To appear in: AGU Monograph on Magnetospheric Current Systems MHD Simulations of Current Systems in Planetary Magnetospheres: Mercury and Saturn

Tamas I. Gombosi∗ International Space Science Institute, Hallerstr. 6, CH-3012 Bern, Switzerland

Darren L. DeZeeuw, Clinton P.T. Groth, Kenneth C. Hansen, Konstantin Kabin, Kenneth G. Powell The University of Michigan, Ann Arbor, Michigan

Abstract. The study of planetary magnetospheres can provide valuable insight into a wide range of phenomena and processes acting in the terrestrial magnetosphere. This paper uses global MHD simulations to investigate the large scale configuration and current systems in two very different planetary magnetospheres. Mercury has a weak intrinsic magnetic moment and it is exposed to a high density, very variable solar wind. It has no ionosphere or plasmasphere and its slow rotation is unimportant. Under typical conditions in the solar wind, Mercury’s magnetosphere is very “open”, the last closed field-line being at a latitude of 40◦–50◦. At the other end of the spectrum, the interplay between solar wind and planetary rotation driven processes, combined with strong plasma sources, generates new and interesting configurations and current systems in the magnetosphere of Saturn. In particular, our simulations predict two current systems connecting plasma sources in the rings/icy satellites region and in Titan’s torus to the high-latitude regions of Saturn’s ionosphere.

1. Introduction spheric configuration and associated current systems in two vastly different planetary magnetospheres. Among magne- The planets Mercury, Earth, Jupiter, Saturn, Uranus and tized planets Mercury has the weakest intrinsic magnetic Neptune possess significant intrinsic magnetic fields. Since field (its magnetic moment is about 3,000 times smaller than the underlying plasma-physical processes are the same in the terrestrial magnetic moment), while Saturn’s magnetic these magnetospheres, qualitative or quantitative analogies moment is the second largest among all solar system planets with the terrestrial magnetosphere can help us to understand (580 times larger than the magnetic moment of Earth). Mag- poorly sampled planetary magnetospheres. Conversely, sim- netospheric current systems in these two planetary magneto- ilarities in planetary magnetospheres, in spite of differences spheres clearly exhibit many of the most interesting features in configurations, plasma and energy sources and sinks, can relevant to Earth and many astrophysical magnetospheres. help us to understand better the full range of phenomena and This paper uses global MHD simulations to study the processes in the Earth’s magnetosphere. Planetary magneto- large-scale configuration of the Hermean and Kronian mag- spheres help us to extend observed magnetospheric phenom- netospheres. The high performance BATS-R-US simulation ena into different parameter regimes. The study of magne- code has been developed at the University of Michigan and tospheric current systems is a very powerful tool in gaining it solves the equations of ideal magnetohydrodynamics on a global perspective of the multiscale coupling between var- an adaptively refined grid [Powell et al., 1999]. The code ious regions in planetary magnetospheres. has been successfully used to simulate solar system plasmas In this paper we investigate the large-scale magneto- ranging from the 3D expansion of solar wind [Groth et al., 1999] to the interaction of the heliosphere with the magne- ∗On leave from the The University of Michigan, Ann Arbor, Michigan

1 2 GOMBOSI ET AL.

tized interstellar medium [Linde et al., 1999], to the mag- formulation B1 does not have to be small, therefore this de- netospheres of Earth [Gombosi et al., 1998; 1999], Venus composition is completely general. [Bauske et al., 1998], Saturn [Hansen et al., 1998], comets [Gombosi et al., 1996; Haberli¨ et al., 1997], and to the 3. Mercury magnetospheric interaction of planetary satellites, such as Io [Combi et al., 1998], Europa [Kabin et al., 1998a] and Titan Mercury’s magnetosphere is surprisingly poorly studied, [Kabin et al., 1998b]. and consequently, poorly understood. It has been visited only by Mariner 10, which encountered Mercury three times 2. Model between March 1974 and March 1975 (however, one of the three encounters was so far upstream that it completely The BATS-R-US (Block Adaptive-Tree Solar-wind Roe- missed the magnetosphere). type Upwind Scheme) code solves the governing equations The first estimate of Mercury’s magnetic moment was 3 of ideal magnetohydrodynamics. The high-resolution fi- between 284 and 358 nT RM [Ness, 1975]. However, the nite volume solution scheme is based on an approximate poor spatial coverage during the two magnetospheric flybys Riemann solver for magnetohydrodynamics [Powell, 1994; of Mariner 10 make the evaluation of the intrinsic moment of Powell et al., 1995]. In this approach, the hydrodynamic Mercury very complicated and the results are highly depen- and electromagnetic effects are solved for in a fully three- dent on the physical assumptions [Ness, 1975; Connerney dimensional tightly coupled manner, rather than in separate and Ness, 1988]. steps [Gombosietal., 1994; Powell et al., 1995; 1999]. A tenuous atmosphere was observed at Mercury by the The code uses a limited reconstruction that ensures second- Mariner 10 spacecraft [Broadfoot et al., 1976]. This atmo- order accuracy away from discontinuities, while simultane- sphere is mainly composed of hydrogen, helium and oxy- ously providing the stability that ensures nonoscillatory so- gen, with traces of sodium and potassium. The H, He, and lutions. In addition, the code employs two accurate approx- O components are thought to be of solar wind origin, while imate Riemann solvers: the Roe [1981] scheme [Powell, sodium and potassium atoms are probably produced by sput- 1994] and the Linde [1998] solver. The resulting scheme tering [Lammer and Bauer, 1997]. The total column density works equally well across a range of several orders of mag- of the neutral atmosphere is estimated to be less than 1012 nitude in plasma β (β is the ratio of the kinetic and magnetic cm−2, which is essentially negligible from the perspective pressures). of magnetospheric interaction. In the Mercury simulations The basic data structure used in the BATS-R-US ap- shown in this paper all atmospheric effects are neglected. proach is that of adaptive blocks [Stout et al., 1997; Powell In our simulation Mercury was approximated by a solid et al., 1999]. Adaptive blocks partition space into regions, nonmagnetic sphere with a radius of RM =2, 440 km. The each of which is a regular Cartesian grid of cells, called a intrinsic magnetic field was approximated by a dipole mo- 3 block. If the region needs to be refined, then the block is re- ment of 330 nT RM , with the magnetic moment vector point- placed by 8 child subblocks (one for each octant of the parent ing south (the same sense as Earth). The surface conduc- block), each of which is a Cartesian grid of cells containing tivity was assumed to be zero, thus neglecting the effects the same number of cells as the parent block. If coarsening of a photoelectron sheath which may form around Mercury is needed, then the 8 children are replaced by their parent. [Grard, 1997]. Magnetic flux was allowed to cross the sur- The blocks in the grid, at their various levels of refinement, face of the planet, but no particle flux could penetrate the are stored in a tree data structure. surface. The boundary conditions on the surface were im- BATS-R-US was specially designed to handle objects posed by utilizing cut cells [DeZeeuw and Powell, 1992], with strong intrinsic magnetic fields. It achieves improved which allows second order (piecewise linear) reconstruction solution accuracy by solving for B1, which is the measure of the boundary geometry. of the deviation of the full magnetic field from the intrin- The upstream plasma flow conditions around Mercury sic field, B◦, and is defined as B1 = B − B◦ . This ap- may vary significantly depending on several factors, includ- proach was first employed by Ogino and Walker [1984] and ing the position of the planet on its trajectory and solar Ogino [1986] (and later applied to Godunov-type schemes activity. In this paper we present simulations for “typi- by Tanaka [1995]) and can lead to improved numerical solu- cal” solar wind conditions near perihelion: n =73cm−3, tions by alleviating the necessity of resolving the often large T = Te + Ti =14eV, B =46nT, u = 430 km/s, spatial gradients associated with the intrinsic fields and by ion-acoustic sound speed a =74.2 km/s, Alfven´ speed ∼ ensuring that the divergence of the intrinsic component of VA = 120 km/s, mean molecular mass 1 amu, and specific the magnetic field is by definition zero. Note that in this heat ratio 1.67. The corresponding ion-acoustic Mach num- CURRENT SYSTEMS IN THE MAGNETOSPHERES OF MERCURY AND SATURN 3

Figure 1. Three-dimensional rendering of Mercury’s magnetosphere. The electric current density is shown in gray scale in the noon-midnight meridian and in a cross sectional plane in the tail. Closed magnetic field lines are shown by dark solid lines, while open magnetic field lines connected to the northern high latitude region are represented by light solid lines. The open-closed magnetic field boundary is marked by a circle.

Figure 2. Equatorial (left panel) and noon midnight meridian (right panel) cuts of the Hermean current system. The IMF vector is in the equatorial plane. 4 GOMBOSI ET AL. ber is 5.8 and Alfvenic´ Mach number is 3.6. At Mercury’s pushed together, while they are clearly separated on the dusk orbit the Parker spiral magnetic field forms an angle of 20◦ side. with the solar wind direction. However, we must emphasize In the equatorial plane the current is strongest in a rel- that these parameters may vary significantly. A parametric atively narrow region on the dawn side. This is the region study of the effect of various solar wind conditions on the where the field lines strongly bend as they enter the magne- Hermean magnetosphere will be presented in a later paper. totail. It should be noted that due to the presence of a sig- × × The size of the simulation box was 900 600 600 RM nificant By component the cross tail current sheet is twisted and it was divided into ∼270,000 computational cells. The into an S shape and rotated. The strong current density on smallest cell was 0.02 RM in each direction, and we used 11 the dawn side is the region where the strong cross tail current levels of refinement. The inner boundary of the simulation is close to the equatorial plane. was located at the surface of Mercury. The Mercury simu- The right panel of Figure 2 shows the noon-midnight lation was carried out with a version of BATS-R-US which cross section of the current system. The cross-tail current runs on high-end workstations. intersects this plane just below the equatorial plane. This is Figure 1 shows a three-dimensional rendering of the sim- another manifestation of the twist and rotation of the cross- ulation results. The electric current density is shown in gray tail current. It is interesting to note that in this plane the scale in the noon-midnight meridian and in a cross sectional magnetopause current is stronger on the northern side. This plane located at 4 RM behind Mercury in the magnetic tail. is also due to the distortion of the tail configuration. Closed magnetic field lines are shown by dark solid lines, Overall, our simulation indicates that Mercury has a highly while open magnetic field lines originating from the high compressed magnetosphere which is dominated by the global latitude region are represented by light solid lines. The open- magnetopause-tail current system. Peculiar features include closed magnetic field boundary is marked by a circle on the very large areas of the open field lines on the surface of Mer- surface of the planet. The solar wind is approaching the cury, very small size of the magnetosphere compared to the planet from the left. The figure also shows the adaptively size of planet itself and a nearly merged quasi-parallel shock refined computational cells in the two planes. and magnetopause on the dawn side. Inspection of Figure 1 clearly reveals two major current systems in Mercury’s magnetosphere: the magnetopause 4. Saturn current and the cross tail current. An additional current is also present due to the magnetic field jump across the bow Saturn’s magnetosphere is quite complex due to the in- shock. It can be seen that the closed magnetic field lines are fluence and interaction of the solar wind, the planetary rota- rotated and twisted due to the presence of a By component in tion and the plasma sources, each of which is in some way the IMF. This effect has been observed at Earth [Kaymaz and drastically different from Earth. The solar wind, for exam- Siscoe, 1998] and reproduced by global MHD simulations of ple, has quite different characteristics at Saturn than at Earth. the terrestrial magnetosphere [Gombosietal., 1999]. The density is much lower, the magnetic field magnitude is The interplanetary magnetic field vector is in the equato- smaller, and the nominal Parker spiral gives a magnetic field ◦ rial plane (Bz =0) and it points 20 degrees from the radial that is almost completely azimuthal (θ =85). All these direction. The By component is from dawn to dusk. Due to factors combine to determine the overall size and configu- the presence of a By component the closed magnetic field ration of the magnetosphere. In addition, Saturn’s rotation lines are pushed down on the dawn side and pushed up on modifies the structure of the inner magnetosphere. Saturn’s the dusk side. A similar twist can be also observed for the large radius and short rotation period produce enough torque open magnetic field lines. In addition, the axis of the mag- on the plasma of the inner magnetosphere to cause it to coro- netotail is also shifted duskward. The twist and rotation of tate with the planet. Finally, the Kronian system has several the magnetotail can be well observed in the equatorial and neutral gas sources. These include Saturn, the rings, the icy non-midnight cuts shown in Figure 2. satellites, Titan’s neutral gas torus and Titan itself. The neu- Figure 2 shows the equatorial (left panel) and noon-mid- trals from these sources are ionized by various processes in- night meridian (right panel) cuts of the simulated Hermean cluding charge exchange and photoionization and lead to a current system. The IMF vector is in the equatorial plane. significant source of plasma in the inner magnetosphere. The cross-tail and magnetopause currents clearly form a uni- In order to model the important physical processes while fied current system and the cross tail current closes through at the same time limiting the complexity of our calculation, the magnetopause current. It is interesting to note that on the several simplifications have been made. First, we assume dawn side the near terminator magnetopause and the quasi- that the planetary magnetic field is a pure dipole aligned with parallel segment of the planetary bow shock are closely the rotation axis. For Saturn this is a very good approxi- CURRENT SYSTEMS IN THE MAGNETOSPHERES OF MERCURY AND SATURN 5

Figure 3. 3D rendering of Saturn magnetosphere. The grayscale represent the mass density in the equatorial and noon- midnight meridian planes. The Figure also shows the computational grid in these two planes, indicating the refinement near the planet. White lines represent plasma flow lines in the inner magnetosphere. mation. Second, we approximate the plasma sources in the sumed that outside the equatorial plane the source decreases − 2 2 Saturnian system by neglecting the sources and sinks associ- as exp( z /H ), where the scale height, H is 0.35 RS .The ated with Saturn itself but include sources corresponding to total mass loading rate from the rings and icy satellites is as- the rings, icy satellites and the neutral gas torus associated sumed to be ∼ 1.5 × 1027 s−1 with a peak production rate ∼ × −6 −3 −1 with Titan (but not Titan itself). In a later publication the ne- of 160 10 cm s at 4.6 RS . glected sources will be taken into account. The MHD source The solar wind parameters used in the simulation are the terms associated with the mass loading effects are given by following: heliocentric distance 9.54 AU, n =0.1 cm−3, Gombosietal.[1996] and Combietal.[1998]. u = 400 km/s, T =1.8 × 105 K, a =50km s−1,andB = The neutral cloud that results from Titan’s presence in 0.5 nT. At Saturn’s orbit the IMF is assumed to be in the y the magnetosphere is modeled as an axially symmetric torus direction (Parker spiral) pointing from dawn to dusk. These centered around the orbit of Titan. The torus is taken to be parameters correspond to an ion-acoustic Mach number of 8 filled with neutral particles of mass mn =14amu. The andanAlfvenic´ Mach number of 3.9. The specific heat ratio model takes into account the effects of photoionization, elec- is 5/3. tron impact ionization and charge transfer. Details about the The planetary parameters were taken to be the following: × −4 neutral gas distribution in the Titan torus and the associated radius RS =60, 268 km, angular velocity Ω=1.66 10 −1 plasma source terms are given by Barbosa [1987] and Ip s , equatorial magnetic field Be =0.208 G,thedipoleis [1992]. The total mass loading rate from the Titan torus is non-tilted and oppositely oriented than the terrestrial dipole. ∼ × 26 −1 assumed to be 2.3 10 s with a peak production rate The outer boundaries of the simulation domain are lo- ∼ × −6 −3 −1 of 0.3 10 cm s at Titan’s orbit (20.3 RS ). cated at 192 RS upstream and 588 RS downstream. The

The plasma source associated with the icy satellites and other boundaries are located at 192 RS . This large computa- rings were taken from Ip [1997] and Richardson [1998]. tional domain ensures that the influence of the boundaries on These rates refer to the equatorial plane of Saturn. We as- the solution is negligible. The boundary conditions applied 6 GOMBOSI ET AL. at the outer boundaries are those of the free streaming solar two effects nearly cancel and the plasma nearly stagnates. wind. The inner boundary associated with Saturn is applied The low plasma velocity naturally leads to high densities. − at 3 RS . At this radius the density and pressure are allowed Tailward from about x = 20 RS the effects of corota- to float and the magnetic field is taken to be only the in- tion become increasingly negligible and solar wind driven trinsic planetary dipole. The velocities are fixedtocoincide magnetospheric convection starts to dominate. We note that with the rotation of Saturn. The simulation involved about a magnetic X-line is formed at around this distance (not 6 ∼ 10 computational cells. The smallest cell was 0.19RS in shown in the Figures). each direction, and we used 8 levels of refinement. The right panel in Figure 4 shows the grayscale coded Figure 3 is a 3D representation of the solution. The electric current density in the noon-midnight meridian. One grayscale represents the mass density in the equatorial and of the most prominent features seen in this panel is a thin noon-midnight meridian planes. The Figure also shows the equatorial current ring extending from about 4 RS to approx- computational grid in these two planes, indicating the refine- imately 12 RS . This current ring is formed by the pickup ment near the planet. White lines represent plasma flow lines current associated to the inner plasma source due to the rings in the inner magnetosphere. and icy satellites. The plasma source peaks at around 5 RS . It can be seen in Figure 3 that a bow shock forms up- At this distance the current is diverted from the current disc stream of the planet. The subsolar distance of the shock is and connects to the high-latitude ionosphere along magnetic about 30 RS . The magnetopause separates the shocked so- field lines. lar wind from the region dominated by the planetary mag- Another current system seen in Figure 4 is associated netic field. The subsolar point of the magnetopause is lo- with mass loading in the Titan torus. This current system cated at around 20 RS . Since the Titan torus is centered connects to the high-latitude ionosphere poleward from the around 20 RS , a significant plasma source is located in the icy satellite/ring current system. It is interesting to note that magnetosheath between the shock and the dayside magne- on the nightside the Titan torus current system extends to- topause. This plasma source results in additional decelera- wards the magnetotail and connects to the cross-tail current. tion and heating of the shocked plasma flow, thus compress- On the dayside the Titan torus current is split into two parts: ing the Kronian magnetosphere. one is connected to the source inside the magnetopause, Inspection of Figure 3 reveals that the plasma density is while the second one connects to the torus source outside highest near the equatorial plane. This is due to the com- the magnetopause. The two parts of the current system are bined effect of rapid rotation and the concentration of plasma separated by a gap. The Titan torus current system is also a sources near the equatorial plane. Near the equatorial plane pickup generated current. the plasma within Titan’s orbit rotates with the planet. Be- yond Titan’s orbit the corotation breaks down due to mass 5. Summary loading and weakening magnetic field. In this region the plasma exhibits a complicated convection pattern as can be We presented global MHD simulations of the interaction seen by examining the convection streamlines in Figure 3. of the solar wind with two very different magnetized planets, The plasma convection pattern in the equatorial plane is Mercury and Saturn. The simulations were carried out with shown in the left panel of Figure 4. The panel also shows BATS-R-US, a newly developed high performance adaptive the plasma mass density distribution (grayscale coded). It MHD code. Similarities in planetary magnetospheres, in can be seen that the plasma density is significantly enhanced spite of differences in ionospheric conductances, configu- in the innermost region (within about 10 RS ), where mass rations, plasma and energy sources and sinks, can help us loading from the rings and icy satellites plays a major effect. to understand better the full range of phenomena and pro-

The density has a minimum between about 10 and 15 RS cesses in the Earth’s magnetosphere. Planetary magneto- where there is no major plasma source. This minimum ex- spheres help us to extend observed magnetospheric phenom- tends to Titan’s orbit at around 1400 LT. This density min- ena into different parameter regimes. imum is formed because the magnetopause is near Titan’s Both simulations considered the interaction of the “nom- orbit in this region and the incoming mass loaded plasma is inal” solar wind (with Parker spiral IMF) with the two plan- diverted into the magnetosheath (outside the magnetopause) ets. Mercury was assumed to be a non-conductive body or diverted towards the tail through high latitudes (inside the with negligible plasma sources in the Hermean environment. magnetopause). On the other hand Saturn was assumed to have two major At around 2000 LT a density maximum is formed near Ti- plasma source regions: one associated with the rings and icy tan’s orbit. This maximum is a consequence of the interplay satellites and the other with the neutral torus around Titan’s between solar wind driven convection and corotation: the orbit. CURRENT SYSTEMS IN THE MAGNETOSPHERES OF MERCURY AND SATURN 7

Figure 4. Left panel: Grayscale coded mass density distribution in Saturn’s inner magnetosphere. Arrows represent plasma velocity vectors. The circle shows Titan’s orbit. Right panel: Grayscale coded current density distribution in the noon- midnight meridian plane of Saturn’s inner magnetosphere.

In the case of Mercury the intrinsic magnetic field is very Icarus, 72, 53–61, 1987. weak, so that most of the field lines emanating from the sur- Bauske, R., A. F. Nagy, T. I. Gombosi, D. L. DeZeeuw, K. G. face of the planet are connected to the IMF either upstream Powell, and J. G. Luhmann, A three-dimensional MHD or downstream. Closed field lines appear only at latitudes study of solar wind mass loading processes at Venus: Ef- ◦ less than 50 . The whole magnetosphere is twisted and ro- fects of photoionization, electron impact ionization, and tated due to the presence of a significant dawn to dusk By charge exchange, J. Geophys. Res., 103(A10), 23625– component of the IMF. The simulation clearly shows the for- 23638, 1998. mation of a delicately connected current system consisting Broadfoot, A. L., D. E. Shemansky, and S. Kumar, Mariner of the tail and magnetopause currents. 10: Mercury atmosphere, Geophys. Res. Lett., 3, 577– In the case of Saturn a very interesting and complicated 580, 1976. configuration arises from the interplay between mass load- Combi, M. R., K. Kabin, T. Gombosi, D. DeZeeuw, and ing, rapid planetary rotation and solar wind driven convec- K. Powell, Io’s plasma environment during the Galileo tion. In the equatorial plane corotation was obtained within flyby: Global three-dimensional MHD modeling with Titan’s orbit, while outside Titan’s orbit solar wind driven adaptive mesh refinement, J. Geophys. Res., 103(A5), convection dominates the plasma motion. Mass loading gen- 9071–9081, 1998. erates two current systems which connect the ring/icy satel- Connerney, J. E. P., and N. F. Ness, Mercury’s magnetic lite current disk and the Titan torus to the high-latitude iono- field and its interior, in Mercury, edited by F. Vilas, C. R. sphere of Saturn. Chapman, and M. S. Matthews, pp. 494–513, The Uni- versity of Arizona Press, 1988. Acknowledgments. This work was supported by the NSF- DeZeeuw, D. L., and K. G. Powell, An adaptively-refined NASA-AFOSR interagency grant NSF ATM-9318181 and by the Cartesian mesh solver for the Euler equations, J. Comput. NASA HPCC Computational Grand Challenge cooperative agree- Phys., 104, 55–68, 1992. ment award CAN NCCS5-146. One of us (TIG) gratefully ac- Gombosi, T. I., K. G. Powell, and D. L. DeZeeuw, Axisym- knowledges the support provided by the International Space Sci- metric modeling of cometary mass loading on an adap- ence Institute during his sabbatical leave. tively refined grid: MHD results, J. Geophys. Res., 99, 21525, 1994. References Gombosi, T. I., D. L. DeZeeuw, R. M. Haberli,¨ and K. G. Powell, Three-dimensional multiscale MHD model Barbosa, D., Titan’s atomic nitrogen torus: Inferred proper- of cometary plasma environments, J. Geophys. Res., ties and consequences for the Saturnian magnetosphere, 101(A7), 15233–15253, 1996. 8 GOMBOSI ET AL.

Gombosi, T. I., D. L. DeZeeuw, C. P. T. Groth, K. G. Powell, Ness, N. F., K. W. Behannon, R. P. Lepping, and Y. C. and P. Song, The length of the magnetotail for northward Whang, The magnetic field of Mercury, J. Geophys. Res., IMF: Results of 3D MHD simulations, in Phys. Space 80, 2708, 1975. Plasmas (1998), edited by T. Chang, and J. R. Jasperse, Ogino, T., A three-dimensional MHD simulation of the in- vol. 15, pp. 121 –128, MIT Press, 1998. teraction of the solar wind with the Earth’s magneto- Gombosi, T. I., D. L. DeZeeuw, C. P. T. Groth, and K. G. sphere: The generation of field-aligned currents, J. Geo- Powell, Magnetospheric configuration for Parker-spiral phys. Res., 91, 6791, 1986. IMF conditions: Results of a 3D AMR MHD simulation, Ogino, T., and R. J. Walker, A magnetohydrodynamic simu- Adv. Space Res., 1999, in press. lation of the bifurcation of tail lobes during intervals with Grard, R., Photoemission on the surface of Mercury and re- a northward interplanetary magnetic field, Geophys. Res. lated electrical phenomena, Planet. Space Sci., 45, 62– Lett., 11, 1018, 1984. 72, 1997. Powell, K. G., An approximate Riemann solver for magneto- Groth, C. P. T., D. L. DeZeeuw, T. I. Gombosi, and K. G. hydrodynamics (that works in more than one dimension), Powell, Three-dimensional MHD simulation of coronal Tech. Rep. 94-24, ICASE, Langley, VA, 1994. mass ejections, Adv. Space Res., 1998, submitted. Powell, K. G., P. L. Roe, R. S. Myong, T. I. Gombosi, and Haberli,¨ R. M., T. I. Gombosi, D. L. DeZeuuw, M. R. D. L. DeZeeuw, An upwind scheme for magnetohydrody- Combi, and K. G. Powell, Modeling of cometary x-rays namics, in Proceedings of AIAA 12th Computational Dy- caused by solar wind minor ions, Science, 276, 939–942, namics Conference, p. 661, San Diego, AIAA-95-1704, 1997. 1995. Hansen, K. C., T. I. Gombosi, D. L. DeZeeuw, C. P. T. Groth, Powell, K. G., P. L. Roe, T. J. Linde, T. I. Gombosi, and and K. G. Powell, A 3D global MHD simulation of Sat- D. L. DeZeeuw, A solution-adaptive upwind scheme for urn’s magnetosphere, Adv. Space Res., 1999, submitted. ideal magnetohydrodynamics, J. Comput. Phys., 1999, in Ip, W., The nitrogen tori of Titan and Triton, Adv. Space press. Res., 12(8), (8)73–(8)79, 1992. Richardson, J. D., A. Eviatar, M. A. McGrath, and V. M. Ip, W., On the neutral cloud distribution in the Saturnian Vasyliunas, OH in Saturn’s magnetosphere: Observations magnetosphere, Icarus, 126, 42–57, 1997. and implications, J. Geophys. Res., 103, 20,245–20,255, Kabin, K., M. R. Combi, T. I. Gombosi, A. F. Nagy, D. L. 1998. DeZeeuw, and K. G. Powell, On Europa’s magneto- Roe, P. L., Approximate Riemann solvers, parameter vec- spheric interaction: An MHD simulation of the E4 flyby, tors, and difference schemes, J. Comput. Phys., 43, 357– J. Geophys. Res., 104, 1999a, in press. 372, 1981. Kabin, K., T. I. Gombosi, D. L. DeZeeuw, K. G. Powell, and Stout, Q. F., D. L. DeZeeuw, T. I. Gombosi, C. P. T. Groth, P. L. Israelevich, Interaction of the Saturnian magneto- H. G. Marshall, and K. G. Powell, Adaptive blocks: A sphere with Titan: Results of a 3D MHD simulation, J. high-performance data structure, in Proc. Supercomput- Geophys. Res., 104(A2), 2451–2458, 1999b. ing’97, 1997. Kaymaz, Z., and G. L. Siscoe, Open geometry of the mag- Tanaka, T., Generation mechanisms for magnetosphere- netotail cross section, J. Geophys. Res., 103(A7), 14829– ionosphere current systems deduced from a three- 14836, 1998. dimensional MHD simulation of the solar wind- Lammer, H., and S. J. Bauer, Mercury’s exosphere: origin magnetosphere-ionosphere coupling process, J. Geophys. of surface sputtering and implications, Planet. Space Sci., Res., 100(A7), 12,057–12,074, 1995. 45, 73–79, 1997. Linde, T. J., A three-dimensional adaptive multifluid MHD T.I. Gombosi, D.L. DeZeeuw, C.P.T. Groth, K.C. Hansen model of the heliosphere, Ph.D. thesis, University of and K. Kabin, Department of Atmospheric and Oceanic Sci- Michigan, Ann Arbor, Michigan, 1998. ences, The University of Michigan, Ann Arbor, MI 48109. Linde, T. J., T. I. Gombosi, P. L. Roe, K. G. Powell, and (e-mail: [email protected]) D. L. DeZeeuw, The heliosphere in the magnetized local K.G. Powell, Department of Aerospace Engineering, The interstellar medium: Results of a 3D MHD simulation, J. University of Michigan, Ann Arbor, MI 48109. Geophys. Res., 103(A2), 1889–1904, 1998. Ness, N. F., The magnetosphere of Mercury, in Solar system plasma physics. Vol II, edited by C. Kennel, L. J. Lanze- This preprint was prepared with AGU’s LATEX macros v4, with the ex- rotti, and E. N. Parker, pp. 183–206, North Nolland, Am- tension package ‘AGU++’ by P. W. Daly, version 1.5b from 1996/10/24. sterdam, 1979.