Dust Charging in Collisional Plasma in Cryogenic Environment

J. Plasma Fusion Res. SERIES, Vol. 9 (010) Dust Charging in Collisional Plasma in Cryogenic Environment Natsuko UOTANI, Jumpei KUBOTA, Wataru SEKINE, Megumi CHIKASUE, Masako SHINDO an Osamu ISHIHARA Faculty of Engineering, Yokohama National University 79-5 Tokiwaai, Hoogaya-ku, Yokohama 40-8501, Japan (Receive: 30 October 009 / Accepte: 31 January 010) Dust charging in a plasma in cryogenic environment is stuie experimentally. RF helium plasmas are prouce at cryogenic temperature as well as at room-temperature. Dust particles introuce into a plasma are tracke by CCD camera an analyze by PTV (Particle Tracking Velocimetry) metho. Dust charges in a wie range of temperature an pressure are etermine by two ways, (1) oscillating trajectory of a ust particle aroun an equilibrium position in a sheath an () eflecte trajectory of a charge ust particle coming out of plasma in DC electric fiel. Dust charge in cryogenic environment is foun to be lower than the one at room-temperature. The observe lower charge states are explaine by a moel with cryogenic ion temperature an ion-neutral collisions. Keywors: complex (usty) plasma, strongly couple system, ust charge, collisional effect, temperature effect, liqui helium, echarging process 1. Introuction Dust particles in a plasma have been stuie extensively over the last few ecaes. A complex (usty) plasma is a plasma with micron size ust particles an has been attracting much attention to the community of inustrial plasma, space plasma as well as laboratory plasma [1,]. Recent stuy of complex plasma has been extene to fusion plasma since ust particles originate from plasma-surface interaction were observe in fusion evices [3,4]. In fusion, inustrial or space plasmas ust particles are born in a plasma, but laboratory complex plasma can be prouce easily by injecting soli (conuctive or ielectric) particles into a plasma. Dust particles immerse in a plasma are charge negatively because of higher mobility of electrons than ions. The charge of a ust particle with a raius of 1~10 μm is typically -10 3 e~-10 5 e, where e is elementary charge. Because of the nature of large charge of a ust particle, Coulomb coupling parameter Γ efine by a ratio between Coulomb potential energy an kinetic energy of ust particles coul be higher than 1 uner laboratory plasma conitions. Larger coupling parameters (Γ 1) characterize the orere structure of ust particles calle Coulomb crystal [5-7]. Recent experiments on complex plasmas are focuse on microgravity conition to investigate the nature of a complex system in a three-imensional symmetrical plasma [8,9]. A cryogenic complex plasma is an emerging fiel to stuy ust-plasma interaction in an extreme conition [10,11]. Earlier experimental stuies suggeste the possible prouction of cryogenic plasma by pulse ischarge in liqui helium [1,13] an ultracol plasma by a metho of laser cooling [14]. A DC ischarge plasma with ust particles in cryogenic conition was prouce an interparticle istance between ust particles was reporte to ecrease with ecreasing temperature [15-17], while our experiment showe constant interparticle istance in a backgroun temperature of 77K an 300K [18]. Figure 1 shows our recent experimental results in the range of 4.K to 300K. Theoretical stuy on cryogenic complex plasma suggeste two-imensional ust structure on the surface of liqui helium [19] an a quantum effect on a pair of ust particles [11]. The Coupling parameter Γ coul be much higher than 1 on the surface of liqui helium, so the two-imensional system of charge ust particles is expecte to be observe in the crystal phase. Dust charge is a funamental parameter for a complex plasma an is neee to be explore in etail uner a cryogenic conition. Interactions of ust particle with electrons, ions an ust particles are etermine by their charge states. We etermine ust charge experimentally by using two experimental setups. Dust Fig. 1. Observe Coulomb cluster of ust particles in horizontal plane for [T n (K), P(Pa)] = (a) [4., 0.9] (b) [77, 60] (c) [300, 60]. Interparticle istance is ~0.5mm. author s e-mail: 09g08@ynu.ac.jp (N. U.) 404 010 by The Japan Society of Plasma Science an Nuclear Fusion Research

particles are introuce to a helium plasma prouce in cryogenic gas [18,0] or in liqui helium vapor [1]. In this paper, we present backgroun temperature an collisional effects on ust charges. In Sec., experimental observation of ust oscillations uner cryogenic conition an a moel for charge etermination are escribe. In Sec. 3, we show eflecte trajectories of ust particles in the vapor of liqui helium between parallel electroes an echarging process of ust particles. In Sec. 4, etermine ust charge state is iscusse. The paper is conclue with results an iscussion in Sec. 5.. Helium plasma in cryogenic gas (YD-1) A. Experimental setup Our experimental setup was escribe briefly in Ref. [18]. In our earlier experiment, ynamics of ust particles in RF helium plasma was stuie in vertical long glass tube at room-temperature [] as well as at cryogenic temperature [18,0]. The cryogenic experimental apparatus YD-1 (Yokohama Dewar No. 1) is a ouble silver-coate glass Dewar bottles with the inner iameter of 9.6 cm an the height of 80 cm. Two Dewer bottles have about 1 cm wie vertical uncoate slit on their sies for observation of a complex plasma. The inner Dewar bottle fille with liqui helium (LHe) or liqui nitrogen (LN ) is place in outer Dewar bottle. Outer Dewar bottle fille with liqui nitrogen helps keeping cryogenic liqui longer by avoiing inflow of heat. A ischarge glass tube set in inner Dewar bottle is shown in Fig.. The glass tube is ~70 cm in length consisting of a thin upper part of 60 cm in length with 1.6 cm in inner iameter an a thick lower part of ~1 cm in length with 5 cm in iameter. The glass tube is connecte to an external stainless steel pipe at the flange attache to the inner Dewar bottle. An RF helium plasma with a neutral gas pressure P = 0.1~100 Pa is prouce in the lower part of the glass tube by applying RF (13.56 MHz) voltage of ~50 V between two ring plate electroes of 4 cm in outer raius an 1 cm in inner raius. Neutral pressure is measure by capacitance iaphragm gauge place above the flange. The plasma is characterize by the electron ensity of n e ~ 10 15 m -3 an electron temperature T e of a few ev, while ions lose their kinetic energy through collisions with coole neutrals. The backgroun gas temperature is controlle by containing the cryogenic liqui, liqui helium or liqui nitrogen, in the inner Dewar bottle. Acrylic particles (ust particles) of a = 0.4~10 μm in raius with a mass ensity of ρ = 1. g/cm 3 are roppe from ust ropper situate about 80 cm high from the bottom of the glass tube. The ust particles charge in the plasma are suspene aroun an equilibrium position where the sheath electric force balances with the ownwar gravitational force. The equilibrium height from the bottom of the glass tube h eq = 5~30 mm epens on the temperature an pressure conitions. The ust particles illuminate by green laser (λ = 53 nm) are visible by nake eyes. To observe vertical motion of a ust particle in the plasma, particles are roppe from the ust ropper. Dust particles are accelerate in the long glass tube uner the gravity. The ust particles immeiately charge after entering the plasma go further below the equilibrium position an go eeper in the sheath. The electric force acts upwar on a negatively charge ust particle in the sheath moves the particle upwar against gravity. Dust motion is recore by high-spee CCD camera from the sie at a frame rate of 100~400fps, an analyze by using PTV (Particle Tracking Velocimetry) metho. In PTV metho velocity an acceleration are measure by etection of the particle position in each frame. Our earlier experiment showe two ust particles to form vertical pair moving upwar along the ion flow in the sheath affecte by the wake fiel []. Fig.. Experimental setup of YD-1. RF helium plasma is prouce in a glass tube surroune by cryogenic liqui. Fig. 3. Dampe ust oscillations aroun equilibrium positions at 4.K for (1) 0.6 Pa an () 0.9 Pa. The equilibrium position, the oscillation frequency an ecay time constant epen on the neutral pressure. 405

Fig. 4. Dust charge with iameter a = 0.8, 1.5 μm as a function of pressure for 300 K, 77 K an 4. K. Dust charges change with temperature while ust charges remain nearly constant with the variation of pressure. Fig. 5. Experimental setup of YD-. Plasma is prouce in the liqui helium vapor. B. Neutral temperature in helium plasma Temperature of neutral particles in RF helium plasma is etermine by observing vertical ust oscillation in a liqui nitrogen conition [18]. Figure 3 shows typical ampe oscillations aroun equilibrium positions of a = 0.8 μm in a cryogenic (LHe) conition for various pressures. Dust trajectory uner cryogenic temperature as well as room temperature is escribe by the equation of motion for a ampe harmonic oscillator, m h +γh +k(h-h eq )=0, where m is mass of a ust particle, h is vertical height of a ust particle, γ is friction coefficient of neutral gas an k is a spring constant in the ust oscillation motion. Frequency of ust oscillation ω, equilibrium height h eq an amping time constant τ is measure from the trajectories. The friction coefficient γ etermine by m /τ is typically ~10-15 kg/s for neutral ensity n n ~ 10 m -3 an backgroun helium temperature T n ~ 4. K, which agrees reasonably well with the friction coefficient given by Epstein [3] as 4 ( Tn ) n nmna cn ( Tn ), (1) 3 where δ is a constant value with 1.0~1.44 epening on the type of reflection, m n is mass of a neutral particle an c n =(πk B T n /8m n ) 1/ is mean velocity of neutrals (k B : the Boltzmann constant). The backgroun helium gas temperature in the glass tube is sufficiently coole by surrouning cryogenic liqui while proucing RF helium plasma [18]. C. Dust charge in cryogenic helium plasma Experiment at cryogenic temperature is carrie out. Various sizes of ust particles with a = 0.8, 1.5, 3, 5, 10, 0 μm are roppe from the ust ropper an are fully charge in the plasma. Smaller ust particles are suspene in the sheath electric fiel, while lager ust particles reach the bottom of the glass tube without suspension. The ust suspension is observe for a 10μm at 300K, a 5μm at 77K an a 3μm at 4.K. Dust charge number Z is etermine by [18,4,5] Z am h ( ) / e, () 0 0 where ε 0 is permittivity of vacuum an h 0 =h eq -m g/k (g: gravitational acceleration). Typical values of ω = 30~150 ra/s, τ -1 = ~15 sec -1 an h eq = 5~30 mm epen on temperature an pressure. Dust frequency ω an inverse ecay time constant τ -1 are foun to increase with pressure, while equilibrium height h eq is lowere. Figure 4 shows ust charge with a = 0.8 an 1.5 μm. The charge is foun to ecrease with ecreasing backgroun temperature T n. Dust charges with a = 0.8 μm are smaller than the values of ust charges with a=1.5 μm in the temperature range of 4.K to 300K. 3. Plasma above liqui helium surface (YD-) A. Experimental setup The cryogenic apparatus YD- (16 cm in inner iameter an 1 m in height) is use to prouce a plasma in a liqui helium vapor as shown in Fig. 5. A localize plasma in the liqui helium vapor is prouce by applying RF voltage between neele electroes. The RF ischarge plasma is prouce by applying voltage (10kHz, ~6kV) to tungsten wire neele electroes. The two neeles are separate by 1~ mm an mounte on an acrylic plate having the central hole 18 mm in iameter. The liqui helium is kept in a superflui state by ecreasing the pressure below 0.1 atm. The plasma with neutral ensity of n n ~ 10 6 m -3 is prouce locally near the electroes in high gas pressure (6~8kPa) with the electron ensity n e ~ 10 15 m -3 an electron temperature T e ~ 5 ev, characterizing the electron Debye length De ~ 0.5 406

Fig. 6. (a) Charge variation in y irection. (b) Deflecte ust trajectory in (x, y) plane. Distance y is measure from the lower ege of the localize plasma. Dust charge ecreases with istance away from the plasma. Time interval between recore points is.5 msec an ust particles are shown to move faster at 4 K than 300 K. mm. Dust particles are supplie from a ust ropper near the flange an fall through thin stainless steel tube of 1 m in length with mm in iameter. Once ust particles reach the neeles, they are charge by the plasma. Dust particles gain enough energy by gravitational fiel before reaching the plasma to move through the plasma an go ownwar further away from the plasma. Then charge ust particles enter the region where two parallel plates prouce electric fiel in the horizontal irection. Dust particles are eflecte in the electric fiel an their trajectories are recore by CCD camera. Since the plasma extens harly to the region between the parallel electroes, as confirme by a probe, electric fiel between two parallel electroes is approximate by the vacuum fiel. B. Moel of charge etermination The trajectories of the ust particles with ust charge Q = Z e an mass m in the electric fiel E are escribe by Q m Ε ( x γx ), (3) E where x an x are velocity an acceleration of a ust particle at location x, respectively. An x =(x,y), x is in the horizontal irection an y is in the gravitational irection with the origin at the center of the neele electroes. The friction on a ust particle is cause by collisions between ust particles an neutral helium atoms. The friction coefficient γ is given by g x g 1. (4) g g x By setting E=Ee x an g=ge y. Eq. (3) can be expresse in terms of velocity components as Q m 1 [ v x ( v y g) tan ], (5) E where tanθ=v x /v y. The values of θ, v x an v y are measure by PTV metho. The variable DC voltage in the range of ±300 V is applie between the two parallel plates (8 cm by 3.4 cm) separate by 4. cm. The electric fiel uner the plasma is prouce uniformly in the x irection. Any effect by the iffuse plasma to the electric fiel is negligible because of the localize nature of the plasma. Charge ust particles are observe to fall without eflection in the absence of electric fiel. C. Deflecte trajectory between DC electroes The bright ischarge plasma extens to a region of about ~1 mm in thickness an ~1 cm in with. The falling ust particles pass through the hole on the acrylic plate with the thickness of 5 mm. The perio to cross the plasma region is about 0.01 sec, which is sufficiently longer than charging time ~10-7 sec. Observe positions of typical ust particles an their charges at the point are shown in Fig. 6. Deflecte irection of trajectories confirms the charging state of ust particles as negative. Charges of ust particles are foun to ecrease exponentially as ust particles leave the plasma. To confirm the cryogenic effect on the echarging process, we prouce helium plasma at 300 K, 1~10 kpa with the same backgroun neutral ensity in the liqui helium vapor an measure charges of ust particles. Charges of a ust particle are foun to be several times larger than the one in cryogenic environment. The friction 407

coefficients are estimate as γ ~ 10-1 kg/s at 300 K an γ ~ 10-13 kg/s at 4 K. The viscosity of helium gas ecreases as temperature reuction. We foun Q ~ -500e for a = 1.5 μm, ρ = 1. g/cm 3. Since many electrons are attache to ust surface a massive ust particle behaves as a negative charge career in a plasma. Charge to mass ratio of a particle characterizes its ynamics in a complex plasma. Charge to mass ratio of a ust particle Q /m ~5 10-3 C/kg is much smaller than electron charge to mass ratio e/m e = 1.76 10 11 C/kg. But the charge of ust particle is enough to respon to electric force. It shoul be note that some ust particles are observe to be trappe in the plasma or eflecte by the plasma in spite of injecting velocity ~15 cm/s at the upper plasma bounary. Dust particles fall through a thin stainless tube of 1 m in length with mm in iameter. Dust particles collie with the tube while they fall an the velocities of ust particles at the exit of the tube are not uniform. Dust particles having velocity less than 15 cm/s are trappe easily in the plasma. There may be neutral flow over the plasma by thermophortic force. 4. Discussion A. Decharging process in the liqui helium vapor Decharging process in a vapor above the superflui liqui helium as well as in a helium gas at room-temperature is iscusse in this section. Experiments on echarging process were conucte in ischarge afterglow uner microgravity conition [6] as well as an on-groun conition by using thermophoretic force [7]. Electric fiel with a frequency of a few Hz was applie to the ust particle floating in the afterglow plasmas, an a rest charge on a ust particle was estimate base on the ynamics of ust motion. It shoul be note that ust particles stay in afterglow plasma in these experiments, while ust particles pass through the localize plasma an move out of the plasma in our experiment. Deflecte ust trajectory an spatial variation of ust charge are shown in Fig. 6. As can be seen in Fig. 6, ust charge ecreases exponentially with time as Z (y) = Z exp(-y/l y ), where l y is echarging length an l y = 10~100 mm at 4 K an l y ~ 4 mm at 300 K. The charging frequency ω c in a collisionless plasma is given by ω c ~(a/λ Di )ω pi [1], while ω c ~(l i /λ Di )ω pi in collsional plasma [8], where ω pi =(n i e /ε 0 m i ) 1/ is ion plasma frequency, n i is ion ensity an m i is a ion mass. In the plasma above liqui helium surface, charging frequency is ω c ~ 10 6 ra/s. Since ust particles have velocity on the orer of v y ~ 10cm/s, ω c /π is much higher than the value of v y /l y ~ 10 sec -1. Time epenence of echarging process of ust charges was stuie in an afterglow plasma [6,7], while we have measure space epenence of ust charges above liqui helium surface Fig. 7. Normalize ust charge z as a function of collision parameter λ D /l i. Experimental values, theoretical values of collisionless OML theory an collisional OML theory are shown. by observing ust trajectories passing through a localize plasma. B. Lower charge state in a cryogenic plasma The ust charges etermine by two ifferent methos suggest that charges ecrease with ecreasing temperature. Comparing the results of YD-1 an YD- at the same temperature conition, charge obtaine by YD- is smaller than YD-1. Lower charge state of ust particles is iscusse in this section. It was shown by simulation that charge exchange of ion on neutrals affects the charge state at room-temperature [9] as well as cryogenic temperature [17]. A cross section of charge exchange collision σ is σ ~ 5 10-19 m. Ion mean free path l i in YD-1 is estimate as l i ~ 1 mm at 300 K, l i ~ 1mm at 77 K an l i ~ 0.1 mm at 4. K. In YD- with higher neutral pressure the ion mean free path is l i ~ 0.1 μm at 4 K, l i ~ 0.01 mm at 300 K. Ions in the plasma are assume to be coole by neutral-ion collisions (T i ~ T n ) since imensions of plasma L (L ~ 50 mm in YD-1 experiment, L ~ 10 mm in YD- experiment) are much larger than the ion mean free path (L l i ). Because of the energy supplie to maintain the plasma an the longer nature of mean free path of electrons than ions, electrons keep their thermal energy. For our experiments, electron Debye length λ De of our plasma is λ De ~ 0.5 mm, while ion Debye length λ Di changes its value λ Di = 4~40 μm at 4~300 K. The effect of ion-neutral collisions on charging was shown in series of experiments [30,31]. Ion current in the presence collisions is given by [31] I 8π a n v zτ[1 + 0.1zτ( λ/ l )], (6) i i Ti where v Ti =(k B T i /m i ) 1/ is thermal velocity of ions, τ is temperature ratio τ=t e /T i, z is normalize ust charge i 408

z e z, (7) 4 ak T 0 B e To calculate the ust charge it is necessary to equate the ion flux to the electron flux I e = 8 a n e v Te exp(-z), where where v Te =(k B T e /m e ) 1/. The ust charges by collisionless OML theory an collisional OML theory are compare to our experimental ata. Figure. 7 shows normalize ust charge z as a function of normalize collision parameter λ D /l i. The ambiguity of our experimental ata in normalize collision parameters is erive with λ De or λ Di. The lower charge state in cryogenic conition an in collisional situation is clearly shown to agree with theoretical preictions as shown in Fig 7. 5. Conclusions RF helium plasmas are prouce in cryogenic gas as well as in liqui helium vapor. Dust particles introuce into the plasmas are tracke by CCD camera an analyze by PTV metho. Dust charges in a wie range of temperature an pressure are etermine by two ways, oscillating trajectory of ust particles aroun equilibrium position an eflecte trajectory of charge ust particles in DC electric fiel. The ust charge in cryogenic environment is foun to be much lower than the one at room-temperature. Backgroun cryogenic temperature an collisions lea lower charge state at cryogenic conition. Acknowlegments This work is supporte by Asian Office of Aerospace Research an Development uner awar number AOARD-08-4116 an JSPS (Japan Society for the Promotion of Science) Grant-in-Ai for Scientific Research (B) uner Grant No.19340173. References [1] O. Ishihara, J. Physics D: Appl. Phys. 40, R11 (007). [] G. E. Morfill an A. V. Ivlev, Rev. Mo. Phys. 81, 1353 (009). [3] J. Winter, Plasma Phys. Controlle Fusion 40, 101 (1998). [4] N. Ohno, M. Yoshimi, M. Tokitani, S. Takamura, K. Tokunaga an N. Yoshia, J. Nucl. Mater. 390, 61 (009). [5] J. H. Chu an Lin I, Phys. Rev. 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