Electric field variability and classifications of Titan's magnetoplasma environment

The atmosphere of Saturn's largest moon Titan is driven by photochemistry, charged particle precipitation from Saturn's upstream magnetosphere, and presumably by the diffusion of the magnetospheric field into the outer ionosphere, amongst other processes. Ion pickup, controlled by the upstream convection electric field, plays a role in the loss of this atmosphere. The interaction of Titan with Saturn's magnetosphere results in the formation of a flow-induced magnetosphere. The upstream magnetoplasma environment of Titan is a complex and highly variable system and significant quasi-periodic modulations of the plasma in this region of Saturn's magnetosphere have been reported. In this paper we quantitatively investigate the effect of these quasi-periodic modulations on the convection electric field at Titan. We show that the electric field can be significantly perturbed away from the nominal radial orientation inferred from Voyager 1 observations, and demonstrate that upstream categorisation schemes must be used with care when undertaking quantitative studies of Titan's magnetospheric interaction, particularly where assumptions regarding the orientation of the convection electric field are made.


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Titan is Saturn's largest moon and the only moon in the solar system known to have a thick

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The upstream magnetoplasma environment of Titan is a complex and highly variable system 45 and is modulated by internal magnetospheric effects, including apparent longitudinal 46 asymmetries, and external forcing by the solar wind. At Titan's orbital distance (semi-major 47 axis = 1.22×10 6 km=20.27 R S where 1 R S =60268 km) the observed magnetic field can 48 become radially stretched at locations just outside Saturn's magnetodisc current sheet, itself a 49 principal external field source (Arridge et al., 2008c). Vertical motions of this magnetodisc 50 (Arridge et al., 2008a;Bertucci et al., 2009;Simon et al., 2010a) can place Titan alternately 51 inside this current sheet or in the lobe-type regions adjacent to the sheet, which are relatively 52 devoid of plasma. The plasma is centrifugally confined in this magnetodisc whereas the 53 energetic particles are more free to extend to higher latitudes (e.g., Achilleos et al., 2010; 54 ARRIDGE ET AL.: CONVECTION ELECTRIC FIELD UPSTREAM OF TITAN Sergis et al., in press). A number of authors have attempted to classify the upstream 55 environment of Titan (Rymer et al., 2009;Simon et al., 2010a;Garnier et al., 2010) using a 56 variety of criteria to produce categories such as "plasma sheet" or "current sheet" or "lobe".

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The classifications have proven to be useful in understanding flyby-to-flyby variability of 58 Titan's atmosphere (e.g., Westlake et al., 2011). However, such classifications necessarily 59 produce a relatively coarse description of the upstream environment, which does not reduce 60 their value but emphasises that care must be applied in their use, especially for quantitative 61 studies.

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Two examples highlight the need for caution.  Sittler et al., 2009;Johnson et al., 2009;and references therein). If the electric field magnitude 78 were also to change then this might also increase the magnitude of any atmospheric loss due 79 to pickup.

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During the Voyager 1 flyby of Titan the convection electric field was thought to be directed

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In this letter we explore the effect of such variability in the upstream magnetic field and 92 quantify the associated variability in the convection electric field. We refer these results to 93 previously established classification schemes and show that classifying Titan's upstream These results are therefore of relevance in trying to understand the dynamics and evolution of 96 Titan's atmosphere (e.g., Johnson et al., 2009;Sittler et al., 2009) and for interpreting 97 spacecraft data near Titan (e.g., Simon et al., 2007).

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Starting with the definition of E and assuming zero radial flow for the magnetospheric plasma 111 one finds the following components of the electric field as measured in the rest frame of Titan: 112 113 the plane of Titan's orbit is close to Saturn's equatorial plane Titan will appear to move with 132 respect to an observer in the co-moving frame of the plasma sheet. At any given time, Titan 133 may be located at some particular position with respect to this current sheet; it may be located 134 above, in, or below the centre-plane of the sheet. To determine the time derivative of the 135 electric field in Titan's rest frame we need to evaluate the total derivative DE/dt=∂E/∂t-u z dE/dz 136 where the negative sign has been introduced to account for the fact that when the plasma 137 sheet is moving up with u z >0 Titan is actually moving down through the plasma sheet. We 138 assume that the electric field at a fixed point in the sheet to be constant hence ∂E/∂t=0 and 139 the total derivative then reduces to the convective derivative associated with the relative 140 motion of the plasma sheet and satellite.

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We write the total derivative DE/Dt=-u z dE/dz and replace the spatial derivative of the

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Note that ∂u z /∂z is set to zero implying that the axial speed of the plasma sheet does not 150 change across the height of the plasma sheet. Applying this formalism and using these 151 assumptions we find:

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Hence we can see that there is a strong dependence of the time derivative of the convection 156 electric field on how quickly the azimuthal velocity varies with L (velocity shear, ∂u φ /∂L), how 157 stretched the field is (∂L/∂z) and of course how rapidly the plasma sheet is moving in the axial 158 direction (u z ). There is also a dependence on the vertical acceleration of the plasma sheet.

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Hence in a highly stretched magnetodisc with a large velocity shear and intense flapping one

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The location of the current sheet/lobe boundary has been estimated from the criteria of Simon

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In figure 3 the derivatives given by equations (2)

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At the centre of the current sheet near z=0 the electric field is radial and the largest derivative 220 is DE z /dt consistent with E z >0 above the equator and E z <0 below the equator (odd- The total time derivative of E z is completely dominated by the second term on the right-hand-242 side, u φ ∂B ρ /∂z, due to the rapid azimuthal plasma speed and the large vertical gradients in the 243 radial field produced by the current sheet. The shear in the azimuthal plasma velocity (∂u φ 244 /∂L) was found to be fairly small thus contributing to the small magnitude of the first term.

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Similarly the total time derivative of the E ρ is dominated by the u φ ∂B z /∂z term even though the 246 vertical gradients in B z are relatively small. The next important term is the u z ∂B φ /∂z term and is 247 smaller than the u φ ∂B z /∂z term because the axial speed of the plasma sheet is much smaller 248 than the azimuthal convection speed of Saturn's magnetospheric plasma (17 km s -1 Vs. ~120 schemes must be aware that such modulations might not be captured by these schemes.

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However, it is important to note that this does not devalue methods for classifying Titan's 260 plasma environment but does highlight the need for caution in their use, particularly for 261 quantitative studies.

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The picture of a quasi-static upstream environment where either the spacecraft is in a

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Further work is required to address the consequences of such rapid changes in the electric 275 field on Titan's induced magnetosphere, ionosphere and atmosphere.