Saturn ’ s ring current : Local time dependence and temporal variability

[1] Radial profiles of the azimuthal current density between ∼3 and 20 RS in Saturn’s magnetosphere have been derived using plasma and magnetic field data from 11 near‐equatorial Cassini orbits spanning a 10 month interval. The current density generally shows only modest variations with local time and from pass to pass within this region, rising rapidly near ∼5 RS to peak at ∼90 pAm at ∼9 RS and falling more gradually to below ∼20 pA m at 20 RS. The pressure gradient current is overall the most important component, the dominant inertia current in the inner region being significantly canceled by the oppositely directed pressure anisotropy current. These characteristics principally reflect the properties of the warm water plasma originating from the Enceladus torus to distances of ∼10 RS encompassing the usual current peak, inside of which distance the plasma properties are generally unvarying within factors of less than ∼2. Increased variability is present at larger distances where the pressure of the hot magnetospheric plasma plays the more important role. In this region the dominant pressure gradient current is found to be strongest in the dusk to midnight sector and declines modestly, by factors of ∼2 or less, in the midnight to dawn and dawn to noon sectors. Pass‐to‐pass temporal variability by factors of ∼2–3 is also present in the outer region, particularly in the dawn to noon sector, probably reflecting both hot plasma injection events as well as solar wind–induced variations.


Introduction
[2] The presence of an eastward flowing ring current in Saturn's middle magnetosphere was first inferred from Pioneer 11 magnetic field data [Smith et al., 1980], and further studied using magnetic field and plasma particle data from the Voyager flybys [Ness et al., 1981[Ness et al., , 1982;;Connerney et al., 1981;Krimigis et al., 1983;Richardson and Sittler, 1990;Richardson, 1995].The ring current acts to radially distend the equatorial magnetic field lines outward from the planet, thus weakening the equatorial field near the planet, while strengthening it further away.These magnetic perturbations were found to be well modeled using an empirical axisymmetric current disk, whose parameters are the cylindrical radii of its inner and outer edges (R 1 and R 2 ), its half thickness (D), and a parameter describing the current density in the disk (m 0 I 0 ), assumed to fall inversely as the cylindrical radial distance from the magnetic axis [Connerney et al., 1983;Bunce and Cowley, 2003;Giampieri and Dougherty, 2004].The current density within the disk is then taken to be given by j φ = I 0 /r, where r is the perpendicular distance from the magnetic/spin axis.
[3] Fits to the magnetic field data obtained on the Pioneer 11 and Voyager flybys revealed a ring current with a radial extent between ∼7 and ∼15 R S , and a total current near ∼10 MA (R S is Saturn's equatorial radius, equal to 60268 km).More recently, the same model, here termed the CAN (Connerney, Acuña, and Ness) model, has been applied to magnetic field data from a set of near-equatorial Cassini orbits by Bunce et al. [2007], showing that the ring current is significantly influenced by the size of the magnetosphere as initially suggested by Alexeev et al. [2006].The strength and radial extent of the current increases as the magnetosphere expands outward due to decreasing solar wind dynamic pressure.The field in the outer magnetosphere thus takes the form of a magnetodisc when the magnetosphere is expanded, but becomes quasi-dipolar when it is compressed [Bunce et al., 2008;Arridge et al., 2008a].Kellett et al. [2009] have also studied Cassini magnetic field and plasma electron data from several north-south passes through the ring current at radial distances between ∼9 and ∼15 R S .They showed that the ring current has a half thickness of ∼1.5 R S on the dayside, with more variable conditions on the nightside, though with an average half thickness also of ∼1.5 R S .
[4] Physically, the existence of Saturn's ring current is due to a combination of plasma currents resulting from the spatial gradient of the perpendicular plasma pressure, the anisotropy of the plasma pressures parallel and perpendicular to the field lines in the presence of field line curvature, and the inertia of the flowing (near-corotating) plasma.Examination of Voyager plasma and magnetic field data suggested the importance of the inertia current in the outer ring current [McNutt, 1983[McNutt, , 1984] ] and the pressure gradient current in more central regions [Mauk and Krimigis, 1985], supported by early findings from the Cassini spacecraft [Arridge et al., 2007].However, Cassini has subsequently provided a much more extensive magnetic field and plasma parameter data set [e.g., Sergis et al., 2007Sergis et al., , 2009; Lewis et al., 2008;Schippers et al., 2008;Wilson et al., 2008;McAndrews et al., 2009;Persoon et al., 2009;Thomsen et al., 2010] from which the contributions of these plasma currents to the total ring current can be estimated.Achilleos et al. [2010aAchilleos et al. [ , 2010b] ] have employed simplified density and pressure profiles based on these data to derive self-consistent axisymmetric models of Saturn's ring current region, while Sergis et al. [2010] and Kellett et al. [2010] have made complementary empirical studies of the equatorial current profile obtained directly from Cassini plasma and field data.Specifically, Kellett et al. [2010] have derived the current contributions on two individual Cassini passes through the dayside magnetosphere spanning the radial range ∼3-20 R S , while Sergis et al. [2010] combined data from a number of such passes to investigate average conditions in the radial range 6-15 R S .Within their limitations, these two studies indicate that the total eastward current in the equatorial plane rises sharply with radial distance at ∼5 R S to peak at ∼100 pA m −2 at ∼10 R S , and then declines below ∼25 pA m −2 beyond ∼15 R S .The current profiles were found to be in overall agreement with those obtained by current disk modeling of the simultaneous magnetic disturbances in the two individual cases studied by Kellett et al. [2010].
[5] The present paper employs the same pass-by-pass methodology as Kellett et al. [2010], but extends the data set to a wider range of orbits to explore both local time (LT) and pass-to-pass temporal variations in Saturn's ring current.Likely contributors to such variations include daynight asymmetries associated with the variable magnetospheric compression by the solar wind [e.g., Cowley et al., 2005;Belenkaya et al., 2006;Bunce et al., 2007Bunce et al., , 2008;;Arridge et al., 2008a], together with the effects of periodic injections of hot plasma in the outer nightside magnetosphere which are observed to drift around the planet via dawn and decay due to charge exchange [e.g., Paranicas et al., 2005;Krimigis et al., 2007;Carbary et al., 2008a,b;Mitchell et al., 2009;Brandt et al., 2010].Here we thus consider magnetic field and plasma particle data from both the inbound and outbound passes of eleven near-equatorial Cassini orbits that span the radial range ∼3 to 20 R S , together with a wide range of LTs.The LT dependence and variability of the ring current is investigated by deriving profiles of the azimuthal current density from the magnetic field and plasma data for each pass, which are then compared and combined to consider the mean current profiles and the range of variation about the mean.

Data Set and Methodology
[6] We now provide details of the data sets employed in this paper, together with an outline of the analysis methodology.As indicated above, the methodology largely follows that of Kellett et al. [2010], to which we thus refer for further details.We begin by considering the theoretical expression for the azimuthal current density resulting from the physical effects outlined above which has been applied to the data.

Theoretical Background
[7] The local electric current density j ?flowing perpendicular to the magnetic field B in a magnetized plasma may be derived either by integrating the particle drift and magnetization currents over the local distribution functions, or equivalently by considering local stress balance via Newton's second law.The general expression resulting from either approach is given [e.g., Vasyliunas, 1984] by where r m is the plasma mass density, V the bulk speed, b = B/B the unit vector along the field, and P k and P ? the fieldparallel and field-perpendicular plasma pressures, respectively, assuming a gyrotropic plasma.The first term on the right side of equation ( 1) is the inertia current, the second the perpendicular pressure gradient current, and the third the pressure anisotropy current, which goes to zero in the limit of isotropic pressure (P k = P ?= P).
[8] For practical application to Cassini data, this expression must first be simplified using suitable approximations.As discussed previously by Kellett et al. [2010], the main assumption is that of approximate local axisymmetry about the planet's spin and magnetic axis, such that spatial gradients in the radial direction are taken to be much larger than those in the azimuthal direction.Thus specifically, the variations in the equatorial perpendicular plasma pressure observed on a given pass from which the pressure gradient term in equation ( 1) is estimated are taken to relate primarily to radial rather than to azimuthal effects.The primacy of radial variations should remain valid even in the presence of hot ion injection events according to the modeling results of Brandt et al. [2010], while the overall validity of this assumption can be checked a posteriori from the results (section 4).We also assume that quasi-steady conditions prevail on given passes.Although we cannot in principle separate temporal from spatial variations using data from a single spacecraft, the general validity of this assumption can again be assessed from the pass-to-pass variability.In correspondence with the assumption of approximate local axisymmetry, we also assume that the plasma velocity is purely azimuthal at speed V φ .No further assumptions are made about the direction of the magnetic field, however, such that b = (b r , b , b φ ), though the colatitudinal field component is usually dominant close to the equatorial plane such that b ≈ 1 with |b r | and |b φ | both smaller.
[9] With these assumptions, equation (1) yields the following expression for the principal azimuthal component of the field-perpendicular current density where r is the radial distance, and R is the local radius of curvature of the field lines.Of the quantities in this equation, only the radius of curvature R in the pressure anisotropy current cannot be determined directly from near-equatorial data.However, the anisotropies of prime interest here are the strong P ?> P k anisotropies in the warm ion populations in the inner part of the system, within ∼10 R S .Inside such distances the equatorial field does not usually depart strongly from a near-dipolar form [Bunce et al., 2008;Arridge et al., 2008a], for which R = r/3, an approximation we therefore employ here.

Data Coverage
[10] The data examined in this paper were obtained during 11 Cassini periapsis passes on revolutions (Revs) 15-25, spanning September 2005 to July 2006, thus yielding 22 traversals of Saturn's ring current.These passes were all closely equatorial, the spacecraft being located within half a degree of latitude of Saturn's equatorial plane throughout.Figure 1 shows the relevant segments of the trajectories plotted in the planet's equatorial X-Y plane, with the Sun at the top.The coordinate system employed is such that Z points along the planet's spin (and magnetic) axis, the X-Z plane contains the Sun, and Y points toward dusk, completing the right-handed system.All 11 trajectories are shown labeled by the Rev number, with inbound and outbound segments being colored blue and red, respectively, inside the radial range of 20 R S examined here, while being shown black outside this range.The trajectory for Rev 20, data from which are employed in section 2.3 to illustrate the methodology, is shown by the solid line, with black circles plotted at the beginning of each day of year (DOY) of 2006 as marked.The trajectories of other Revs are shown by dashed lines.We note that the results presented by Kellett et al. [2010] were derived using data from the inbound passes of Revs 15 and 16, spanning the dayside sector from prenoon to dusk, which also form part of the data set employed here.
[11] The black dot-dashed lines in the top part of Figure 1 show for reference the Kanani et al. [2010] model magnetopause positions for solar wind dynamic pressures of 0.01 and 0.1 nPa, spanning the usual range at Saturn.It can be seen that the data segments inside 20 R S should generally lie within the magnetosphere on the dayside, unless unusually high solar wind dynamic pressure conditions prevail.All dayside data have thus been screened to exclude magnetosheath intervals.Overall, it can be seen from Figure 1 that good radial coverage is obtained at all LTs from the postdusk to the prenoon sector.However, radial coverage is limited to the inner part of the system, within ∼9 R S , in the noon to dusk sector.

Plasma Properties, Data Sources, and Methodology
[12] We now consider how the Cassini data have been employed to determine the azimuthal current density from equation (2).The main particle populations in Saturn's magnetosphere that contribute to the density and pressures in this equation are the warm (few tens to few hundreds eV) and hot (few keV to few hundred keV) water ions and protons [e.g., Krimigis et al., 2007;Wilson et al., 2008;McAndrews et al., 2009;Mitchell et al., 2009], together with cold (few eV to few tens eV) and warm (few hundred eV to a few keV) electrons [e.g., Lewis et al., 2008;Schippers et al., 2008].Energetic electrons at tens of keV and above provide only small contributions and are not considered here.The warm ions and cold electrons originate in the Enceladus torus and are dominant in the inner part of the system, while the hot ions and warm electrons become more important further out.Given the bulk parameter profiles of these populations, all of the terms in equation ( 2) can be determined on individual passes through the ring current, thus making it possible to estimate the local azimuthal current density.However, not all parameters are routinely measured, such that it becomes necessary to augment available data with empirical models as described below.
[13] As in the work by Kellett et al. [2010], the routinely available Cassini data sets employed in this study are as follows.Brief details are provided in Table 1 for easy reference.
[14] 1. Magnetic field data at 1 min resolution are available from the fluxgate magnetometer of the magnetic field investigation [Dougherty et al., 2004].
[15] 2. Hot ion density and pressure data at 5 min resolution for ≥3 keV protons (H + ) and water group ions (W + ) combined are derived from MIMI/CHEMS and LEMMS data by integration over the energy range from 3 keV to >200 keV, the water group ion spectrum being extrapolated to 3 keV from minimum measured energies of 9 keV [Krimigis et al., 2004;Sergis et al., 2007Sergis et al., , 2009]].Hot ion anisotropies are not believed to be large, such that as in previous works the corresponding pressure is taken to be isotropic.
[16] 3. Total electron density values at 8-16 s resolution are obtained from measurements of the upper hybrid resonance frequency by the RPWS instrument [Gurnett et al., 2004;Persoon et al., 2009].These data are generally available between periapsis and radial distances of ∼8-10 R S .
[17] 4. Total electron density and pressure data at 1 min resolution are obtained from CAPS/ELS data by integration over the energy band from 0.6 eV to 28 keV [Young et al., 2004], together with partial density and pressure values in the upper part of the energy range from 20 eV to 28 keV.The pressures are again taken to be isotropic.Total density and pressure values can only be derived from these data at radial distances beyond ∼10-12 R S where the spacecraft potential is positive, the data then being corrected for this potential with the removal of the contribution of trapped spacecraft photoelectrons.Inside these radial distances the spacecraft potential is up to a few volts negative such that the cold electron population is not fully measured.However, the partial density and pressure of the electrons with energy ≥20 eV are still available, and are not strongly affected by the spacecraft charge.
[18] One major plasma component missing from this list is the warm ion population with energies below ∼3 keV, the parameters of which are not routinely available due to fieldof-view restrictions on the CAPS/IMS instrument that covers this energy range.However, the number density of these ions is in effect known from the difference between the total particle number density derived from the wave and electron data (items 3 and 4 above) and that of the hot ions (item 2), assuming the ions are principally singly charged.The warm ion bulk parameters can then be estimated using empirical models derived from CAPS/IMS data obtained during special intervals when the spacecraft was oriented such that the warm ion populations were adequately viewed by the instrument.These model profiles are shown in Figure 2, plotted versus equatorial radial distance over the range 3 to 20 R S .Brief details are again provided in Table 2 for easy reference.Figure 2a shows the ratio of the water ion (taken to be mass 17) to proton number density from which the warm ion mass density can be calculated given the total number density, required for the inertia current term in equation (2). Figure 2b then shows the warm ion temperatures for water ions (green) and protons (yellow) both perpendicular (solid lines) and parallel (dot-dashed lines) to the magnetic field, from which the warm ion pressures can similarly be calculated, required for the pressure gradient and anisotropy current terms.These profiles are based on the Cassini CAPS/IMS measurements of Wilson et al. [2008] and McAndrews et al. [2009], augmented in the innermost region by Voyager results presented by Richardson [1995].It can be seen in Figure 2b that the warm ion temperatures are strongly anisotropic in the inner region where T ? ) T k , while approaching isotropy at and beyond ∼12 R S .Figure 2c then shows the azimuthal bulk velocity of the plasma, also required for the inertia current, where the dashed line shows rigid corotation.This model follows the CAPS/IMS results of Wilson et al. [2009] inside 10 R S (thus being modestly updated from the Wilson et al. [2008] model employed by Kellett et al. [2010] in this regime), and the model of Achilleos et al. [2010a] at larger distances, the latter being based on the MIMI/INCA results of Kane et al. [2008] in that region.It can be seen that the azimuthal velocity remains modestly lower than rigid corotation throughout the region investigated.
[19] The Cassini warm ion parameters shown in Figure 2 were derived by Wilson et al. [2008] and McAndrews et al. [2009] using convecting bi-Maxwellian fits to the CAPS/ IMS data.These fits characterize the ion distribution function at energies up to several times the thermal energy, and since the energy of the dominant water ion population is typically a few hundred eV (Figure 2b), the fits thus characterize the ion population up to energies of a few keV [see, e.g., Wilson et al., 2008, Figure 5].However, at higher energies these Maxwellians fall well below the observed ion distribution, which instead consists of a power law tail extending typically to a few tens of keV, together with a distinct hot population with energies from a few tens to several hundred keV [Dialynas et al., 2009].The total ion bulk parameters can thus reasonably be taken to be given by the sum of those for the warm ions derived from the "difference" density and the CAPS/IMS models in Figure 2, which characterize the ion populations to energies of a few keV, together with those for the hot ions at energies above 3 keV derived from the MIMI data, thus characterizing the whole ion population without a major energy gap or overlap.The match between these data sets is less good in the inner part of the system where the warm ion energies fall to a few tens of eV, but here the plasma properties are overwhelmingly domi-Figure 2. Plots of empirical model plasma parameter profiles that are combined with pass-by-pass Cassini data to derive plasma current density profiles.These show (a) the ratio of the number density of warm water group ions to protons, (b) the field-perpendicular (solid lines) and fieldparallel (dot-dashed lines) temperatures of warm water group ions (green) and protons (yellow), (c) the azimuthal velocity of the plasma (solid line) compared with rigid corotation (dashed line), and (d) the temperature of the cold electrons.The source information on which these profiles are based is given in section 2.3, largely following Kellett et al. [2010].nated by the warm ions (see section 2.4) such that this is not of great significance.
[20] A second important missing component is the cold electron population in the inner region.As indicated in item 4 in the above list, at distances beyond ∼10-12 R S the potential of the spacecraft is positive, such that the full electron distribution is measured by CAPS/ELS up to energies of ∼28 keV (well above usual energies characteristic of the plasma electrons [e.g., Schippers et al., 2008]).In this regime, therefore, the electron density and pressure is determined by integration over the distribution after correcting for the spacecraft potential.Inside these distances, however, the spacecraft potential becomes a few volts negative, such that the low-energy plasma electrons cannot be observed, while the properties of the higher-energy electrons, taken here as above 20 eV, are not strongly affected.The number density of the lower-energy electrons is again known, however, from the difference between the total number density obtained from RPWS wave data (item 3 in the above list) and the density of the ≥20 eV electrons, and their pressure can again be estimated by use of an empirical temperature model (see Table 2).The latter is shown in Figure 2d, based on the model of Persoon et al. [2009] derived from RPWS and CAPS/ELS data over the radial range between 3.5 and 10 R S , here slightly extrapolated inward to 3 R S as shown by the dashed line in Figure 2d.The value is typically a few eV in the inner region, and is taken to plateau at ∼10 eV beyond 10 R S in line with the CAPS/ELS measurements of Schippers et al. [2008].In the inner region where the spacecraft potential is negative, the total electron pressure is thus taken to be given by the sum of the cold electron pressure derived from the "difference" density and the electron temperature model in Figure 2, which typically characterizes the population up to energies of around 10 eV, together with the partial pressure of the electrons above 20 eV, thus again characterizing the whole population without a major energy gap or overlap.

Plasma Parameter Profiles
[21] Application of the above methodology is illustrated in Figures 3a and 3b, where we show results for the inbound and outbound passes of Rev 20, respectively.These passes span radial distances between periapsis at ∼5.5 R S and 20 R S , and LTs between 8.5 and 16.8 h on the inbound pass and 16.8 and 1.1 h on the outbound pass (Figure 1).The first and second panels in Figures 3a and 3b show radial profiles of equatorial density and pressure values, respectively, where colored dots show the primary data employed as described in section 2.3, and similarly colored lines join values averaged over 0.25 R S intervals.Colored lines without dots in the pressure plots then indicate values derived indirectly using the model profiles in Figure 2 as part of the input.
[22] We first examine the density data in the first panels of Figures 3a and 3b.These show profiles of the total electron number density obtained from RPWS data in the inner region (yellow), and from integration of the potentialcorrected CAPS/ELS data (blue) in the outer region where the spacecraft potential is positive.As indicated in section 2.3, there usually exists a few-R S gap between the RPWS data in the inner region and the CAPS/ELS data in the outer region, which we close by a log linear interpolation shown by the green line, thus forming an overall total electron number density profile spanning the full radial range.The red data and line in the first panels in Figures 3a and 3b then show the number density of the hot (≥3 keV) water ions and protons combined, obtained by integration of the MIMI data.As discussed in section 2.3, the difference between this density and the total density is then taken to be density of the warm ions.It can be seen that typically the hot ion number density is at least an order of magnitude less than the total number density, such that the warm ions dominate the number density at all radial distances.The magenta data and line similarly show the partial density of the ≥20 eV electrons obtained by integration of CAPS/ELS data.As also indicated in section 2.3, in the inner region where the spacecraft potential is negative such that the electron total density data (blue) are no longer available, the difference between this density and the total density (yellow and green lines) is taken to be density of the cold electrons.
[23] The second panels of Figures 3a and 3b similarly show the pressure profiles.The red data and line again show the pressure of the hot (≥3 keV) water ions and protons combined, obtained by integration of the MIMI data.The green and yellow lines then show the perpendicular (solid) and parallel (dot-dashed) pressures of the warm water ions and protons, respectively, obtained by combining the warm ion density derived from the "difference" data in the first panels in Figures 3a and 3b with the density ratio and temperatures models in Figures 2a and 2b.The blue data and line in the outer region where the spacecraft potential is positive then show electron pressure values obtained by integration of the potential-corrected CAPS/ELS data.The blue line continued into the inner region where the spacecraft potential is negative then shows the electron pressure

Figure 3a
. Radial profiles of particle and field parameters for the inbound pass of Rev 20, shown over the radial range from periapsis at ∼5.5 R S to 20 R S .The first panel shows the particle density (m −3 ), where the yellow and blue data show the total electron number density from RPWS and CAPS/ELS, respectively, the latter being derived only in the outer region where the spacecraft potential is positive.Similarly colored solid lines join values averaged over 0.25 R S intervals.The green solid line shows the log linear interpolation between these two data sets.The magenta data show the partial density of ≥20 eV electrons from CAPS/ELS, while the red data show the hot (>3 keV) ion density obtained from MIMI/CHEMS and LEMMS (water group ions and protons combined).The second panel shows related radial profiles of the plasma pressure (nPa).The red data show the hot (>3 keV) ion pressure from MIMI, while the blue data show the electron pressure based on CAPS/ELS data as described in section 2.3.The green and yellow solid lines show the perpendicular pressure of the warm water group ions and protons, respectively, while the similarly colored dot-dashed lines show the parallel pressures of these ions.The total perpendicular and parallel pressures are shown by the solid and dot-dashed black lines.The third panel shows the total perpendicular plasma pressure (black line), polynomial fits to these data (red), the total magnetic pressure (blue), and the pressure of the colatitudinal component of the magnetic field (green).A magnetic field strength scale (nT) is also shown on the right side.The purple dot on the red line marks the point at which inner (fifth-order) and outer (third-order) polynomial fits join.The fourth panel shows profiles of the current density derived from equation (2).The green line shows the inertia current density, and the blue line shows the pressure anisotropy current density (zero beyond 12 R S ), while the orange line inside 12 R S shows their sum.The red line shows the perpendicular pressure gradient current density.The black line shows the total current density summed over these contributions.At the bottom we also give the latitude (degrees) and LT (hours) of the spacecraft at various radial distances on the pass concerned.
obtained by combining the partial pressure of ≥20 eV electrons (not shown) with the pressure of the cold electrons, the latter obtained by combining the cold electron density derived from the "difference" data in the first panels in Figures 3a and  3b with the cold electron temperature model shown in Figure 2d.The ≥20 eV electron pressure typically dominates outside ∼7 R S , while the cold electron pressure dominates inside these distances where the ≥20 eV electron densities in the first panels in Figures 3a and 3b become strongly reduced.The total perpendicular (solid) and parallel (dot-dashed) pressure profiles are then shown by the black lines, obtained by summing the pressures of the warm ions (green and yellow lines), the hot ions (red), and the electrons (blue).
[24] Examining these pressure data, it can be seen that the warm water ion pressure (green) dominates the warm proton pressure (yellow) by more than an order of magnitude over the whole radial range.The warm water ion pressure also dominates the hot ion pressure (red) inside ∼10 R S , while the hot ion pressure becomes comparable with and larger than the warm ion pressure at larger distances.The electron pressure (blue) is typically an order of magnitude less than the total pressure over the whole range.

Current Density Profiles
[25] These plasma parameter profiles are then employed to derive the values of the various current density terms in equation ( 2).The inertia current requires the mass density r m of the plasma, dominated throughout by the warm ions, determined by combining the total number density with the water ion to proton number density ratio in Figure 2a.This is then combined with the azimuthal velocity model shown in Figure 2d and magnetic field parameters, of which the total field strength B is shown in the third panels of Figures 3a and 3b (blue data); a field strength scale is provided on the right-hand side, which also shows the colatitudinal component of the field, B (green), for use in later discussion.The inertia current density so determined is then shown by the green curve in the fourth panels of Figures 3a and 3b.It peaks in the innermost region sampled at values of ∼70 pA m −2 , and falls quite rapidly outside ∼7 R S both inbound and outbound to values of ∼10 pA m −2 and below at distances beyond ∼13 R S .
[26] Similarly, the pressure anisotropy current density in equation ( 2) is determined from the difference between the perpendicular and parallel pressures, which thus involves only the warm ion population in this formulation, combined with magnetic field parameters and the R ≈ r/3 approximation.This is shown by the blue curve in the fourth panels of Figures 3a and 3b, where, due to the P ?> P k conditions prevailing, this current has large negative (westward directed) values of ∼−45 pA m −2 in the innermost region, rising rapidly toward zero at and beyond 12 R S where the ion distributions become near isotropic.The pressure anisotropy current thus cancels a significant fraction of the inertia current in the inner region, a finding which Kellett et al. [2010] argued to be a direct consequence of the ion pickup process from Enceladus-related neutrals in this region.The combination of the two currents inside 12 R S is shown by the orange curve in the fourth panels in Figures 3a and 3b, which peaks near ∼7 R S at ∼35 pA m −2 , half the peak inertia current value, and falls more gradually to smaller values beyond.
[27] While the inertia and pressure anisotropy current densities depend only on individual values of plasma and field parameters as measured or estimated, the pressure gradient current density must be determined from the variation of the perpendicular pressure along the spacecraft track, assumed to be steady state and due principally to radial rather than to LT variations as indicated in section 2.1.This is done by least squares fitting polynomial functions to the total perpendicular pressure data, as shown in the third panels of Figures 3a and 3b.The black lines show the total perpendicular pressure as determined in the second panels of Figures 3a and 3b, while the red lines show the polynomial fits, where a fifth-order polynomial has been fitted in the inner region, and a third-order polynomial in the outer region, ensuring that the pressure and its gradient are continuous at the join between, marked by the purple dots.Some pressure data have been omitted from the fit on the outbound pass, indicated by the dashed line portion of the red curve in Figure 3b, where the spacecraft appears temporarily to have left the hot central plasma sheet region.It can be seen that these polynomials provide good overall fits to the pressure data while smoothing over small-scale variability, some of which may be related to hot plasma injection events.We also note that comparison of the per-pendicular plasma pressure (black) and magnetic field pressure (blue) in the third panels of Figures 3a and 3b relates directly to the local plasma b value (the perpendicular pressure divided by the magnetic pressure).It can be seen that b is small but increasing with radial distance in the inner region reaching b ≈ 1 at ∼8-9 R S , while b ≥ 1 conditions generally prevail throughout the outer equatorial magnetosphere, as found previously by Sergis et al. [2010].
[28] The perpendicular pressure gradient current density derived using the polynomial fits combined with magnetic field parameters is shown by the red line in the fourth panels of Figures 3a and 3b.Values are omitted in regions where the fitted curves are not representative of the pressure data (shown dashed), under which condition the fitted profile cannot appropriately be combined with the simultaneously observed field data.It can be seen that the current increases from values of ∼20 pA m −2 in the inner region to peak at ∼65 pA m −2 at ∼8.5 R S and ∼55 pA m −2 at ∼7.5 R S for the inbound and outbound data, respectively, before falling again in the outer region, more quickly on the inbound (dayside) pass than on the outbound (nightside) pass.
Comparison with the combined inertia-pressure anisotropy current (orange then green lines) shows that the two components are comparable in the innermost region at ∼6 R S , while the inertia-pressure anisotropy current then falls to roughly half the pressure gradient current at radial distances ∼8 to ∼13 R S , and to even smaller fractions beyond.The total current density, shown by the black line in the fourth panels in Figures 3a and 3b, thus has a profile similar to that of the pressure gradient current, but elevated by overall factors of ∼1.5 in agreement with the results of Kellett et al. [2010] based on Revs 15 and 16 inbound data, the factor being somewhat larger than this in the innermost region, and somewhat smaller in the outermost region.
[29] With regard to the significance of the current densities determined in Figure 3, and on other passes, we note that due to the near-equatorial nature of the spacecraft trajectory, the currents determined will generally correspond to the central equatorial current layer where the current density maximizes with respect to latitude.North-south displacements of the spacecraft from the equatorial plane are typically ∼0.1 R S or less throughout, small compared with the current layer half thickness of ∼1.5 R S determined by Kellett et al. [2009].Beyond radial distances of ∼10 R S , however, previous studies have shown that the current sheet center becomes increasingly displaced northward of the planet's equatorial plane due to the action of the solar wind flow during the southern summer conditions that prevailed throughout the study interval [Arridge et al., 2008b;Kellett et al., 2009].Estimates of this effect based on the modeling results of Arridge et al. [2008b] suggest that the displacement of the current sheet center northward of the spacecraft may increase typically to ∼1 R S at the 20 R S outer radial limit considered here.However, with a half thickness of ∼1.5 R S this still implies that the spacecraft will lie within the main part of the equatorial current layer at such distances.Furthermore, as discussed in section 2.5 in relation to Figure 3b, apparent exits from the main current layer observed on some passes in the outer nightside region are readily identified and excluded from the analysis.Conse-quently, our results should provide representative values of the current density within the central equatorial ring current over the full radial range considered here.

Comparison With Field Modeling Results
[30] In Figure 4 we show a comparison of these total current density profiles with those obtained from CAN model fits to the magnetic field data, where we show results for the inbound (Figures 4a and 4b) and outbound (Figures 4c and 4d) passes of Rev 20.Figures 4a and 4c show the CAN model fits (gray dashed lines) to the colatitudinal component of the magnetic field (blue dots), from which the Cassini Saturn Orbit Insertion (SOI) internal field model of Dougherty et al. [2005] has been subtracted.The residual field results principally from the ring current, and has strong negative values inward of ∼10 R S , increasing to small positive values for the dayside inbound pass and weaker negative values for the nightside outbound pass in the outer region (>15 R S ).This minor day-night asymmetry is an effect due mainly to magnetopause and tail currents flowing at larger distances.Significant field variations are also present associated with the global field oscillations near the planetary period [e.g., Andrews et al., 2008Andrews et al., , 2010], which we attempt to "average through" in the fitting.
[31] The methodology employed to obtain the CAN model fits is described by Bunce et al. [2007], except that here we use a current sheet half thickness of 1.5 R S following the results of Kellett et al. [2009].The remaining three ring current model parameters (as described in section 1) for the inbound pass are inner and outer radii of 7 and 23 R S , and a current parameter m 0 I 0 = 50 nT, while for the outbound pass these parameters are 7 and 16.75 R S , and 50 nT.In addition we also use a simple representation of the day-night asymmetry effect of the more distant currents to improve the fits, given by a colatitudinal field that varies linearly with the X coordinate [see Bunce et al., 2007] from −1.0 nT at X = 20 R S to +4.0 nT at X = −20 R S .The resulting fits to the data are seen to be good for both passes, with RMS deviations of 1.9 and 2.1 nT for the inbound and outbound passes, respectively, compared with peak perturbations in excess of ∼10 nT.
[32] The CAN model azimuthal current density profiles are then shown by the gray dashed lines in Figures 4b and  4d, while the solid black lines show the total current density obtained from the plasma data in the fourth panels of Figures 3a and 3b.Comparison of these two empirical estimates shows good agreement between their gross features, thus showing that the current density deduced from the plasma data, combined with a full layer width of ∼3 R S , is compatible with the perturbations observed in the equatorial magnetic field.In particular, the peak current densities deduced from the plasma data on the inbound and outbound passes have values of ∼95 pA m −2 at ∼8 R S and ∼85 pA m −2 at ∼7 R S , respectively, compared with ∼95 pA m −2 at ∼7 R S for the inbound and outbound CAN models.However, for the inbound pass, the current density deduced from the plasma data then decreases more rapidly with increasing radial distance than the 1/r dependence assumed in the CAN model (r being the cylindrical radial distance from the axis equal to r in the equatorial plane), as previously noted by Sergis et al. [2010].This is not the case for the outbound pass, however,  (c and d) outbound.Figures 4a and 4c show the colatitudinal component of the magnetic field (nT) from which the "Cassini SOI" model of the internal field has been subtracted (blue).The CAN model fit to these data is shown by the gray dashed line, the parameters of which are given in the text.Figures 4b  and 4d show the total current density derived from the plasma data (black solid line) as shown in the fourth panels of Figures 3a and 3b, together with the current density profile corresponding to the CAN model fit shown in Figures 4a and 4c  where the current deduced from the plasma data decreases at a slower rate with radius than on the inbound pass, more comparable with that of the CAN model.

Overall Results
[33] Having thus described the analysis of the data from one Rev in detail, we now survey and compare the results obtained from all 22 ring current passes.

Local Time Dependence
[34] We begin by providing an overview of the dependence on LT of the principal plasma and field parameters and the resulting current density components.These are shown in Figures 5-7, where we have divided values calculated at 0.25 R S radial resolution into four LT quadrants, corresponding to midnight to dawn, dawn to noon, and so on, and have determined mean profiles versus radial distance.With this choice, radial coverage is good in all Figure 5. Radial profiles of mean plasma and magnetic field parameters separated into four LT quadrants, namely, midnight to dawn (blue lines), dawn to noon (orange), noon to dusk (red), and dusk to midnight (green).The solid colored lines show the mean values in each quadrant of the 0.25 R S radial resolution data obtained from each pass, while the gray shaded region represents the associated standard error of the mean for each profile (shown individually for each quadrant in Figure 9).(a) The number of available data points (passes) for the plasma parameter profiles, (b) the mean total number density, (c) the mean total plasma pressures perpendicular (solid lines) and parallel (dot-dashed lines) to the field, and (d) the mean colatitudinal component of the magnetic field.
quadrants except noon to dusk, where data are available only in the inner region out to radial distances of ∼9 R S .
[35] In Figure 5 we show radial profiles of the plasma and field parameters, where the blue lines correspond to 0-6 h LT, orange to 6-12 h, red to 12-18 h, and green to 18-24 h.Green and blue thus correspond to the nightside, and orange and red to the dayside.The gray shaded regions on each profile indicate the associated standard errors of the mean (shown individually in Figure 9).Figure 5a first shows the number of available passes that contribute to each mean plasma parameter value.Figure 5b shows profiles of the total number density, while Figure 5c shows the total perpendicular (solid lines) and parallel (dot-dashed lines) plasma pressures summed over the contributions of warm ions, hot ions, and electrons.Figure 5d then shows profiles of the main colatitudinal component of the magnetic field that appears in the numerator of the inertia current and the denominator of the pressure gradient current.In Figure 6 we show the individual contributions to the plasma pressure, where for each quadrant we show radial profiles of the perpendicular (solid) and parallel (dot-dashed) pressures of the warm ions (water group plus protons, green), hot ions (water group plus protons, red), and electrons (blue).
[36] If we first consider the total number density profiles shown in Figure 5b, dominated by the warm plasma population throughout, it can be seen that the mean densities are essentially independent of LT in the inner region between ∼5 and ∼9 R S .Increasing variability between the quadrants Figure 6.Radial profiles of the mean perpendicular (solid) and parallel (dot-dashed) pressures of warm ions (water group plus protons, green), hot ions (water group plus protons, red), and electrons (blue), divided into LT quadrants corresponding to (a) dawn to noon, (b) noon to dusk, (c) dusk to midnight, and (d) midnight to dawn. is evident at larger distances, but typically only by factors of ∼2, and without a clear systematic dependency on LT.Indications can be seen of a day-night asymmetry in the dusk sector in the innermost region between ∼3 and ∼5 R S , with modestly larger densities on the nightside than on the dayside.While this result is based on data from only two passes (Revs 15 and 16), the effect is present in both these data sets.
[37] Turning now to the pressure data, we first note that since the warm ion pressures are derived in our formulation by combining the warm ion density with the temperature models in Figure 2b, these profiles, shown separately in Figure 6, also display little systematic variation with LT.The mean electron pressures in Figure 6 similarly show a lack of systematic LT effects, though these provide only modest contributions (∼10% or less) to the total pressure throughout.The mean hot ion pressures in Figure 6, on the other hand, become important in the outer region, typically rising to exceed the mean warm ion pressures by factors of ∼2 beyond ∼10-12 R S .In this outer regime they again display only modest LT dependencies of factors of ∼2, however, with a tendency for somewhat higher mean pressures and densities in the dusk to midnight sector, possibly reflecting a similar asymmetry in energetic ENA emissions reported by Carbary et al. [2008b].The hot ion pressures and densities are considerably more variable in the inner region inside ∼9 R S , but here they generally provide only small contributions to total values.As a consequence of these behaviors, the mean total plasma pressure values in Figure 5c also show a marked lack of dependency on LT, particularly between ∼5 and ∼9 R S , though with a tendency for the perpendicular pressure in the dusk to midnight sector (green) to be marginally higher than those in other quadrants outside this range.
[38] Figure 5d shows that the strength of the colatitudinal field also has a modest LT dependence, with values beyond ∼9 R S becoming increasingly larger on the dayside (at least in the dawn to noon sector) than on the nightside, reaching almost factors of ∼2 at ∼15 R S and beyond.A similar effect is not seen in the total field strength in the outer magnetosphere, however, which again shows little dependency on LT (not shown).From equation (2) we note that this field effect enhances the pressure gradient current in the outer region on the nightside compared with the dayside for given pressure gradients.It also enhances the inertia current on the dayside compared with the nightside for given centrifugal "forces," but as already noted in relation to Figure 3 this component is generally less important than the pressure gradient current in the outer region.
[39] Corresponding radial profiles of the mean current density similarly divided into LT quadrants is shown in Figure 7, in a similar format to Figure 5.In Figure 7a we show the mean inertia and pressure anisotropy current densities, Figure 7b shows their sum, while Figure 7c shows the mean perpendicular pressure gradient current density.Figure 7d shows the mean total current density.Figure 7e then shows the mean colatitudinal component of the magnetic field with the "Cassini SOI" internal field subtracted, principally showing the overall magnetic effect of the ring current.
[40] As may be anticipated from the discussion of Figure 5, it can be seen that the inertia and pressure anisotropy currents in Figure 7a both have very similar profiles in all four LT quadrants, particularly in the inner region to radial distances of ∼9 R S .The inertia current rises from small values of ∼15 pA m −2 at ∼3 R S , peaks at ∼70 pA m −2 at ∼6 R S , and falls with radial distance to values of ∼10 pA m −2 beyond ∼15 R S .The pressure anisotropy current similarly increases in magnitude from small values at ∼3 R S to a negative peak ∼−40 pA m −2 near ∼5.5 R S , approximately half the peak inertia current value, and then decreases in magnitude back toward zero at and beyond ∼12 R S where the pressure becomes near isotropic.The combined inertiapressure anisotropy current shown in Figure 7b thus peaks at ∼35-40 pA m −2 at ∼7 R S , and falls gradually to smaller values in the outer regions, where the nightside current (blue and green) appears somewhat more variable than the dayside current (orange).
[41] Considering the pressure gradient current in Figure 7c, we similarly see that the profiles are all quite similar in the inner region to ∼9 R S , but are more variable in the outer region beyond.The current is small and negative in the innermost region where the perpendicular pressure rises with radial distance, passes through zero at ∼5 R S where the pressure maximizes, and peaks at ∼60 pA m −2 at ∼8.5-9.0R S for the LT quadrants from midnight to dusk via dawn and noon (blue, orange, and red lines).In the dusk to midnight sector (green), however, the mean current initially peaks at smaller ∼40 pA m −2 values at ∼6.5 R S , before increasing further with radial distance, reaching ∼80 pA m −2 at ∼10.5 R S .Beyond these distances the pressure gradient current then decreases in the outer region, with all profiles reaching ∼10-20 pA m −2 by ∼20 R S .
Overall, the strongest pressure gradient current in the outer region beyond the peaks is found in the dusk to midnight sector, declining in the midnight to dawn sector, and further in the dawn to noon sector.These differences reflect the similar behavior of the perpendicular pressure gradient in these sectors, overall differences being factors of ∼2 or less, combined with the effect of the day-night asymmetry in the colatitudinal field strength shown in Figure 5d.Comparison of the profiles of the pressure gradient current with the combined inertia-pressure anisotropy current shows that these currents are comparable at radial distances between ∼5 and 7 R S , beyond which the inertia-pressure anisotropy current falls to roughly half the pressure gradient current at distances ∼8 to ∼14 R S , and to smaller fractions in the outermost regions.The mean total current density profiles shown in Figure 7d are thus similar to those of the pressure gradient current, but are elevated in value relative to the latter by factors of ∼1.5-2.0, the factor being somewhat larger in the inner region than in the outer.
[42] Overall these results show that within the limits of the data coverage, the mean current density in Saturn's ring Figure 8.Comparison of current density profiles on the inbound (dayside) and outbound (nightside) passes of (a-e) Rev 16 and (f-j) Rev 20, in a similar format to Figure 7.The inbound and outbound passes on each Rev are represented by the blue and red lines respectively.Figures 8a and 8f show the inertia and pressure anisotropy current densities, while Figures 8b and 8g show their sum.Figures 8c and  8h show the pressure gradient current density, while Figures 8d and 8i show the total current density.Figures 8e and 8j show the residual colatitudinal component of the magnetic field.
Figure 9 current does not vary greatly with LT, though being modestly larger on the nightside than on the dayside by factors of ∼1.5, particularly in the dusk sector, in the region beyond ∼10 R S .The magnetic perturbations relative to the planetary field observed in the equatorial magnetosphere correspondingly also show relatively modest LT variations, as seen in Figure 7e, though again being somewhat larger on the nightside than on the dayside in conformity with the above discussion.
[43] These principal features are found to be true not only of the mean values shown in Figure 7, but also on individual Revs that traverse the dayside sector on the inbound pass and the nightside sector on the outbound pass, separated in time typically by ∼2 days.This is illustrated in Figure 8, which shows results for Revs 16 (Figures 8a-8e) and 20 (Figures 8f-8j).We note that the inbound pass of Rev 16 was previously discussed in detail by Kellett et al. [2010], while the detailed data for Rev 20 are shown in Figure 3.The trajectories of both passes are shown in Figure 1.The current density profiles derived from the inbound (dayside) and outbound (nightside) passes of these Revs are shown by the blue and red lines, respectively, in a similar format to Figure 7. Thus Figures 8a and 8f show the inertia and pressure anisotropy current densities, Figures 8b and 8g show their sum, Figures 8c and 8h show the pressure gradient current density, while Figures 8d and 8i show the total current density.Figures 8e and 8j show the residual colatitudinal field.
[44] In these cases the inbound and outbound current density profiles are similar to each other in the inner region to ∼7-8 R S where the current rises to peak values of ∼100 pA m −2 , though showing a tendency for the rise to occur at slightly smaller radii on the outbound (nightside) pass than on the inbound (dayside) pass particularly for Rev 16.This reflects the related day-night asymmetry in the density of the warm ion population in the innermost region noted above in the discussion of Figure 5.The peak currents on both Revs are then sustained over a somewhat larger radial range on the dayside than on the nightside, before the dayside values fall more rapidly to drop below the nightside values in the outer region beyond ∼10 R S , an effect that results mainly from the pressure gradient current.

Pass-to-Pass Temporal Variability
[45] In Figures 9 and 10 we now examine in more detail the pass-to-pass temporal variability in the data that were used to construct the mean radial profiles for each LT quadrant in Figures 5-7.In Figures 9 and 10 separate plots are shown for each LT quadrant, specifically for noon to dusk (Figures 9a and 10a), dawn to noon (Figures 9b and  10b), dusk to midnight (Figures 9c and 10c), and midnight to dawn (Figures 9d and 10d).The solid black line shows the mean value of the parameter concerned, with the gray shaded region indicating the associated standard error, as in Figures 5-7, while the individual 0.25 R S data values used to construct the plots are shown by dots, color coded for each Rev as shown in Figures 9a and 10a. Figure 9 shows from top to bottom the total plasma number density, the perpendicular pressures of the warm ions (water group plus protons), hot ions, and electrons (note the change in range in the electron pressure plot), the total perpendicular pressure, and the colatitudinal field strength.Figure 10, similar to Figure 7, shows from the top the inertia and pressure anisotropy current densities, their sum, the perpendicular pressure gradient current density, and the total current density.
[46] It can first be seen from Figures 9 and 10 that there is no strong pass-to-pass variability in the total density, plasma pressure, or current density values in the inner region extending outward toward the usual peak in the current density profile at ∼9 R S .This is particularly evident in the noon to dusk sector shown in Figures 9a and 10a, where all eleven Revs contribute data.Correspondingly, the current density values generally lie within ∼±10-15 pA m −2 of the mean values in this region, compared for example with peak values of ∼90 pA m −2 .There is thus no evidence of major variability in the dominant warm ion population in this region over the ∼10 month interval of this study.Beyond these distances, however, the pass-to-pass variations generally grow in amplitude in all quadrants for which data exists, both in the plasma parameters and the current values.This is particularly notable in the dawn to noon sector shown in Figures 9b and 10b, where the scatter in the data beyond ∼9 R S , especially in the hot ion pressure, results in scatter in the current densities rising to ∼±20 pA m −2 , compared for example with typical current density values in this region of ∼50 pA m −2 .In addition, large pass-to-pass variations in the current density are evident in the dusk to midnight sector shown in Figure 10c, specifically at central radial ranges between ∼8.5 and ∼11.5 R S .While some profiles show rather steadily declining current densities with radial distance in this region, exemplified by Rev 20 outbound shown in Figures 3b and 6b (pale blue dots in Figures 9 and 10), others show a significant secondary peak in this region, in one case (Rev 25) reaching estimated total current densities of ∼200 pA m −2 (brown dots) resulting from enhancements in both the inertia and pressure gradient currents in this region.
[47] In Figure 11 we present individual examples illustrating the variability of the current on the dayside.Specifically we show current and field profiles for the inbound passes of Revs 17 (red), 18 (green), and 19 (blue) in a format similar to Figure 8, the corresponding data being shown by dots with shades of green in Figures 9 and 10.These passes share essentially the same trajectories as each Figure 9. Plots showing each individual 0.25 R S radial resolution data point that contributes to the mean plasma and field profiles in Figure 5, the data values from each Rev being color coded as shown in Figure 9a.Separate results are provided for the four local time quadrants as indicated in the plot, specifically for (a) noon to dusk, (b) dawn to noon, (c) dusk to midnight, and (d) midnight to dawn.The black lines and gray shaded regions show the mean values and their standard error, as in Figure 5.The plots for each quadrant show from top to bottom the total number density; the perpendicular pressures of the warm ions (water group plus protons), the hot ions, and the electrons; the total perpendicular pressure; and the colatitudinal field strength.
Figure 10.Plots showing radial profiles of the current density components in the same format as Figure 9.The plots for each quadrant show from top to bottom the inertia and pressure anisotropy current densities, their sum, the pressure gradient current density, and the total current density.other separated in time by ∼28 days, spanning the prenoon sector in the outer region beyond ∼9 R S , and the noon to dusk sector inward to periapsis at ∼4.5 R S (Figure 1).It can be seen that the currents are similar to each other in the inner region up to peak values at around 8-9 R S , but differ more markedly in the dawnside outer region.Most notably, while the currents in the outer region are very similar to each other on Revs 17 and 19, the current on Rev 18 is weaker by a factor of up to ∼2, due principally to a significant reduction in the perpendicular pressure gradient current.Examination of the plasma parameters shows, however, that this is not principally due to changes in the perpendicular pressure profiles, but rather to the presence of a stronger colatitudinal field in the case of Rev 18 than for Revs 17 and 19.The fifth panel of Figure 11 shows that the negative perturbation fields for Revs 17 and 19 are very similar (as are the current profiles), while that for Rev 18 is significantly smaller in magnitude (consistent with smaller currents), meaning that the total equatorial B field is stronger in that case.A likely possibility is that this effect results from differing upstream solar wind conditions during these passes such that the magnetosphere was more compressed during Rev 18 than on Revs 17 and 19.These observations may then relate to the results of Bunce et al. [2007] based on CAN modeling of the magnetic field perturbations, who found weaker currents for more compressed magnetospheres.Figure 11 also illustrates a further difference in the current profiles between these Revs, in the presence on Rev 17 of a major secondary peak in the current density in the radial range from ∼11 to ∼13 R S .This originates from the inertia current term, and is due to a relatively localized peak in the plasma number density.
[48] Plots illustrating the appearance of secondary current maxima near ∼10 R S in the premidnight sector are shown in Figure 12.In Figure 12a we show plasma, field, and current profiles for Rev 21 outbound which exhibits such a peak (dark blue dots in Figures 9 and 10), which we compare with the corresponding profiles for Rev 20 outbound shown in Figure 3b which does not (light blue dots in Figures 9  and 10).From Figure 1 we note that these Revs again share essentially the same trajectory separated in time by ∼39 days, outbound in the dusk to premidnight sector, crossing the meridian into the postmidnight sector at ∼14 R S .The current and field profiles from these Revs are compared in Figure 12b in the same format as Figures 8 and 11.The principal difference again involves the pressure gradient current, but unlike the dayside example in Figure 11, this is not now due to differences in the equatorial field strength as seen from the fifth panel of Figure 12b, but rather to differences in the radial profile of the perpendicular pressure.Comparison of these profiles in the third panels of Figures 3b  and 12a shows that the pressure profile is somewhat flatter in the inner region to distances of ∼8 R S for Rev 21 than for Rev 20, leading to smaller pressure gradient currents in the former case than in the latter in this region.However, the pressure profile for Rev 21 then dips more rapidly to smaller values than for Rev 20 beyond ∼10 R S , leading to a corresponding peak in the pressure gradient current in the former case, located between ∼8 and ∼12 R S .Similar effects are also seen on the outbound passes of Revs 22, 23, and 25, all of which span the dusk to midnight sector (Figure 1), while the current profile for Rev 24 appears more similar to Rev 20.

Overall Mean Profiles
[49] Although we have focused above on the LT dependence and temporal variability that occur in the plasma and field parameters in Saturn's ring current region, and in the consequent current densities, it should nevertheless be emphasized that these variations are overall modest in nature, typically factors of ∼2 or less, such that discussion of overall properties is meaningful.In Figure 13 we thus show overall mean profiles of the plasma and field parameters obtained by averaging the data from all 22 near-equatorial passes examined here, irrespective of LT, while in Figure 14 we similarly show the current density components.The mean values are shown by the solid lines, while the gray shaded regions again indicate the associated standard error of the mean.Specifically, Figure 13a shows the number of data points contributing to each 0.25 R S radial interval, Figure 11.Current density and magnetic field profiles versus radial distance for the inbound passes of Revs 17 (red), 18 (green), and 19 (blue).The format is similar to Figure 8.
Figure 13b shows the total number density (blue), and the partial densities of the warm (≥20 eV) electrons (magenta) and hot ions (red), Figure 13c shows the perpendicular (solid) and parallel (dot-dashed) pressures of the warm ions (water group plus protons, green), hot ions (water group plus protons, red), and electrons (blue), while Figure 13d shows the total perpendicular (solid) and parallel (dotdashed) pressures.Figure 14 similarly shows the mean values of the current components in the same format as Figure 7, where the dashed lines in Figures 14d and 14e also show a mean CAN model profile as will be discussed further below.
[50] It can again be seen from Figure 13 that the warm ions dominate the plasma density throughout, and hence the inertia current density.In our formulation they are also the only contributor to the anisotropy current density.The warm ions also dominate the plasma pressure to distances of ∼10 R S , while the pressure of the hot ions typically exceeds that of the warm ions by factors of ∼2 at distances beyond ∼12 R S .Thus the pressure gradient current is also determined mainly by the properties of the warm ions in the inner region to ∼10 R S , encompassing the rapid rise in this current component with radius and the usual region of peak values, while the hot ions are the more important component by factors of ∼2 in the outer region beyond ∼12 R S where the pressure gradient current more slowly declines.
[51] Turning now to Figure 14, it can be seen that the mean inertia current increases from small values in the inner region to peak at ∼70 pA m −2 at ∼6 R S , before decreasing with radial distance to values of ∼10 pA m −2 by ∼15 R S .The pressure anisotropy current peaks in magnitude at ∼−40 pA m −2 at ∼5.5 R S , and declines toward zero at and beyond ∼12 R S where the pressure becomes near isotropic.The combined inertia-pressure anisotropy current thus increases from small positive values to peak at ∼40 pA m −2 at ∼7 R S , approximately half the peak inertia current, and then gradually decreases with increasing radial distance.The pressure gradient current has negative values of ∼−15 pA m −2 inside of ∼5 R S where the perpendicular pressure increases with radius, then increases rapidly to peak at ∼60 pA m −2 at ∼9 R S , before decreasing slowly with increasing radial distance to values of ∼15 pA m −2 by ∼20 R S .The total current follows a similar profile to the pressure gradient current, but is augmented in strength by the combined inertia-pressure anisotropy current by factors of ∼2 in the inner region, and by lesser factors at larger distances.The current has small negative values in the innermost region, crosses through zero at ∼4.5 R S , and continues to increase to its peak at ∼90 pA m −2 at ∼9 R S after which it falls off with increasing radial dis-tance at a similar rate to that of the pressure gradient current.These results are overall very comparable to the mean values obtained by Sergis et al. [2010] in the central radial range 6-15 R S which they investigated, although our estimates of the mean pressure gradient current are somewhat elevated in the inner region to ∼10 R S , and are somewhat reduced beyond.
[52] The mean CAN model profiles shown in Figures 14d  and 14e have been derived simply by averaging the model parameters obtained from the fits to the field perturbations for each individual pass.Along with a current sheet half thickness of 1.5 R S , the mean inner and outer radii are 6.6 and 19.9 R S , respectively, while the mean current density parameter is m 0 I 0 = 53.2nT.The dashed line profiles shown in Figures 14d and 14e then simply represent results for a CAN model employing these mean parameter values.No additional fields representing the effect of more distant magnetopause and tail currents are now included, since these data generally cover a wide range of LTs at a given radial distance.Nevertheless, the model fit to the mean perturbation fields shown in Figure 14e is seen to be reasonably good, with a RMS deviation of 1.6 nT compared with peak negative values of ∼−12 nT.Comparison of the mean total current density profile derived from the plasma data with the mean CAN model profile in Figure 14d also shows reasonable agreement of the gross features.Specifically we note similar peak current densities of ∼100 pA m −2 located at comparable radial distances of ∼7-9 R S , with rapid rises of the current inside those distances, and more gradual falls beyond.However, the model current profile with its assumed sharp inner cutoff clearly cannot account for the details of the rise in current with radius in the inner region, while beyond the peak the mean current density falls off somewhat more rapidly with distance than the model.

Summary and Discussion
[53] We have derived radial profiles of the azimuthal current density in Saturn's ring current region between distances of ∼3 and 20 R S , using plasma bulk parameter and magnetic field data obtained from the inbound and outbound passes of eleven consecutive closely equatorial Cassini orbits that span a 10 month interval from September 2005 to July 2006.These current densities are expected to be representative of the central part of the equatorial ring current layer over the full radial range, though the spacecraft may typically be located toward its southern boundary at the largest radial distances due to the northward displacement of the current layer under the southern summer conditions prevailing [Arridge et al., 2008b;Kellett et al., 2009].Radial coverage is generally good in all LT sectors, except for the noon to dusk sector where coverage extends only to ∼9 R S .Within this limitation, however, the data set allows exploration of both the LT dependence and pass-to-pass temporal variability of the plasma, field, and current density within the above radial range, thus expanding significantly on the study of averaged conditions by Sergis et al. [2010] and the initial results of a related study by Kellett et al. [2010] based on two passes through the dayside sector.
[54] Our principal finding is that the plasma parameters, azimuthal current, and perturbation field in the above region generally show only modest variations in both LT and from Figure 12b.Current density and magnetic field profiles versus radial distance for the outbound passes of Revs 20 (red) and 21 (blue).The format is the same as Figures 8 and 11. pass to pass over the interval of the study.This is particularly true of the inner region up to the usual peak in current density at radial distances near ∼9 R S , though factor of ∼2-3 variability is present in the outer region beyond.It seems likely that a significant contributor to the latter variability is the presence of periodic hot ion injection events in the outer region [e.g., Brandt et al., 2010], together with solar wind-related variations [e.g., Bunce et al., 2007Bunce et al., , 2008]].
[55] These findings thus provide significant justification for our main analysis assumptions of approximate temporal invariance and local axisymmetry, such that parameter variations observed on a given spacecraft pass are attributed primarily to radial rather than to temporal or to LT effects.In particular with regard to approximate local axisymmetry, if we consider the perpendicular pressure profiles shown in Figure 5c, then at radial distances beyond ∼5 R S we can write (∂P ?/∂r) ≈ −P ?/L r , with L r ≈ 3 R S .Similarly, considering the azimuthal variations at given radius we can write |∂P ?/∂φ| ≈ P ?/p for factor of ∼2 variations with LT at radial distances beyond ∼10 R S , also not inconsistent with the azimuthal gradients during injection events according to the modeling results of Brandt et al. [2010].The ratio of these pressure gradients at radius r is then 1 r @P ?j =@φj @P ?=@r j such that with L r ≈ 3 R S , the radial gradients are more than an order of magnitude larger than the azimuthal gradients at radii of interest (r ≈ 10 R S and larger).These considerations together with lack of major pass-to-pass variability thus justify our basic assumption that the pressure variations observed on particular spacecraft passes are primarily due to radial variations.
[56] The total azimuthal current density derived on this basis rises rapidly from near-zero values inside ∼5 R S to peak at ∼90 pA m −2 at ∼9 R S , and then falls more slowly with increasing radial distance to values below ∼20 pA m −2 at the 20 R S outer limit of our study.Comparison with the current profiles obtained from CAN modeling of the magnetic perturbations, assuming the current layer has a full thickness of 3 R S based on the results of Kellett et al. [2009], shows good agreement between their gross features, though the details of the radial profiles differ somewhat as may be expected.The gross agreement shows, however, that the current density deduced from the plasma data is overall compatible with the simultaneous perturbations observed in the magnetic field data, though further work is required to examine their mutual consistency at a more detailed level.
[57] Of the components that form the total current, the most important overall is the perpendicular pressure gradient current.In the inner region the inertia current dominates, but is significantly canceled by the oppositely directed pressure anisotropy current.The combined inertia-pressure anisotropy current is thus reduced to comparability with the pressure gradient current at radial distances ∼5-7 R S inside the current peak, while falling to roughly half the latter values at larger distances.These findings are in agreement with the initial results of Kellett et al. [2010], who argue that the significant reduction of the inertia current by the pressure anisotropy current in the inner region follows directly from the nature of the source of the dominant warm water plasma in this region.These plasma particles originate from ionization of Kepler-orbiting neutrals in the Enceladus gas torus, which are then "picked up" by the significantly faster flow of the near-corotating plasma.This process results in the pickup ion population being strongly peaked perpendicular to the field in velocity space, with a consequent dominant perpendicular pressure giving rise to the pressure anisotropy current that is directly related to the near-corotational plasma flow speed that also gives rise to the inertia current.Estimates show that these current components should then be comparable in magnitude and opposite in direction, as found here in the inner region.
[58] With regard to the plasma populations that principally determine the currents, we note that the warm ion plasma that originates in the Enceladus torus in the inner magnetosphere dominates both the inertia and the anisotropy currents throughout, together with the pressure gradient current to radial distances of ∼10 R S .The properties of this population thus govern the rapid growth in the current with radius in the inner part of the system, extending to the region just beyond the usual peak in the total current density at ∼9 R S .Inside this region the warm plasma parameters and related current densities are found to be relatively unvarying with LT and from pass to pass, typically within factors of less than ∼2.At larger distances the hot (≥3 keV) ion pressure becomes more important, typically exceeding the pressure of the warm ions by factors of ∼2 at radial distances beyond ∼12 R S .This corresponds to the region where the total current density, of which the pressure gradient current is the most important component, falls more slowly with increasing distance.In this region both warm and hot plasma parameters and resulting current densities vary more strongly with LT and from pass to pass, but again typically within factors of ∼2-3.The overall relative invariance of the plasma parameters and currents is correspondingly reflected in the relatively modest variations in the magnetic perturbations in the inner magnetosphere noted previously by Bunce et al. [2007] and Leisner et al. [2007].
[59] This overall relatively steady picture contrasts significantly with related conditions at Earth, where the ring current within the quasi-dipolar magnetosphere changes by significant factors over time both in magnitude and radial extent [e.g., Lui et al., 1987;De Michelis et al., 1997].The equivalent perturbation field in the inner region, monitored, e.g., as the D ST index by equatorial magnetic observatories, consequently also changes by significant factors over time, from typical quiet time values of ∼10 nT to storm time values up to a few hundred nT.Similar to Saturn, the terrestrial ring current results mainly from the perpendicular pressure gradient current, but the dominant plasma population involved in the latter case is the dynamically variable hot magnetospheric plasma which is injected into the inner magnetosphere from the nightside during substorms, and can build up to large values during extended magnetically disturbed intervals.No equivalent to Saturn's relatively unvarying warm plasma population is present in this case, the Earth's plasmasphere (of ionospheric origin) producing negligible magnetic effects.As we have noted above, periodic nightside plasma injection dynamics do occur at Saturn, involving ions with energies of a few tens of keV and above [e.g., Krimigis et al., 2007;Mitchell et al., 2009;Brandt et al., 2010], but this activity evidently does not usually perturb the equatorial plasma bulk parameters and resulting currents beyond the extent reported here.While the hot ion parameters are evidently highly variable in the inner part of the system, inside ∼9 R S , they usually make only a small contribution to the total current in this regime.
[60] Of the LT variations that are observed at Saturn, the most significant occur in the outer region beyond ∼10 R S , where the mean azimuthal current density is strongest in the dusk to midnight sector, and declines gradually in the midnight to dawn, and dawn to noon sectors (data being unavailable in the noon to dusk sector in this region).This effect is due to corresponding LT variations in the perpendicular pressure gradient of the plasma, possibly reflecting a similar asymmetry in energetic ENA emissions reported by Carbary et al. [2008b], with overall differences generally being less than factors of ∼2, combined with colatitudinal fields that are weaker on the nightside than on the dayside by factors of a comparable magnitude.Corresponding differences are found in the dayside (inbound) and nightside (outbound) current density profiles on individual spacecraft Revs separated by minimum intervals of ∼2 days, suggesting that this asymmetry is a consistent feature.
[61] Pass-to-pass variability is also present in the outer region, even on spacecraft trajectories that are essentially identical, but now separated in time by ∼30-40 days.An example has been presented in which the current density in the outer dayside region, specifically the dominant perpendicular pressure gradient current, varies by a factor of ∼2 between successive passes, in this case due mainly to changes in the equatorial field strength rather than in the pressure profile.It seems likely that this effect is due to variations in the upstream solar wind conditions leading to compressions and expansions of the dayside magnetosphere, connected to those found by Bunce et al. [2007] from CAN modeling of the magnetic field perturbations.Investigation of the dependency of the current profiles on external conditions remains a topic for future work.Other variability is undoubtedly due to the effect of periodic hot ion injection events, such as that modeled by Brandt et al. [2010].The appearance of a significant second peak in the current density, centered near ∼10 R S , is also found to be a common but not invariable feature in the premidnight sector.These current peaks again mainly involve the perpendicular pressure gradient current, sometimes the inertia current too, but are now found to be due to somewhat subtle variations in the radial pressure profile.
[62] We finally note that the properties of the ring current beyond ∼9 R S in the noon to dusk sector remains to be investigated.This region was not covered by the set of eleven near-equatorial Cassini orbits examined here, but has now been sampled during subsequent near-equatorial phases of the Cassini mission.Investigation of these data also represents a topic for future work.
[63] Acknowledgments.Work at Leicester was supported by STFC grants ST/H002480/1 and ST/H001972/1.S.K. was supported by a STFC Quota Award.M.K.D. was supported by STFC funding to Imperial College, and A.J.C. was supported by STFC rolling grant funding to UCL-MSSL.C.S.A. was supported by a STFC Postdoctoral Fellowship.Cassini radio and plasma wave research at the University of Iowa was supported by NASA through JPL contract 1279973.Work at the Academy of Athens was supported by subcontract 950782 with the JHU/APL.We thank S. Kellock and the Cassini team at Imperial College for access to the processed magnetic field data, G. R. Lewis and L. K. Gilbert for CAPS/ELS processing at MSSL, S. M. Krimigis for facilitating the use of MIMI data, and M. F. Thomsen and H. J. McAndrews for access to ion moment data.
[64] Masaki Fujimoto thanks the reviewers for their assistance in evaluating this paper.

Figure 1 .
Figure 1.Near-equatorial Cassini periapsis pass trajectories for Revs 15-25 plotted in Saturn's equatorial X-Y plane, with noon at the top and dusk to the left.Inbound and outbound segments within radial distances of 20 R S are shown in blue and red, respectively, and are shown in black beyond that distance.The trajectory for Rev 20, whose data are shown in Figure 3, is indicated by the solid line, with black circles being plotted at the beginning of each day, marked with day of year (DOY) numbers of 2006.The trajectories of other Revs are similarly shown by the dashed lines.The black dot-dashed lines in the top part show the Kanani et al. [2010] model magnetopause positions for solar wind dynamic pressures of 0.01 (outer line) and 0.1 nPa (inner line), spanning the usual range at Saturn.

Figure 3b .
Figure 3b.As in Figure 3a except for the outbound pass of Rev 20.In the third panel, perpendicular pressure values (black line) are omitted from the outer polynomial fit (red line) where the spacecraft appears temporarily to have exited the hot central plasma sheet (dashed portion of the red line).Current values in the fourth panel are omitted in this interval.

Figure 4 .
Figure 4. Radial profiles of the magnetic field and current density for Rev 20 (a and b) inbound and (c and d) outbound.Figures4a and 4cshow the colatitudinal component of the magnetic field (nT) from which the "Cassini SOI" model of the internal field has been subtracted (blue).The CAN model fit to these data is shown by the gray dashed line, the parameters of which are given in the text.Figures4b and 4dshow the total current density derived from the plasma data (black solid line) as shown in the fourth panels of Figures3a and 3b, together with the current density profile corresponding to the CAN model fit shown in Figures4a and 4c(gray dashed line).
Figure 4. Radial profiles of the magnetic field and current density for Rev 20 (a and b) inbound and (c and d) outbound.Figures4a and 4cshow the colatitudinal component of the magnetic field (nT) from which the "Cassini SOI" model of the internal field has been subtracted (blue).The CAN model fit to these data is shown by the gray dashed line, the parameters of which are given in the text.Figures4b and 4dshow the total current density derived from the plasma data (black solid line) as shown in the fourth panels of Figures3a and 3b, together with the current density profile corresponding to the CAN model fit shown in Figures4a and 4c(gray dashed line).

Figure 7 .
Figure 7. Radial profiles of the mean current density components and magnetic field separated into four LT quadrants, in the same format as Figure 5. (a) The mean inertia (upper) and pressure anisotropy (lower) current densities, (b) their sum, (c) the mean perpendicular pressure gradient current density, (d) the mean total current density, and (e) the mean colatitudinal component of the perturbation magnetic field (nT), from which the "Cassini SOI" model of the internal field has been subtracted.

Figure 12a .
Figure 12a.Radial profiles of particle and field parameters for the inbound pass of Rev 21, in the same format as Figure 3.

Figure 13 .
Figure 13.Overall mean radial profiles of plasma and magnetic field parameters for all LTs combined.The mean values are shown by the solid and dot-dashed lines, while the gray shaded regions indicate the associated standard error of the mean.(a) The number of data points contributing to each 0.25 R S radial interval; (b) the number densities of hot ions (red), warm (≥20 eV) electrons (magenta), and the total number density (blue); (c) the perpendicular (solid) and parallel (dot-dashed) pressures of the warm ions (water group plus protons, green), hot ions (red), and electrons (blue); and (d) the total perpendicular (solid) and parallel (dot-dashed) pressures.

Figure 14 .
Figure 14.(a-e) Overall mean current density and magnetic field profiles shown in a similar format to Figure 7.The overall mean parameter values are shown by the black solid lines, while the gray shaded regions indicate the associated standard error of the mean.The dashed black lines in Figures 14d and 14e correspond to a representative CAN model obtained by averaging the model parameters determined from individual fits to the field data from each pass.

Table 1 .
Cassini Physical Parameters Employed