Chapter 1 Introduction The magnetosheath lies between the bow shock and the magnetopause and is formed by the deflected, heated, and decelerated solar wind with a minor magnetospheric plasma component. The terrestrial magnetosheath field and flow structure have been extensively studied because they affect the transfer of mass, momentum, and energy between the solar wind and the Earth’s magnetosphere. When magnetic shear across the magnetopause is high and dayside reconnection is occurring, the coupling between the solar wind and the magnetosphere is substantially enhanced relative to periods when there is no reconnection [ Paschmann et al ., 1979; Sonnerup et al ., 1981]. The magnetosphere becomes energized leading to phenomena such as the aurora. When the terrestrial magnetosphere is closed, or when the solar wind dynamic pressure is sufficiently high, magnetic field lines pile up near the magnetopause forcing out the normally resident plasma leading to the formation of a plasma depletion layer. Because of the limited amount of available data, the Jovian magnetosheath has been less extensively studied than the Earth’s magnetosheath. Factors that control the size, shape, and rigidity of the magnetosheath are much different at Jupiter and the Earth. At Jupiter the solar wind dynamic pressure is down by more than an order of magnitude and the Alfvén Mach number is nearly double the mean values observed near Earth. Furthermore, at Jupiter the force balance at the magnetopause is not well approximated by balancing the contributions of the external solar wind dynamic pressure against the internal magnetic pressure. Magnetospheric energetic particles, thermal plasma, and dynamic pressure associated with the rapid rotation of Jupiter provide non-negligible contributions to the internal pressure [ Smith et al ., 1974]. In addition, the combination of magnetospheric plasma and the rapid rotation of Jupiter stretches the field lines near the magnetic equator into a magnetodisk configuration such that the obstacle presented to the solar wind is flattened and less blunt than the Earth’s [ Engel and Beard , 1980]. As a result, the ratio of the bow shock to magnetopause stand-off distance is smaller at Jupiter than at Earth. As solar wind plasma crosses a planetary bow shock it is compressed and heated. Anisotropic heating of the plasma is commonly observed downstream of quasi- perpendicular bow shocks [ Song et al ., 1992; 1994]. Anisotropic plasmas (T⊥ > T|| ) where the ratio of the thermal plasma pressure to the magnetic pressure ( β) is large are unstable to the growth of both mirror modes and ion cyclotron waves. However, the field must be uniform for several ion gyro periods in order for ion cyclotron instability to result in wave growth and this condition is not common in the turbulent flows of the magnetosheath. When the field is non-uniform, mirror mode structures can form even though their growth rate in a uniform plasma is typically slower than that of cyclotron waves [ Gary et al ., 1994]. Mirror mode structures are frequently observed in both magnetosheaths but we focus primarily on analyses of the Jovian magnetosheath. The 1 large size of the Jovian magnetosheath allows us to easily subset our data into spatial regions based on local time and distance from the system boundaries so that we can begin to understand how the mirror structures evolve as the plasma in which they are embedded flows through the magnetosheath. 1.1. Outline This dissertation combines the results from four separate but related studies. In Chapter 2 we define the size and shape of the steady-state Jovian magnetosheath. At the Earth, the magnetospheric boundary locations are well known and easily tested by a wealth of observations but this is not the case at Jupiter. Here we develop probabilistic models of the size and shape of the bow shock and magnetopause using a combination of MHD simulation results to determine shape, and observations to determine the probable locations. In Chapter 3 we statistically compare the characteristics of the solar wind input to the two systems including pressure (dynamic, thermal, and magnetic), temperature, Mach number (magnetosonic and Alfvén), field strength, and plasma beta (β). This chapter focuses on differences in the near-Jupiter and near-Earth solar wind properties that may help to explain differences in the behavior of the system boundaries at the two planets. After defining the size and shape of the Jovian magnetosheath and the solar wind input to the Jovian system, we analyze mirror mode structures in the Jovian magnetosheath in Chapter 4. We present a methodology for identifying mirror structures of the different forms that are observed, show how the different forms are distributed in the magnetosheath, and present a model for the evolution of the form of these structures based on signatures observed in the magnetic field. Unfortunately, plasma data in the Jovian magnetosheath are sparse and generally do not have the time resolution necessary to properly analyze mirror structure formation and evolution. Consequently, in our final study (Chapter 5) we consider mirror structures observed in the terrestrial magnetosheath where high time resolution plasma data are available. We perform a case study of an event observed by the five THEMIS spacecraft where each of the mirror structural forms is observed by one or more spacecraft. In this analysis we compare the plasma distribution functions observed within different mirror structure forms to distributions predicted by theory and models developed in the previous chapter. 1.2. The Shape and Location of the Earth’s Bow Shock and Magnetopause In the next sections we briefly summarize the previous research into the topics that are covered in this dissertation, beginning with terrestrial magnetospheric boundary locations. The shape and size of the Earth’s bow shock and magnetopause have been extensively studied by many authors. Here we summarize the key results of others beginning with Fairfield [1971] who gives one of the early empirical models of the time 2 Figure 1.1 Observed magnetopause crossings (top, after Fairfield , 1976). ) and the distribution of stand-off distances (bottom, after Fairfield , 1971) dependent locations of the bow shock and magnetopause. Fairfield [1971] reported that the average magnetopause and bow shock locations in the ecliptic plane are at geocentric distances of 11.0 and 14.6 Earth radii (R E) respectively in the sunward direction, at 15.1 and 22.8 R E in the dawn meridian, and at 15.8 and 27.6 R E in the dusk meridian. This study notes that the bow shock orientation is consistent with the direction expected when the aberration of the radial solar wind is considered and that the stand-off distance is influenced by the size of the Alfvén Mach number. The magnetopause location was found to depend primarily on the momentum flux with the IMF orientation being a secondary factor; the boundary lies closer to the Earth when the IMF is southward. The top panel in Figure 1.1 shows the locations of 1821 magnetopause crossings reported by Fairfield [1976] and the bottom panel shows the distribution of stand-off distances from in the direction of the sun and in the orthogonal plane. Fairfield’s early models were 3 based on fits to the observed boundary crossing locations obtained by using a conic section symmetric about the aberrated Sun- Earth line. Nearly all boundary shape modeling since Fairfield [1971] has employed the same technique of fitting an ever increasing number of boundary crossing locations to functional forms parameterized by solar wind conditions and IMF strength and orientation. Petrinec et al., [1991] examined in detail the influence of the solar cycle on the size and shape of the magnetopause during northward and southward IMF. They reported that average dynamic pressure modulates over the solar cycle with its minimum near solar maximum and it peak during the descending phase of the cycle and that magnetopause stand-off distance is directly correlated with the pressure variation. During the entire solar cycle, the stand-off distance is greater during northward IMF than during southward IMF by approximately 0.5 R E. Petrinec and Russell [1993, 1996a] analyzed solar wind control on the size and shape of the near-Earth magnetotail and found that the flaring angle increases as the IMF becomes more southward but remains fixed for northward IMF. Petrinec and Russell [1996b] studied the influence of the combination of magnetic latitude and dipole tilt angle on the magnetopause stand-off distance normalized for IMF orientation and dynamic pressure effects and report that the larger the sum of those angles, the smaller the stand-off distance. Terrestrial bow shock models have evolved in much the same way as the magnetopause models. Seiff [1962] showed that the standoff distance of the bow shock (∆) normalized by the radius of the obstacle (D) is nearly linearly proportional to the inverse density ( ρ) ratio across the shock through the relationship: ∆ ρ = 1.1 1 (1.1) D ρ 2 where the constant of proportionality was determined empirically and subscripts 1 and 2 indicate the upstream and downstream values. Spreiter [1966] noted that in gas dynamics the density ratio can be rewritten in terms of the compressibility of the medium and the upstream Mach number so that Equation 1.1 becomes: 2 ∆ (γ − )1 M 1 + 2 = 1.1 2 (1.2) D (γ + )1 M 1 This equation matches observations reasonably well for large Mach numbers but does not go to infinity when the Mach number is equal to one. Farris and Russell [1994] extended this work to properly account for the behavior of the shock stand-off distance at low Mach numbers and by including an obstacle radius of curvature component. Farris and Russell noted that the upstream Mach number is effectively reduced by the upstream IMF strength but that the upstream Mach number can be computed from the asymptotic value of the downstream Mach number through the Rankine-Hugoniot equations.