories of dusts may not be ruled d tentialwell, asecondaryDCplasmasourceisused41. As out, because the camera having limited depth of focus these particles come into the plasma volume, they start due to limited illuminated zone, sees a 2D image of a 3D to flow in the ambipolar electric field of diffused plasma structure. and found to confine in the potential well created by the Themanuscriptisorganizedasfollows: SectionIIdeals diffused plasma41. These confined dust particles are illu- with the detailed description on the experimental setup, minated by the combination of a tunable red diode laser plasma and dusty plasma production and their charac- (632nmwavelengths,1–100mW powerand3mmbeam terization. The experimental observations of co–rotating diameter) and cylindrical lens (plano-convex). The dy- multiple dust vortices and their dynamics are discussed namics of the dust particles are then captured by a IM- inSectionIII.Quantitativeanalysisoftheoriginofmulti- PREX make CCD camera having frame rate of 16 fps pledustvorticesinthedustyplasmamediumisdescribed and spatial resolution of 2352 × 1768 pixels. A standard in Section IV. A brief summary of the work along with zoom lens of variable focal length (from 18 mm to 108 concluding remarks is provided in Section V. mm) is also used for the magnification purpose during the experiments. Maximum field of view at minimum zoom mode is 150 × 75 mm2 and it reduces to 25 × II. EXPERIMENTAL SETUP AND DIAGNOSTICS 12.5mm2 atmaximumzoommode. Thereisaprovision to image the dust cloud either in the X–Y or in the X–Z The experiments are performed in a cylindrical linear planesbychangingtheorientationofthecylindricallens, device, which is described elsewhere41 in details. The laser and camera. A video image of the full view of con- schematic of the experimental assembly with an operat- fineddustcloudintheX–YplaneatZ∼12cmisshown ing configuration is depicted in Fig. 1(a). In this experi- in Fig. 1(c). The series of images are then stored into a mentalconfigurationZ=0cmandZ=60cmcorrespond high-speed computer and later analyzed with the help of to the left and right axial ports (as shown in Fig. 1(a)), ImageJ and Matlab based available PIV software. 3 Rotary pump (a) Z = 12 cm Buffer Levitated particles RF Chamber Gas feed CCD Camera Flow Right axial port X Left axial port Dust reservoir Z = 0 cm Cylindrical Lens Z = 60 cm Z Z = 35 cm Laser P = 6 W (b) (C) 3 cm p = 0.0 4mb ar X = - 4 cm (x = 0, y = 0) Dust cloud axis Y Y X Y = - 4 cm X FIG.1. (a)Schematicofexperimentalconfiguration(topview). (b)AsnapshotofthediffusedplasmainX–Yplaneat∼12cm argongaspressurep=0.04mbar andRFpowerP=6W.Whiteclosedlooprepresentstheboundaryoftheleftaxialport(or left view port) and Yellow dotted line represents the boundary of the diffused plasma. Confined dust particles at the bottom of the glow is indicated by white spots. (c) A full image of the confined dust cloud in X–Y plane near the center of source tube(Z∼12cm). Dustparticlesrotationisindicatedbyayellowlinewitharrow. Thecirculararc(duetothereflectedlight) indicatestheinnerboundaryofglasschamber. Positionofdustcloudinthisplanecanbedeterminedbyusingthereferenceof yellowdottedlines. Greendottedlinesrepresentthetypicalmeasurementsaxis(alongXandYaxis)forgivenYandXvalues. Yellow dashed line represents the axis of the confined dust cloud in this plane. III. EXPERIMENTAL OBSERVATIONS ON DUST P = 7.5 W is displayed in Fig. 2(a). At this discharge VORTICES condition, almost all of the particles participate in rota- tionalmotionintheformofseparated,co–rotating,anti– clockwisemultiple(three)vortices. Itistobenotedthat As discussed in Section II, that dust particles are con- the vortices are found to be stable until the discharge fined near the centre of source region (at Z ∼ 12 cm) parameters are not changed. Small change in the ambi- and formed a 3D dusty plasma. Dynamics of the dust ent plasma parameters lead the distortion in the vortex particles in X–Y plane at Z ≈ 12 cm with different RF structures. Further reduction of input power causes the powersatfixedargonpressurep=0.04mbar isdepicted reduction of dust cloud dimension (due to the fall down in Fig.2. Five consecutive frames at time interval of 66 of the particles from the cloud edge) and as a result the ms are superimposed to get the information of the tra- inter–particle separation increases. At input power of jectories of the different particles. The contenious tra- P = 6.3 W, two co–rotating (anti–clockwise) dust vor- jectories are seen in the Fig.2(a)–Fig.2(c) for the par- ticesareobservedinthedustcloud(seeFig.2(b)). Dust ticles which follow a particular trajectory (or directed cloud length and dust density decreases with further re- motion), whereas the randomly moving particles show duction of power to 5.1 W. At this discharge condition, only the dotted points. At RF power of P > 8 W, the the dust particles form a elongated single vortex struc- dust particles participate in the wave motion (similar to ture (as shown in Fig. 2(c)) along the dust cloud axis. It Vaulina et al.19), which is not shown in the figure. The is worth mentioning that dust particles near the mouth dynamics of the particles when RF power is reduced at 4 ofthediffusedplasma(nearbytheplasmasource)always ture is similar to that of described in Sec. IV. exhibit the random motion. IV. ORIGIN OF DUST VORTICES MATLABbasedopenaccesssoftware(ParticlesIm- age Velocimetry) called openPIV45 is used to determine the direction and the magnitude of the particles veloci- For the formation of a steady-state equilibrium dust tiesineachvortexstructure. Forconstructingthevector vortex, as described in Sec. III, energy dissipation of the field, an adaptive 2-pass algorithm (a 64×64, 50% over- particles due to frequent dust–neutral collision and/or lap analysis, followed by a 32×32, 50% overlap analysis) dust–dust interaction has to be balanced by the avail- isconsidered. Thecontourmapoftheaveragemagnitude able free energy to drive the vortex motion. The spatial ofthevelocity,constructedafteraveragingtheflowfields dependence of dust charge is one of the possible mech- of40frames,isshowninFig.3. Thedirectionofthefield anisms to convert the potential energy into the kinetic vectors(shownbyarrowsinthefigure)representsthedi- energy of the dust particles19,25,26, which results in to rection of particles motion in X–Y plane. The average drive the vortex flow in a dusty plasma. The monotonic velocity profile of the rotating particles shows that the variation (gradient) of dust charge in a dusty plasma oc- velocity of particles is not uniform in a particular vor- casionallyoccursduetoinhomogeneityoftheplasmapa- texstructure, asshowninFig.3(a). Theparticlesrotate rameters such as electrons (ions) density (ne(i)) and/or with minimum velocity at the centre of vortex, whereas electrons (ions) temperature (Te(i)). In addition to that, itincreasestowardstheboundary. Thevelocityprofileof non–dispersive nature of the dust particles sometimes thethreevortices(seeFig.3(a))attheirboundaryclearly also plays an important role to create a charge gradi- shows that the particles in the biggest vortex (vortex–I) ent in a dusty plasma. The present studies are carried have maximum velocity and minimum in smallest vor- outinainductivelycoupleddiffusedplasma,whereinho- tex(vortex–III).Itisworthmentioningthattheinterface mogeneity in Te and ne(i) are expected, that causes the (havinganti–parallelflow)oftwoconsecutivevorticesare charge gradient along the length of dust cloud. Theoret- well separated. However, it is noticed that the magni- ical analysis and numerical simulations show such type tudeoftheparticlesvelocityinvortexstructuredepends of dynamical structures (vortices) in the presence of a on the density of dust particles. The maximum velocity dust charge gradient, β(cid:126) = ∇Q = e∇Z , orthogonal to d d oftheparticles(atboundary)inthevortexstructurede- a nonelectrostatic force F(cid:126) such as gravitational force non creaseswiththedecreaseofinputRFpowersasshownin (F(cid:126) ), ion drag force (F(cid:126) ), or thermophoretic force (F(cid:126) ) g I th Fig. 3. The maximum velocity (for vortex–I) is observed actingonthedustparticlesinthedustcloud19,25,26. The ∼ 4 mm/sec and ∼ 2 mm/sec at input power P = 7.5 roleofnon–electrostaticforces(F(cid:126) )intheformationof non W and P = 5.1 W, respectively. It is also to be noted dynamical structure in the dusty plasma is determined that all the dust particles do not follow a closed path by their capacity to hold the particles in the region of in the X–Y plane (some of the particles move to other non-zero electric field. Vaulina et al.19,25,26 have car- plane) but the dust density remains nearly constant in riedanextensivestudytoexplaintheselfoscillatorymo- the vortices. The radial distribution of the particle rota- tion (acoustic vibrations, vortex etc.) in a dusty plasma tion speed and angular velocity (ω) for vortex–I at P = with inhomogeneous plasma background. In such dusty 6.3 W is displayed in Fig. 4. It is observed that the par- plasma medium, they found that the curl of total force ticlerotationalspeedincreaseslinearlytowardstheouter actingontheindividualparticleisnon-zeroduetoafinite edge of the vortex. The rotational speed of particles is valueofβ(cid:126)×E(cid:126). Inthiscase,theelectricfielddoesthepos- found to be higher with the large number of dust grains itive work in compensating the dissipative energy losses. involving informationofvortexstructure. Itisalso seen As a result an infinitely small perturbation, emerging in thattheangularvelocityofrotatingparticleshasaradial thedustcloudduetothermaland/orchargefluctuation, variation toward the outer boundary of the vortex. will grow in the system in the absence of restoring force As the dust cloud is extended along the axis of the and causes an instability in the dusty plasma, known as experimental chamber (along Z–axis), therefore it needs dissipative instability19. The evolution of this instability to investigate the dynamical structures in the different givesrisetoaregulardynamicstructures(vortices). The X–Y planes (i.e., at different Z location). Observation particle in dust cloud starts to move in the direction of of the dust vortices in different planes are shown in F where particle has its maximum charge value and non Fig. 5(a)–Fig. 5(c). It should be noted that the dust form a vortex structure. In the vortex motion, the vor- cloud has its maximum dimension near the center of the ticity (Ω = ∇×(cid:126)v ) is non zero along a certain closed d source region (Z ∼ 13 cm), which then decreases if one curve. The frequency (ω) of the steady-state rotation of goes away from the source region. Number of vortex particles in a vortex structure is given by19,25,26, structures depends on the dimension of the dust cloud. F β For an example at P = 7.5 W and p = 0.04 mbar, three ω =| non |, (1) M eZ ν vorticesare formedatZ ∼ 13 cm, whereasatotherloca- d 0 fr tions(Z∼10and16cm)onlytwovorticesareobserved. where Z = Q /e is charge on the dust particle at an 0 d0 The velocity distribution of particles in the vortex struc- equilibriumpositionintherotatingplane. Inthepresent 5 (a) I P = 7.5 W 10 mm (b) P = 6.3 W 10 mm (c) P = 5.1W 10 mm III II Y II g I X I FIG. 2. Video images of dust cloud in the X–Y plane at Z = 12 cm. Images ((a)–(c)) are obtained with the superposition of fiveconsecutiveimagesattimeintervalof66ms. Thedynamicalstructuresintheextendeddustcloudinthisplane: Fig.2(a)– Fig.2(c)forinputRFpower(P)7.5W,6.3W,and5.1Wrespectively. Yellowlineswitharrowindicatesthedirectionofvortex motion of dust grains, arrow indicates the direction of gravity, and dashed line corresponds to the axis of dust cloud. The vortexrepresentation(I,II,andIII)aremadebasedonthenumbernotationfromtheedgeofthedustcloud. Kaolinparticles are used to perform the dusty plasma experiments at argon pressure of 0.04 mbar. c e s m/ m 0.5 1 1.5 2 2.5 3 3.5 4 −0.5 −0.5 (a) (b) (c) −1 −0.5 m) −1 −1.5 c ( n −2 −1.5 −1 o ti −2.5 si −2 o −3 −1.5 p Y− −3.5 −2.5 −4 P=7.5W P=6.3W −2 P=5.1W −3 0 1 2 3 4 5 0 1 2 3 0 0.5 1 1.5 2 2.5 X−position (cm) X−position (cm) X−position (cm) FIG. 3. Images show the velocity distribution of dust particles in a vortex structure for different input RF powers (Fig.2). Theimages(Fig.3(a)–Fig.3(c))areobtainedafterPIVanalysisofthecorrespondingstillimages. Velocityvectorsshowingthe direction of rotation of the dust particles in the X–Y plane at Z ∼ 12 cm. Color bar on the images show the value of the dust velocity in mm/sec. Three anti–clockwise co–rotating dust vortices are observed in the extended dust cloud at P = 7.5 W (Fig.3(a)). Dust cloud supports only two co–rotating vortices when input power is 6.3 W (Fig.3(b)). A single anti–clockwise dust vortex is observed at power of 5.1 W (Fig.3(c)) The argon gas pressure is kept fixed at 0.04 mbar I . I experimental configuration, dust cloud is confined in the Y plane is displayed in Fig. 6. According to Matsoukas X–Y plane as shown in Fig. 1(c). It is realized that the and Russel’s47, the charge on the dust grain (Q ) can be d non–electrostatic force F(cid:126) required for the formation expressed as: non of the vortex motion of particle is induced by the di- (cid:18) (cid:19)1 rectional motion of ions relative to the dust particles, Q =eZ ≈C4πrdkBTelnni meTe 2 , (2) i.e. F(cid:126)non = F(cid:126)I (ion drag force)46. Hence F(cid:126)non can be d d e2 ne miTi replaced by F(cid:126)I in the eq.(1) to obtain the angular fre- where rd is radius of the micro-particle, kB is Boltz- quency of the rotation. It should be noted that the force mann’s constant, e is the electron charge, n and n e i experienced by the particle due to gravity is found not are the electron and ion densities, m and m are their e i to be orthogonal to charge gradient therefore its role on masses,andT andT aretheirtemperatures. Foratyp- e i the vortex motion is not included in the calculations. ical argon plasma, the constant comes out to be C ≈ However, its component along the ion drag force also 0.7347. contributes in the vortex motion. The schematic rep- Ion drag force F(cid:126) = F Eˆ, where F is magnitude of I I I resentation of the vortex motion in presence of charge the ion drag force which can be expressed as48: gradient (β) and non–electrostatic force (F ) in the X– I F =n v m v (πb2+4πb2 Λ), (3) I i s i i c π/2 6 3 .5 1 .0 v (m m /s e c ) d 3 .0 w (ra d /s e c ) 0 .9 for different RF powers. Te is observed to be high near plasma source (at X ∼ -7 cm) and decreases along the ) ) 2 .5 0 .8 c length of diffused plasma (from X = - 7 to X = 3 cm). c e se /s Inhomogeneity in Te is also observed along the X–axis / 2 .0 0 .7 d for different Y values (Y = 0 to - 5 cm). The variation mm (ra of Te along the Y–axis at X = - 4 cm and Z = 12 cm is (d1 .5 0 .6 w depicted in Fig. 7(b). It is clear from Fig. 7(b) that Te v is also varied along Y–axis for different RF powers. Sim- 1 .0 0 .5 ilar trend is also observed for different X–values (X = -7 cm to X = 2 cm). It is also observed that T increases e 0 .5 0 .4 with increase in the RF power (4 W to 10 W) at given 1 2 3 4 5 6 X and Y locations. Using the different sets for T pro- e R a d ia l d is t a n c e R ( m m ) files along X and Y–axes, Fig. 7(c) is constructed which shows the variation of T along the axis of confined dust e FIG. 4. Radial variation of rotation speed of particles and cloud. Fig.7(c) confirms that there exists a finite gradi- angular velocity for Vortex-I (Fig. 2(b)) at P = 6.3 W and p entinelectrontemperaturealongthedustcloudaxisata = 0.04 mbar. given RF power. Similar to T , plasma density n is mea- e sured along the dust cloud axis. Typical plasma density variation along the X–axis at Y = -4 cm and along Y– where m is ion mass, v is mean speed of ion, v is ion i s i velocity, b is collection impact parameter48, b is the axisatX=-3cmwithdifferentRFpowersareshownin c π/2 Fig. 8. It is found that the plasma density varies mono- impactparameterwhoseasymptoticangleisπ/2andΛis the coulomb logarithm48. The neutrals (either in rest or tonicallyalongthelengthofdiffusedplasma. Itishigher near plasma source and decreases towards the chamber in motion) affect the motion of the dust particles in the wall. Similar to previous case, the plasma density profile plasma. In the present set of experiments, the direct gas flow inside the chamber is negligible41 thus neutrals are along the dust cloud axis as shown in Fig. 8(c) is ex- tracted from the measured sets of density profiles along assumedinthermalequilibrium(orstationary). Accord- ingtoEpsteinfriction49,theneutralfrictionexperienced X axis at different Y values and along Y axis at different X values. Similar to T there exist a density gradient by the dust particles can be given by e along the dust cloud axis. For the estimation of dust F(cid:126) =−m ν (cid:126)v , (4) charge and its gradient using Eq. (2), an average radius n d fr d of ∼ 2 µm is considered. According to this expression, where ν is the dust–neutral friction frequency and v thereexistsachargegradientduetothepresenceofelec- fr d is dust particle velocity. The expression for ν 50 is tron temperature gradient and plasma density gradient fr as shown in figure Fig. 7(c) and Fig. 8(c). However, the 8√ m (cid:16) π(cid:17) ν = 2πr2 nn v 1+ , (5) effect of density gradient on the dust charge gradient is fr 3 dmd n Tn 8 negligible for a quasi-neutral plasma (see eq. (2)). wherem ,n ,andv arethemass,numberdensity,and For the estimation of electric fields along X and Y di- n n Tn thermal velocity of the neutral gas atoms, respectively. rections near the region where dust particles get levi- To estimate the angular velocity of dust rotation, it is tated, an emissive probe is used to measure the plasma necessary to estimate the dust charge gradient β along potential(V ). Thevariationofplasmapotentialprofiles p the dust cloud axis and ion drag force F , which are as- are plotted in Fig. 9 for different RF powers. Fig. 9(a) I sumed orthogonal to each other. It is described in the shows the potential profile along X–axis for Y = - 4 cm, Sec.III that the dust cloud axis always lies in the X–Y whereas Fig. 9(b) shows the same along Y–axis for X = plane, as shown in Fig. 1(c)). For calculating the dust -4cmatcentreofsourcetube(atZ∼12cm). Itistobe chargegradientalongthedustcloudaxis,plasmaparam- noted that the plasma potential gradient near the glass eters such as n and T are experimentally measured. In wall (or diffused edge) is observed to be higher at higher e e the present experimental configuration, it is very diffi- RF power. The strong gradient gives higher E–field near culty to trace the plasma parameters along the axis of the glass wall. The vertical E–field (along Y–axis) com- the dust cloud. Therefore, the plasma parameters are ponent holds the particles against gravity and the hor- scanned along the X–axis for given Y location and along izontal component (along X–axis) confines the particles theY–axisforgivenXlocationataparticularZposition. as discussed in ref.41. As shown in the Fig. 9(a), the These measurements are used to reconstruct the profiles X–component of E–field is negligible (flat V ) inside the p of plasma density and electron temperature along the dustcloud(fromX=-3to1cm)andithasfinitevalueat axis of the dust cloud. both the boundaries of the dust cloud. It is worth men- ThevariationofT alongtheX–axisatY=-3cmand tioning that the direction of E–field (Eˆ) is perpendicular e Z = 12 cm for different RF powers in absence of parti- to the curved glass wall as shown in Fig. 1(c), which is cles is shown in Fig. 7(a). It is seen in Fig. 7(a) that orthogonal to the dust cloud axis (or along the direction there is non–uniformity (or gradient) in T along X–axis of charge gradient). e 7 (a) Z = 10 cm 5 mm (b) Z = 13 cm 5 mm (C) Z = 16 cm 5 mm Y III II II g II I X I I FIG. 5. Video images of dust cloud in different X–Y planes. All the images are obtained with the superposition of five consecutive images at time interval of 66 ms. Fig.5(a)– Fig.5(c) corresponds to Z = 10 cm, Z = 13 cm and Z = 16 cm, respectively. Yellowlineswitharrowindicatesthedirectionoftherotatingparticlesintheextendedcloud. TheRFpowerand gas pressure are 7.5 W and 0.04 mbar, respectively. Moreover, the direction of rotation of the observed dust vortex is also consistent with the direction predicted in 𝛽 their theoretical model. The characteristic size D of vortices can be obtained 0 fromtheviscosity(η )ofthedustyplasmamedium51,as k 𝐹I D0 = α(cid:0)ηk/(ω∗+νfr)1/2(cid:1), where ω∗ is effective dusty plasmafrequencyandαtakesintothedifferencebetween viscosity in quasi–stationary and dynamic vortex struc- Y ture. The coefficient is estimated as α ≈ 4951. The variation of kinetic viscosity (η ) with a wide range of k discharge parameters and coupling parameter (Γ) is dis- X g cussed by Fortov et al.52. For the present set of experi- Cloud axis ments, effective coupling constant (Γ∗)51 has the values between 10 to 100 for the particle of size (r ) ≈ 2 µm, d FIG. 6. Video image of dust cloud in the X–Y planes with inter–particle distance (d) ≈ 700–900 µm, particle tem- directionofchargegradient(β)andiondragforce(FI). The perature (Td) ≈ 0.2–0.4 eV and dust charge (Qd) ≈ 1–5 directionofrotationisdisplayedbyayellowlinewitharrow. ×10−15C.Inthisparametricregime,thekineticviscosity Dust grains rotate in the direction of the gradient of dust η is considered to be ∼ 0.01 to 0.04 cm2s−1 similar to k charge. the value report in refs52,53. The characteristic size (D ) 0 of the vortices (shown in Fig 2(a)) for the parameters: η = 0.02–0.03 cm2s−1, ν ∼ 8 s−1, dust Debye length k fr Thechargegradientalongtheaxisofthedustcloudis (λ )≈130µmandω∗ ≈40s−1comesouttobe∼11–15 D defined as ∇Q = (Q −Q )/(d −d ), where d and mmwhichisinclosematchwiththeexperimentallymea- d d2 d1 2 1 1 d are the two spatial points on the dust cloud axis. For sured vortex diameter (12−17 mm). As the dimension 2 a quantitative analysis, only average sized particles (∼ of dust cloud in this discharge condition is L ∼ 55 mm, 2 µm) are considered based on the force balance condi- hence the formation of multiple (n = L/D ∼ 3) vortex 0 tions. As shown in Fig. 4, the observed value of angular is possible to be accommodate in the dust cloud. In ac- frequency (ω ) at P = 6.3 W and p=0.040 mbar is cordance with the above theoretical estimation, we also exp found to be in the range of ∼ 0.5–0.8 rad/sec. Theo- find three vortices to form in our experiments. As dis- retical estimated value of angular frequency (ω ) comes cussed in the Sec. IV, the length of dust cloud reduces th out to be ∼ 0.5 rad/sec for β/eZ ∼ 0.08 cm−1, M ∼ 8 withloweringtheRFpowerbyloosingtheparticles. The 0 d ×10−14 kg, F ∼ 7 ×10−14 N and ν ∼ 8 sec−1. Sim- length of dust cloud reduces from ∼ 55 mm to ∼ 25 mm I fr ilarly, ω and ω are found to be ∼ 0.6–0.9 rad/sec atP=5.1W.Inadditiontothat,theaveragevortexsize exp th and0.4–1.1rad/secatP=7.5W,respectively. Atlower alongtheaxisofthedustcloudincreasesto∼16–19mm power (P = 5.1 W), experimentally measured angular (see Fig. 2(c). For this discharge condition, the charac- frequency ω ∼ 0.5–0.6 rad/sec is comparable with the teristic size (D ) of the vortex is estimated as ∼ 11–16 exp 0 estimated angular frequency ω ∼ 0.4–0.6 rad/sec. It mm for η ≈ 0.02–0.04 cm2s−1, ω∗ ≈ 30 s−1 and Γ∗ ∼ th k canbeconcludedthatthemeasuredvaluesofangularfre- 60, which agrees well with the observed average size of quencyandthetheoreticallypredictedvalues(byVaulina the vortex. Therefore in this case, the number of vortex et al.25) are in good agreement for different RF powers. becomes n = L/D ∼ 1 as seen the experiment. The 0 8 7 7 8 P = 6 .3 W ( a ) P = 7 .5 W ( b ) P = 7 .5 W ( C ) P = 5 .1 W P = 6 .3 W 7 P = 6 .3 W 6 6 6 )5 5 5 V (e4 4 4 e T 3 3 3 2 2 2 1 -8 -6 -4 -2 0 2 4 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 P o s itio n X ( c m ) P o s itio n Y ( c m ) L e n g th a lo n g th e d u s t c lo u d ( c m ) FIG. 7. (a) Electron temperature (T ) variation along X–axis at Y = - 3 cm and Z = 12 cm for two RF powers P = 6.3 W e and5.1W.(b)Electrontemperature(T )variationalongY–axisatX=-4cmandZ=12cmfortwoRFpowersP=7.5W e and6.3W.(c)Electrontemperature(T )variationalongtheaxisoftheconfineddustcloud. Theargonpressureissetat0.04 e mbar during the experiments. All the measurements are taken in the normal plasma (without dust particles). 2 .0 x1 0 8 (a ) PP == 75..51 WW PP == 76 ..53 WW (b ) 8 x1 0 8 PP == 76 ..53 WW (C ) 6 x1 0 8 1 .5 x1 0 8 6 x1 0 8 -3 (cm)1 .0 x1 0 8 4 x1 0 8 4 x1 0 8 n5 .0 x1 0 7 2 x1 0 8 2 x1 0 8 0 .0 0 0 -8 -6 -4 -2 0 2 4 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 P o s itio n X (c m ) P o s itio n Y (c m ) D is ta n c e a lo n g d u s t c lo u d (c m ) FIG. 8. (a)Plasma density (n) variation along X–axis at Y = - 3 cm and Z = 12 cm for two RF powers P = 6.3 W and 5.1 W. (b) plasma density variation along Y–axis at X = - 3 cm and Z = 12 cm for two RF powers P = 7.5 W and 6.3 W. (c) plasma density variation along the axis of the confined dust cloud for two powers P = 7.5 W and 6.3 W. The argon pressure is set at 0.04 mbar during the experiments. All the measurements are taken in the normal plasma (without dust particles) above preliminary understanding of multiple vortices is charge plasma is struck to introduce the dust particles discussedinthelightofcharacteristicscalelengthofdust into the plasma. These charged particles are drifted in vortex. However, there may be a possibility to exist an the ambipolar electric field of the diffused plasma and expanding Helical trajectories of dusts and the camera, start to confine in the electrostatic potential well, where having limited depth of focus due to the limited illumi- the particles are trapped in the E–field which is result nated zone, sees a 2D image as multiple-vortices of a 3D ofthediffusedplasma(ambipolarE–field)andglasswall expandinghelicalstructure. Thedetailednatureandthe charging(sheathE–field). Ataparticulardischargecon- reason for multiple vortices are still under investigation ditions, well separated, co–rotating, anticlockwise mul- through further experiments and will be reported in fu- tiple vortices are found in the extended dusty plasma ture. medium in the X–Y plane. At moderate RF power, two vortex structures are observed in the dust column. Only one vortex formed in the dusty plasma medium at lower RF power. The rotation speed is found to be non– V. SUMMARY AND CONCLUSION uniform throughout the vortex structure and increases towards the boundary of vortex. The angular frequency In this paper, an experimental observation of the for- of the rotation based on the model provided by Vaulina mation of multiple co–rotating dust vortices over a wide et al.19,25 is found in close agreement with the experi- range of discharge parameters is reported. 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