Department of Physics, University of Colorado, Boulder, Colorado, usa 80309-0390

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Smoky Plasma

Scott Robertson

Department of Physics, University of Colorado, Boulder, Colorado, USA 80309-0390

Zoltan Sternovsky, Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, CO, USA 80309-0392


The mesosphere is a naturally-occurring complex plasma with nanometer-sized smoke particles from the ablation of meteors that remain aloft as a consequence of their low rate of sedimentation. Methods are discussed for creating and diagnosing a relatively uniform smoky plasma in the laboratory for the purpose of investigating mesospheric physics. Metallic particles a few nanometers in radius are created by evaporation of metal into an inert carrier gas. The particles are transported by gas flow into a double plasma device where they are charged by the plasma and confined by the plasma potential. Physics issues for the mesosphere that may be investigated include the origins of positively charged smoke particles and of fluctuating electric fields that have been observed by rocket-borne probes.

Index terms: ionosphere, plasmas, plasma devices

For submission to IEEE Transactions on Plasma Science, special issue on dusty plasmas, April 2007.

I. Introduction and motivation

The largest accessible naturally-occurring complex plasma is the ionosphere. The ablation of meteors creates metallic vapor that condenses into nanometer-sized smoke particles in the lower thermosphere (>90 km altitude). These smoke particles are charged by collection of ionospheric electrons and ions and perhaps by the photoelectric effect. The designation “smoky plasma” is appropriate because smoke particles are often defined as those particles less than 1 m in diameter that have a low rate of sedimentation [1]. Modeling indicates that the density of the meteoritic smoke particles is of order 103 cm-3 and their density is relatively homogeneous on a kilometer scale [2]. The smoke particles diffuse into the mesosphere (5090 km) where they may serve as nucleation sites for the icy particles of noctilucent clouds (NLCs) [3,4] that can grow to 50 nm in radius [5,6]. The largest NLC particles have the greatest rate of sedimentation and are found at the bottom of the cloud layer. NLC particles and their precursors may be kept aloft by relatively weak air currents, even at the low air density characteristic of the mesosphere. Dusty plasma experiments [7] have typically used particles with diameters of a few microns or greater for which the gravitational force cannot be ignored. Micron-sized particles often reside in a layer in the sheath at the lower plasma boundary and thus experiments are performed in plasmas that are not homogeneously loaded with particles. These experiments, however, have the compelling advantage that the micron-sized particles can be recorded by video photography which is an ideal diagnostic for crystalline plasmas and their changes of state [8,9,10,11]. In this paper, we discuss methods for creating and diagnosing homogeneous smoky plasma that will allow laboratory experiments (such as the experiment in Fig. 1) that explore the dusty plasma physics issues of the mesosphere.

Rocket-borne Langmuir probes have observed the disappearance of free electrons at the same altitudes as NLC and these voids in electron density are called “bite-outs” [12]. Rocket-borne detectors for aerosol particles have confirmed the existence of layers of negatively charged aerosol particles coincident with bite-outs [13,14,15]. The charge-density data are consistent with quasineutrality: the sum of the electron and negative aerosol densities is approximately equal to the positive ion density. If the density of aerosol particles exceeds the electron density, all of the negative charge may be captured by the aerosol particles leading to the bite-out. It should be possible to create bite-out conditions in laboratory smoky plasma if the source of ionization is removed so that the electron density decays to a value below that of the smoke particles.

Rocket-borne probes have observed both positively and negatively charged particles in the mesosphere [13,15,16]. Solid particles in plasma are expected to charge negatively because of the greater mobility of the electrons. The origin of positive particles is somewhat of a mystery because the relatively high work function of ice is inconsistent with photoelectric emission [17]. An alternate explanation is that during a bite-out in electron density, the ions attach to the aerosol particles resulting in a unique dusty plasma of positive and negative aerosol particles. Without electron bite-out conditions, these positive particles would be quickly neutralized by collection of free electrons. Electron mobility may also be reduced by the formation of negative ions. In a laboratory smoky plasma, formation of positive particles could be studied in an afterglow plasma or in a plasma with a gas such as SF6 that attaches electrons [18].

Enhanced radar returns from the mesopause called PMSE (polar mesospheric summer echoes) are a consequence of the charged aerosols modulating the density of free electrons [19]. PMSE indicate a modulation of the density of electrons at the Bragg scale, but the relatively rapid diffusion of free electrons tends to smooth out variations at these wavelengths [20,21]. The persistence of electron density modulations has recently been explained in detail as being a consequence of the requirement for quasineutrality and the relatively slow time scale for ambipolar diffusion when smoke particles are present [22,23,24]. The mesosphere shows structure at small scales (down to 1 m) in the neutral gas and in the charged species. Rocket-borne fast ionization gauges have measured the fluctuations in the acoustic range in the neutral gas density [25,26,27,28] and these probably have their origin in breaking atmospheric gravity waves propagating upward [29]. In the presence of neutral air turbulence, the neutral drag force is likely to be the dominant force on the aerosol particles. In the mesosphere, the smoke particle diameter is smaller than the mean free path of neutral atoms and the Epstein drag formula is applicable [30]. The drag force can modulate the density of the smoke particles and thus the frequency and wavenumber of these density fluctuations will be representative of the fluctuations in the neutral air turbulence. The quasineutrality requirement will result in a modulation of the density of free electrons that is seen indirectly radar backscatter and by rocket-borne electric field probes. Pfaff et al. [31] have detected turbulent E-field fluctuations in the acoustic range that are greater in amplitude in NLC/PMSE regions. The above scenario for electron density modulation could be examined in the laboratory by launching ordinary sound waves into a smoky plasma with a sufficiently high neutral gas density to support these waves and to exert a significant force on the smoke particles.

In strong electron bite-out conditions, the reduced electron mobility may allow the formation of large DC electric fields, provided that there is a mechanism to induce charge separation. Winds and gravitation are examples of relatively constant forces that may cause differential motion between ions and charged aerosols. There have been several in-situ experiments carried out by sounding rockets to study the electrical environment inside of NLCs and PMSEs [32,33]. Zadorozhny et al. [34] detected large vertical electric fields, greater than 1V/m, at the same altitudes that NLCs and PMSEs were observed. A more recent study was conducted by Holzworth et al. [35,36] during the DROPPS rocket campaign [37]. Electric field probes on the DROPPS-2 flight detected a ~3 V/m geophysical electric field inside the NLC. A field of this magnitude can only be sustained if the electron mobility is reduced by attachment to aerosol particles. On the DROPPS-1 flight, the probes provided a detailed measurement of the charged wake surrounding the payload inside the NLC/PMSE layer. Sternovsky et al. [38] subsequently showed that this electric field is created by drag force of the shock wave having a different magnitude for the electrons, ions, and aerosol particles thus resulting in a charge separation electric field. The model equations predicted the sign, magnitude and location of the variations in the potential. It should be possible to extend this model to find the coupling of electron density fluctuations to neutral air turbulence and to test the model in laboratory smoky plasma.

In Sec. II below, experimental methods are discussed for creating and diagnosing homogeneous smoky plasma. Experiments relating to the mesosphere made possible by laboratory smoky plasma are discussed in Sec. III. Equations are derived which describe the way in which acoustic turbulence will modulate the smoke particle density and couple to electrostatic waves. Section IV is a brief summary and conclusion.

II. Experimental methods

A. Selection of particle size

A first task is to define the parameter regime in which the term “smoky plasma” might be applied. The particles must not be so large as to reside in a boundary layer at the bottom of the plasma chamber. The particle mass md, the gravitational acceleration g, and the particle temperature Td (in energy units) determine a scale height Td /mdg which should be much greater than the vertical extent of the plasma device. This height is applicable to smoke particles in a neutral gas in thermodynamic equilibrium. For example, uncharged particles of Ag (mass density = 10.5 g/cm3) with radius 4 nm have a scale height of 15 cm at 300 K.

For unmagnetized plasma in the laboratory, negatively charged smoke particles may be confined by the positive electrostatic plasma potential p that confines electrons. For a cylindrical vacuum chamber, the potential profile is approximately parabolic from the axis to the sheath at the wall [39]. In the nearly-parabolic presheath region, the potential falls by approximately Te/q, where q is the elementary charge and Te is the electron temperature. We assume that the laboratory plasma is made in a double-plasma device [40], Fig. 1, with Te = 1 eV and that the ions are argon with initial temperature 300 K. From the standard charging formula for spherical particles [41] we obtain an equilibrium smoke particle potential of 2.7 V,. The corresponding charge for a 4 nm radius particle is approximately 8 q. The electrostatic potential energy for this particle changes by 8 eV between the center of the plasma and the wall. A particle of Ag with a 4 nm radius has a mass of 1.6 x 106 Da (1.6 x 104 Ag atoms) and the gravitational potential energy changes by 0.017 eV from the axis to the wall. Thus 4 nm Ag particles are strongly confined by the presheath potential. The smoke generator creates a range of particles sizes, however, and it is likely that the larger particles will have a greater density near the bottom of the device. If the particle radius were increased a factor of 8 (and the mass by a factor of 512), then the electrostatic confinement would occur only at the lower boundary where the electrostatic potential gradient is strongest. In the limit of small particle size, the smoky plasma is similar to a plasma of heavy negative ions such as SF6 (146 Da) or C60 (720 Da) [42,43,44,45]. The smoky plasma differs from the negative ion plasma in that the mass and charge can have a range of values and the charge may fluctuate.

The potential profile of the presheath and the plasma potential are usually found from a model in which the electrons are assumed Maxwellian with single temperature Te, for example, ref. [46]. If the smoke particles have a significant fraction of charge density, then the presheath and plasma potential should be found using the densities of both negative species. If the smoke particle charge density is much smaller than the electron charge density, then a thermodynamic equilibrium for the smoke particles is one in which the smoke particles (assumed to be at the temperature of the neutral gas) reside in the center of the chamber at the “bottom” of the electrostatic potential well created by the plasma potential. For an accurate description of the smoky plasma, a self-consistent model for the distribution of negative charge is needed which includes the two negative species with different temperatures.

The ion drag force is responsible for the formation of the dust-free voids in radio-frequency (rf) plasmas that have made it difficult to create homogeneous dusty plasma in microgravity [47]. The ion drag force in rf plasmas can be greater than the confining electric force for micron-sized dust particles. The ion drag force can be divided into two parts: (1) the force from collection of ions by the negatively charged particle, and (2) the force from deflection of passing ions [48,49,50,51]. Both of these forces are dependent upon the square of the particle radius. The electric confining force depends upon the plasma potential and the charge on the particle, and thus scales linearly with radius. Thus smaller particles are less likely to be pushed away from the axis than larger particles. For 4 nm smoke particles of Ag in a Te = 1 eV plasma, calculations show that the ion drag force is comparable to the gravitational force at an electron density of ~107 cm3. Experiments with growing particles in rf plasmas have shown that the growing particles are not expelled early in time when their size is small [52]. The thermophoretic force is also small at the low pressures (<10 mTorr) typical of double plasma devices because the relatively long mean free path for gas molecules leads to rapid temperature equilibration.

There are alternate approaches to create homogeneously loaded dusty plasma that do not require nanometer-sized particles. These include continuously replenishing the plasma with falling particles [53] and the use of microgravity conditions achieved by orbital flights [54] or by parabolic flights on aircraft or rockets [47]. It is also possible to suspend micrometer-sized particles near the center of a discharge by increasing the electrostatic potential gradient through the use of strongly-biased anode [55,56]. This technique causes spontaneous wave generation as a consequence of the plasma currents.

B. Smoke particle generation and delivery

Nanometer-sized metallic particles are often made by nucleation and growth in an oven with a low pressure (~1-15 Torr) flowing inert gas such as argon [57,58]. Particles of Ag [59] are of interest for smoky plasma because small atomic clusters of Ag have been reported to have a much higher photoelectron yield than that of the bulk material [60,61]. The high yield is a consequence of a plasmon resonance that has been studied in detail for Ag, Au, Cu and Al using thin metallic films [62]. Zn is also of interest because of the low photoelectric work function and high photoelectron yield. Preparation of Zn nanoparticles can be done with lower evaporation temperatures (< 700 K) because of the relatively high vapor pressure of Zn [63]. Nanometer-sized particles can be grown in situ in rf discharges with silane gas [64,65] or with hydrocarbons that polymerize [66], but these rf plasmas are usually small in volume (with one dimension not large in comparison with a typical wavelength) and have a noisy electrical environment. Atmospheric scientists nucleate and grow smoke particles at atmospheric pressure [67], but the density of particles is greatly reduced when the carrier gas is expanded to the low pressure (<10 mTorr) of typical plasma experiments.

The inert-gas smoke generators typically generate particles with a size distribution that is log-normal with a characteristic size of order 10 nm. The characteristic size increases with oven temperature and is dependent upon the gas flow rate. The lowest-mass particles have numbers of atoms countable by mass spectrometry [68,69]. The largest particles reach micrometers in size, but these particles are often the result of agglomeration that can be minimized by rapidly expanding the carrier gas. The gas flow rate must be ~5 Torr-liter/second in order for the metallic vapor to be cooled sufficiently rapidly. The density of the clusters in the source has been estimated from the metal evaporation rate and the gas flow rate to be of order 1012 cm3 [63], thus about 5 x 1015 smoke particles are generated per second. If plasma is generated in a double plasma device at 1 mTorr pressure and a pump of 50 l/s is used, then the throughput is about 0.05 Torr-l/s. Thus differential pumping is necessary between the generator and the plasma and only about 10-2 of the particles can be used. If we assume that the volume of the vacuum chamber is 100 l, the rate of delivery of smoke particles to the chamber is ~5 x 1010 cm-3/s. Electron densities in double plasma devices are typically less than 109 cm-3, thus the inert-gas evaporation source is more than adequate to load a plasma with smoke particles with number density near to that of the electrons.

The motion of nanometer-sized particles is closely coupled to that of the neutral gas at the ~10 Torr pressure characteristic of the evaporation source. Unsorted particles can be carried into the plasma chamber by having a pinhole or capillary between the smoke generator and the plasma chamber. At 1 mTorr Ar pressure in the plasma chamber, 4 nm radius Ag particles have a terminal velocity of 0.3 m/s. Thus if the dimensions of the experiment are of order 0.1 m, the particles will remain suspended for ~0.1 s after the plasma is turned off. This time is sufficient for study of plasma recombination without significant loss of the smoke particles.

The delivery of a small fraction of the smoke particles from the high pressure region to the lower pressure plasma region can be done in a way that narrows the particle size distribution. For example, if the flow to the chamber is through a bundle of many small tubes, the smallest particles (with the highest rates of diffusion) will be collected preferentially on the tube walls [70]. The largest particles can be removed if the gas flow rate and pressure are adjusted so that they are lost by sedimentation before they reach the plasma chamber.

C. Diagnostic tools for charged smoke particles

Cylindrical and disk Langmuir probes can be used in the usual way in the smoky plasma to find the electron density and temperature. With positive probe bias voltage, the collected current from smoke particles is likely to be much smaller than the electron current. A method for collecting charged smoke particles with a positively biased probe without simultaneously collecting electrons is to use magnetic insulation to prevent electron collection [71]. For example, a wire loop or hairpin of low-resistivity carrying an intermittent current of a few amperes can create a magnetic field at the wire surface sufficient to prevent collection of all but the most energetic electrons. The smoke particles are collected because of their larger Larmor radius. Whether or not the magnetic insulation would be sufficient to make the current of smoke particles greater than the residual collection of electrons depends on a variety of considerations, including whether the smoke particle current is orbit-motion-limited or mobility-limited.

The density of smoke particles can be determined in an approximate way by laser light scattering. Childs and Gallagher [72] have described a laser scattering system using an argon ion laser that has detected smoke particles with radii down to 4 nm at a density of 107 cm-3 [73]. The system is calibrated using Rayleigh scattering from nitrogen. The scattered light is most easily seen in the vicinity of the oven generator where the density of smoke particles is much greater than 107 cm-3 (Fig. 1). The scattering cross section for small particles scales with the sixth power of radius, thus the scattering system is most sensitive to the largest particles. For smoke particles with radii very much smaller than the wavelength of light, the scattering is peaked in the forward direction and the angular dependence of the scattering can be used as an indicator of size if the particles are assumed to be spherical [74,75].

Measurements of the electric mobility of atmospheric aerosol particles are frequently used to deduce their size [76]. For this measurement, an electric field is applied by a set of parallel plates in a small volume outside the plasma, as shown in Fig. 1. If the carrier gas is at rest and sufficiently collisional for motion of the smoke particles to be determined by their mobility, the time for the particles to drift to the collector can be used to determine the particle mass. This measurement requires that a fraction of the particles be charged and that the electric field (or charge) be applied as a step function. For a smoky plasma experiment, this diagnostic would give the largest signal if placed between the source of smoke particles and the plasma. A flashlamp could be used to charge a fraction of the particles by the photoelectric effect and to establish the starting time for the time-of-flight measurement.

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