Anomalous dust temperature in dusty plasma experiments

Article history: Received 23 May 2011 Accepted 6 June 2011 Available online 14 June 2011 Communicated by V.M. Agranovich Dust heating in dusty plasmas due to thermal electric field fluctuations and dust acoustic waves is examined. It is shown that dust particles acquire large random motion in fluctuating electric fields (within dust cloud) of background plasma causing dust electrostatic pressure P E [K. Avinash, Phys. Plasmas 13 (2006) 012109] and corresponding large temperature T E . Due to quadratic dependence on qd and high dust charge (∼ 103–104e), T E is much bigger than the dust kinetic temperature Td and is in the range of 10–300 eV for typical experimental numbers. Using global energy constraints dust heating due to dust acoustic waves is examined. It is shown that dust acoustic waves are potentially capable of heating dust to high temperatures in the range of a few hundreds of eV. © 2011 Elsevier B.V. All rights reserved. A number of recent experiments in dusty plasmas have revealed anomalously high dust temperature in the range of 10– 300 eV at low neutral gas pressures [1–10]. These observations have been confirmed by independent stereoscopic particle image velocimetry techniques where random dust motion corresponding to such high temperature has been seen [4,7,8,10]. Some of these experiments showed high dust temperature without significant wave activity [1,2,4,8,10] while other experiments, in which the dust acoustic (DA) waves [11] were present, the agreement with the theoretical dispersion relation required the assumption of dust temperatures in the range of tens to hundreds of eV [3,5–7]. In this context, the experiment by Fisher and Thomas [8] is particularly noteworthy where dust temperature was measured in dust clouds with DA waves and in stable clouds without DA waves or any other type of non-thermal fluctuations. It was observed that the dust temperature was high without DA waves ( 600 eV) and significantly higher with DA waves (∼ 800 eV) showing the heating of dust both with and without DA waves. Winske et al. [12] performed a one-dimensional electrostatic particle simulation of DA waves driven by drifting ions and showed that both the ions and dust were heated by the DA waves. Joyce * Corresponding author at: RUB International Chair, International Center for Advanced Studies in Physical Sciences, Faculty of Physics and Astronomy, Ruhr University Bochum, 44780 Bochum, Germany E-mail address: [email protected] (P.K. Shukla). 1 Permanent address: Department of Physics and Astrophysics, University of Delhi, Delhi 110007, India. et al. [13] performed numerical simulations using the dynamically shielded dust (DSD) code that included the effects of the twostream (ions-dust) instability in a dusty plasma and dust-neutral collisions. Their numerical results showed that the dust temperature increased with decreasing neutral pressure. Recently, Merlino [14] has shown that DA wave is driven unstable by ion-dust streaming instability in DC and RF discharges over a wide range of plasma and dust conditions. These arguments support the possibility of dust heating via DA waves driven by the ion-dust streaming instability. In this Letter we examine the possibility of dust heating due to thermal electric field fluctuations and DA waves. In the first part of our calculation, described below, we show that heating due to thermal electric field fluctuations is sufficient to account for the high dust temperature observed in stable dust clouds without DA waves or any other type of non-thermal fluctuations. In the second part of our calculation, we examine the possibility of dust heating due to DA waves using global energy constraints. These arguments show that the DA waves are also potentially capable of heating dust to high temperatures. 1. Dust heating due to thermal electric field fluctuations Dust heating due to thermal electric field fluctuations arises as follows. Electrostatic fields within dust clouds in dusty plasma experiments fluctuate due to equilibrium thermal fluctuations in the background plasma. Dust particles acquire random motion in these fluctuating fields causing dust electrostatic (ES) pressure P E [15– 19] and corresponding temperature which is much bigger than the 0375-9601/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2011.06.009 Author's personal copy K. Avinash et al. / Physics Letters A 375 (2011) 2854–2857 2855 dust kinetic pressure and temperature. This is a simple thermodynamic effect related to thermal electric field fluctuations and the following estimate shows that it is enough to account for the high dust temperature. The typical mean screened potential in the dust cloud formed in RF and glow discharges where the screening is predominantly due to cooler ions is on the order of ψ ≈ Ti/q. In these fluctuating fields a dust particle with charge qd acquires a mean kinetic energy ∼ qdψ ∼ ZdTi . At low neutral gas pressure where the frictional drag dust-neutral collision is weak, a good fraction of this energy is retained, in which case the average dust kinetic energies are ∼ ZdTi ∼ 30–300 eV for Ti ∼ 0.03 eV and Zd ∼ 103–104. The large dust kinetic energies are essentially due to the large value of the dust charge. In the following we calculate this effect rigorously. We begin by considering a group of Nd discrete point dust particles each carrying a negative charge qd dispersed within a neutralizing, statistically averaged (uncorrelated) plasma background of temperature T and volume V . The plasma contains Ne electrons, Ni ions such that there is overall quasi neutrality in V i.e. qdNd = q(Ni − Ne). The dust particle cloud is confined locally in a volume Vd (Vd < V ) within the plasma by a suitable configuration of external fields and forces. Let the temperature of dust particles be denoted by Td . The cloud and the plasma are considered to be stable (without DA waves or any other type of non-thermal fluctuations). This system is similar to the one considered earlier [19,20] except that now dust particles are also assumed to have finite temperature. We begin by calculating the entropy of the background plasma which, apart from plasma thermal contributions, contains extra contributions due to electric fields of the background plasma. Since the background plasma is assumed to be ideal, the entropy S is given by the Thomas Fermi expression for the ideal gas S = 5 2 (Ne + Ni)− ∑ α ∫ nα(r) [ lnnαΛ 3 α ] dr, Λα = ( h2 2πmαT )3/2 , α = i, e, (1) where nα is the local number density of α-th species. In thermal equilibrium, the electron and ion densities are given by Boltzmann relations ne = cee , ni = cie−qψ/T where ψ is the potential of the electrostatic field which is localized within Vd and is zero away from it where there no dust particles and ion and electron densities are equal given by ce = ci = n0. We assume qψ/T < 1 in which case Boltzmann relations can be linearized to give electron and ion densities as ni = n0(1−qψ/T ) and ne = n0(1+qψ/T ). Substituting these relations in Eq. (1) and retaining terms of order ψ2 gives [21]