The University of Birmingham

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1 The University of Birmingham School of Physics and Astronomy 2005/6 Literature Survey Construction of Ion Mobility Spectra for Titan s Lower Atmosphere By Peter Stevens Supervisor: Karen Aplin Peter Stevens - 1 -

2 1.0 Introduction Titan has one of the most interesting atmospheres in the solar system because it is similar to primordial Earth. The density of the troposphere has limited our knowledge of the ionic composition. Various theoretical models have been proposed, some of which are based on laboratory experiments. The most appropriate model is chosen as a basis for this project. Ionisation by cosmic rays is ubiquitous in atmospheres throughout the solar system. Photo-ionisation by solar UV radiation is less significant in atmospheres are far away as Titan but it still plays an important role. Subtle electrical properties such as ion-mobility and conductivity help to understand the overall structure of the global electric circuit. This survey also discusses the purpose of size-mobility relationships and how different authors develop them. 2.0 Background 2.1 Atmospheric Structure and Composition Titan s atmosphere is a lot thicker than Earth s and this allows it to extend much further into space. This means that the various atmospheric layers are larger (see figure 1, based on information from Coustenis, 2005). Figure 1: comparison of atmospheric structure between Earth and Titan. The composition of ions in the lower atmosphere of Titan is difficult to determine due to the fact that observations so far have been unable to penetrate the thick atmosphere. The ionic composition has been estimated by means of theoretical chemical modelling with laboratory simulations (Borucki et al. (1987, 2004), Capone et al. (1976, 1980), Fox and Yelle (1997), Lara et al. (1996), Molina-Cuberos et al. (1999, 2000), Wilson and Atreya (2004)) and direct observations (Voyager (1980, 1981), Huygens-Cassini (2005) and limited remote sensing). A good comparison and summary is given by Aplin (2005) and Harrison and Carslaw (2003). Peter Stevens - 2 -

3 2.2 Global Electric Circuit The best model to describe atmospheric electricity on Earth is currently the global electric circuit (GEC). It was first proposed by Wilson (1920) and it can be described as a spherical capacitor with a weakly conductive medium (the air). The upper boundary of this model is the electrosphere, the lower region of the ionosphere. This is the most conductive region of the atmosphere, where the electron density due to ionisation is at its maximum. Free electron density is controlled by the number of electrophiles and aerosols present (Molina-Cuberos, 2000). On Earth free electrons are practically non-existent as there are too many aerosols and large particles to soak them up (Harrison and Carslaw, 2003). The conductivity is mainly dependent on the concentration of small ions present; large ions do not contribute to conductivity due to their high inertia. Current models and observations show that there are two ionospheres in Titan s atmosphere. The upper ionosphere is similar to Earth s in that it is photo-ionised. The concept of Titan having a lower ionosphere was first proposed by Capone et al. (1976), who predicted an electron concentration of 2400±1100 cm -3 at an altitude ranging of 1180±150 km. This ionosphere is the product of cosmic ray ionisation. The density profile for electron density model for the lower atmosphere has been improved by Borucki et al (1987, 2004) and Molina-Cuberos et al. (1999) since the arrival of Voyager in Molina-Cuberos et al. (1999) developed several models for the electron density; the ion-neutral model considers the production of neutral species by galactic cosmic rays (hereafter GCR). This model shows a peak of ~2150 cm -3 at 90 km. An ionosphere composed mainly of covalently bound ions and cluster ions give electron density peaks of ~4000 and ~1000 cm -3 respectively. Borucki et al. (1987) calculated the electron density both with and without the presence of aerosols. The model without aerosols had a peak electron density of ~1600 cm -3 at 95 km. The introduction of aerosol particles only had a major effect on the abundance of electrons above 100 km. Borucki et al. (2004) improved on the previous calculation by including a three-body reaction rate for the recombination of positive ions with electrons in the lower atmosphere. This has the effect of severely reducing the electron concentration below 100 km. Wilson and Atreya (2004) have a very comprehensive model based on microphysical models, recent observations and laboratory data for the upper atmosphere of Titan. They give a detailed ion composition and electron density for 800 km and above. The electron density peak is between 3000 and 4000 cm -3 at ~1100 km. Molina-Cuberos (2000) is the only paper that considers electrophiles seriously. Other authors have predicted the existence of electrophiles (Borucki et al. (1987, 2004), Molina-Cuberos et al. (2000), Lara et al. (1996)) but no one has calculated the abundances of the different species because of a lack of observational information. Peter Stevens - 3 -

4 2.3 Ion Balance Equation The ion balance equation (1) given in Harrison and Carslaw (2003), calculates the rate of change of ion density. It is controlled by the formation rate q (due to ionisation) and the recombination rate of ions. dn± = q α n+ n βn± Z. (1) dt Ion-ion recombination is represented by the coefficient α and when aerosols are present, β is the recombination coefficient and Z is the concentration of aerosols. In Titan s lower atmosphere there is an issue as to whether electrophiles are present. Unpublished preliminary results from the Huygens probe suggest that there are fewer electrons than expected. In the case that ion-electron recombination is significant the ion-balance equation becomes quite complicated. It is discussed in detail by Borucki et al. (1982) for the lower atmosphere of Venus. It is interesting to note that there is no ion-electron recombination with ions on Earth as the electron density is almost non-existent; they are scavenged by aerosols and water molecules etc. 2.4 Ionisation GCR ionisation dominates ion production in the middle and lower atmosphere of Titan where magnetospheric electrons and solar UV radiation do not reach. GCR are composed of protons and a small fraction of heavier ions. Their energies span several orders of magnitude and the higher energy particles produce a cascade when they reach the atmosphere. These include secondary protons, neutrons, pions, electrons and gamma rays; all of these can undergo further cascading (Borucki, 2004). GCR fluctuations on a planetary body are controlled by two geological factors: the planet s magnetic field and solar activity. Titan s lack of a magnetic field implies that there is no latitudinal variation of GCR ionisation. GCR in the solar system are modulated by the Sun s heliospheric magnetic field; planets in the outer solar system are not affected by the magnetic field as much as the inner planets. The strength of the field is determined by the solar activity, but Molina-Cuberos (1999b) states that the ionisation in Titan s atmosphere is not sensitive to the fluctuations below ~60km. Titan s atmosphere can become ionised by magnetospheric electrons when its orbit passes through Saturn s magnetic field. This form of ionisation is only effective above altitudes of ~600km (Molina-Cuberos, 1999a). The dominant form of ionisation on the day-side of the upper atmosphere is UV radiation. It is less effective in planets further away from the Sun as intensity decreases with the square of the distance and on Titan it cannot reach the troposphere due to the dense atmosphere. Gamma radiation contributes to the ionisation process near the surface of Earth. Too little is known about Titan s surface to determine whether there is any gamma radiation to cause any significant ionisation. Peter Stevens - 4 -

5 2.5 Ion Mobility Electric mobility is defined as the average velocity acquired by a small ion as it moves under the force exerted on it by an electric field (MacGorman, 1998). Mechanical mobility is the analogue for a neutral particle moving through an ambient gas. Mobility is mainly controlled by the size of the particle and the mechanical properties of the ambient gas such as temperature, pressure, viscosity etc. Reduced mobility is quite an important concept when the mobility of ions in different atmospheric conditions need to be compared. An example is comparing how the sizes of particles evolve at different altitudes; the mobilities of these particles can be reduced to standard atmospheric conditions to provide an accurate comparison. Reduced mobility is discussed by Tammet (2005), Mereyott (1980) and Hõrruk (2001). One of the main methods for measuring ion mobility is using gerdien condensers (MacGorman, 1998); ions up to a certain mass are collected by setting the electric field within a gerdien condenser. The current produced by the collected ions can be used to find the conductivity of the ambient gas due to those ions. The maximum mobility is inferred from the applied electric field. This project is not concerned with the mathematical process for obtaining this information, but the final data can be displayed as an ion-mobility spectrum. An ion-mobility spectrum shows the mobilities of ions and their respective number densities. Size-mobility relationships are used to determine the size and mass of the ions using the mobilities. Finding the identity and chemical structure of the ions is not entirely accurate though; it is deduced by knowing the composition of the ambient gas and the mass of the ion. Hõrruk (2001) used this method for Earth-based experiments and it will soon be carried out for Titan by using data from the Huygens probe (2005). There are several theoretical equations relating the mobility of a particle to its size and the most relevant ones will be discussed. H. Tammet (1995) based his model on the Millikan equation. This equation is adequate for particles that are large enough such that the ambient gas molecule size is negligible. Macroscopic particle properties break down in the nanometre regime and the size of the ambient gas molecules is no longer negligible, so Tammet makes modifications to the Millikan equation for nanoparticles by adding correction factors. The modified mechanical mobility is given by l δ 1 + exp δ a + b c l B = f 1 f 2, (2) 6πηδ where a, b and c are slip factor coefficients, η is the viscosity of the ambient gas and l is the mean free path. The first correction factor f 1 takes into account the finite mass of the particle. m g 1 (3) m p f = 1+ Peter Stevens - 5 -

6 Collisions between nanometre particles and ambient gas molecules are assumed to be elastic-specular and macroscopic particles undergo inelastic collisions. Tammet states that the transition process between elastic and inelastic collisions is when particles are between 1 nm and 2 nm in size and it is described by the Einstein factor s. This effect is incorporated in the second correction factor f f2 = * (4) (1,1) * a + b Ω T + s r, T 1 ( 4 m δ ) ( ) ( ) ( ) A dipole is induced in a neutral particle when it collides with a charged particle. The ( ) dipole polarisation interaction Ω 1,1 * is also taken into account in f 4 2. The collision distance between the particle and an ambient gas molecule is defined as the sum of radii of the two particles. The modified collision distance δ has an extra parameter called the extra distance h which is interpreted as the difference between the collision radius and the mass radius of a particle. This empirical quantity takes into account effects such as Van der Waals forces and other effects that Tammet does not discuss. Tammet makes an estimate of h and the critical radius r cr (a parameter of the Einstein factor s) by applying the semiempirical model to experimental data. It is advised that these values are treated as preliminary approximations until more advanced experimental data becomes available. Mäkelä et al. (1996) compared several size-mobility relationships including the model developed by Tammet (1995). They define the Kelvin-Thomson diameter using the Kelvin-Thomson equation for ion-induced nucleation and use this as the basis for the comparisons. Tammet s mobility equivalent diameters proved to be in closest agreement with the Kelvin-Thomson diameters in the nanometre range, where the other Millikan-Fuchs based equations did not match. It must be noted that the Kelvin- Thomson model may not be valid for small particles as it was designed for the formation of larger particles rather than particles made of just a few molecules. Mäkelä also argued that the collision cross section is not necessarily directly linked to the physical diameter. Fernández de la Mora et al. (2003) has developed the most recent size-mobility relationship in the free-molecule range that is based on those by Tammet s (1995) and Friedlander (1977). It only takes into account the extra-distance modification as Tammet argued that the polarization effect and the transition between elastic and inelastic collisions are effective below 2nm i.e. h is the dominant modification above this size. It would not be recommended to use this model below 2 nm due to the uncertainties. Fernández de la Mora used recent data for a series of fullerenes that are less heterogeneous than the series of particles that Tammet used to estimate h. A new estimate for the effective diameter of air molecules, d, is found to be 0.53 nm. This gives a new value of h = nm for molecular nitrogen with less uncertainty than the nm predicted by Tammet. Peter Stevens - 6 -

7 3.0 Conclusions Tammet s model is designed to approach the Chapman-Enskog equation in the nanometre particle limit as it is sufficient for this size range. It is also made to approach the Millikan equation for macroscopic particles when considering aerosols. Fernández de la Mora s model is also made to approach the Chapman-Enskog equation but not as accurately as Tammet s model. For this reason it would be sensible to use Tammet s equation despite its complexity. The most complete models for atmospheric ion composition are by Molina-Cuberos (1999a) and Wilson and Atreya (2004) for the lower and upper atmosphere respectively. They will probably be most relevant to this project as they give the abundances of both the electrons and ions at a broad range of altitudes. There is a distinct lack of information about electrophiles in Titan s atmosphere. Unless Huygens (2005) provides more information, some assumptions are going to have to be made with regards to the abundances or electrophiles. 4.0 References 1) Aplin, K.L. 2005, Atmospheric Electrification in the Solar System, Surveys in Geophysics. 2) Bernard, J.M. et al. 2003, Experimental Simulation of Titan s Atmosphere: Detection of Ammonia and Ethylene Oxide, Planet. Space Sci., 51, ) Borucki, W.J. et al. 1987, Predictions of the Electrical Conductivity and Charging of the Aerosols in Titan s Atmosphere, Icarus, 72, ) Borucki, W.J. et al. 1982, Predicted Electrical Conductivity between 0 and 80 km in the Venusian Atmosphere, Icarus, 51, ) Borucki, W.J. et al. 2004, Titan Aerosols and Conductivity, Icarus,(in Press). 6) Capone, L.A. et al. 1976, The Lower Ionosphere of Titan, Icarus, 28, ) Capone, L.A. et al. 1980, Cosmic Ray Synthesis of Organic Molecules in Titan s Atmosphere, Icarus, 44, ) Coustenis, A. 2005, Formation and Evolution of Titan s Atmosphere, Space Science Rev., 116 (1-2), ) Courtin, R. 2005, Aerosols on the Giant Planets and Titan, Space Science Rev., 116, (1-2), ) Cravens, T.E. et al. 2005, Titan s Atmosphere: Model Comparisons with Cassini Ta Data, Geophys. Res. Lett., 32, 12, L ) Fernández de la Mora, J. et al. 2003, Mass and Size Determination of Nanometre Particles by Means of Mobility Analysis and Focused Impaction, Aerosol Science, 34, ) Flasar, F.M. et al. 2005, Titan s Atmospheric Temperatures, Winds and Composition, Science, 308, 5724, ) Fox, J.L. and Yelle, R.V. 1997, Hydrocarbon Ions in the Ionosphere of Titan, Geophys. Res. Lett., 24, 17, ) Harrison, R.G. and Carslaw, K.S. 2003, Ion-Aerosol-Cloud Processes in the Lower Atmosphere, Rev. of Geophys., 41, 3, ) Hõrruk, U. 2001, Air Ion Mobility Spectrum at a Rural Area, Tartu University. Peter Stevens - 7 -

8 16) Keller, C.N. et al. 1998, Model of Titan s Ionosphere with Detailed Hydrocarbon Ion Chemistry, Planet. Space Sci., 46, 9/10, ) Lara, L.M. et al. 1996, Vertical Distribution of Titan s Atmospheric Constituents, J. Geophys. Res., 101, ) MacGorman, D.R., Rust, W.D. 1998, The Electrical Nature of Storms, Oxford University Press. 19) Mäkelä, J.M. et al. 1996, Comparison of Mobility Equivalent Diameter with Kelvin-Thomson Diameter Using Ion Mobility Data, J. Chem. Phys., 105, ) Mereyott, R.E. et al. 1980, The Mobility and Concentration of Ions and the Ionic Conductivity of the Lower Stratosphere, J. Geophys. Res., 85, A3, ) Molina-Cuberos, G.J. et al. 1999a, Chemistry of the GCR Induced Ionosphere of Titan, J. Geophys. Res., 104, E9, ) Molina-Cuberos, G.J. et al. 1999b, Ionisation by Cosmic Rays of the Atmosphere of Titan, Plan. Space Sci., 47, ) Molina-Cuberos, G.J. et al. 2000, Influence of Electrophilic Species on the Lower Ionosphere of Titan, Geophys. Res. Lett., 27, 9, ) Molina-Cuberos, G.J. et al. 2001, Capability of the Cassini/Huygens PWA HASI to Measure Electrical Conductivity in Titan, Adv. Space Res., 28, 10, ) Molina-Cuberos, G.J. et al. 2002, Nitriles Produced by Ion Chemistry in the Lower Atmosphere of Titan, J. Geophys. Res., 107, E11, ) Tammet, H. 1995, Size and Mobility of Nanometre Particles, Cluster and Ions. Tartu University. 27) Waite, J.H. et al. 2002, The Cassini Ion and Neutral Mass Spectrometer (INMS) Investigation, (to appear in Space Science Reviews). 28) Wilson, E.M. and Atrena, S.K. 2004, Current State of Modelling the Photochemistry of Titan s Mutually Dependent Atmosphere and Ionosphere, J. Geophys. Res., 109, E6. Peter Stevens - 8 -