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Plasma Physics of the Local Cosmos 4 Plasma Interactions Plasma populations throughout the universe interact with solid bodies, gases, magnetic fields, electromagnetic radiation, magnetohydrodynamic waves, shock waves, and other plasma populations. These interactions can occur locally as well as on very large scales between objects such as galaxies, stars, and planets. They can be loosely classified into electromagnetic interactions, flow-object interactions, plasma-neutral interactions, and radiation-plasma interactions. Magnetic field lines connecting different plasma populations act as channels for the transport of plasmas, currents, electric fields, and waves between the two environments. In this way, the two plasmas become coupled electromagnetically to one another. Examples of electromagnetic interactions include the transfer of mass, momentum, and energy between Earth’s magnetosphere and ionosphere; the outward transport of angular momentum in the jovian magnetosphere; and the production of accretion disks around protostars. When a flowing magnetized plasma strikes a solid object, an atmosphere, or a magnetosphere, strong interactions of various types can occur. Flow-object interactions range from the simple sputtering of ions from solid surfaces (like the Moon) to the production of flux ropes around unmagnetized planets with atmospheres (like Venus), to magnetic reconnection and the resulting production of large-scale disturbances (like magnetic storms) at planets with magnetospheres. Throughout the solar system and universe, plasmas are generally embedded in a background neutral gas with which they interact. Plasma-neutral interactions range from ion drag and “flywheel” effects in collision-dominated ionospheres; to charge-exchange reactions in the rarefied plasmas of magnetospheres and stellar winds; to dust-plasma interactions in cometary atmospheres, interstellar molecular clouds, protoplanetary disks, planetary rings, and stellar nebulas. Radiation-plasma interactions are important in solar and stellar atmospheres, which respond to and mediate radiation in the form of magnetohydrodynamic waves and shocks emanating from the stellar surfaces and more energetic ultraviolet and x-ray photons propagating downward from the stellar coronas. These interactions will determine, for example, how ultraviolet emissions observed from stellar atmospheres are best interpreted in terms of their vertical structure. Finally, the interactions described here take place over tremendous ranges of temporal and spatial scales. The spatial scales are often classified in terms of microscales (at which individual particle motions
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Plasma Physics of the Local Cosmos are important), mesoscales (which exhibit plasma fluid effects), and macroscales (comprising large structures such as coronal mass ejections and entire magnetospheres). Often the mesoscale and macroscale dynamics are produced by microscale phenomena (as magnetic reconnection leads to coronal mass ejections and magnetospheric substorms), while macroscale phenomena can drive dynamics at the smaller scales (as the Kelvin-Helmholtz instability is generated by large-scale flows of plasma along a boundary layer). As discussed in the preceding chapter, it is a fundamental property of space and astrophysical plasmas that efficient communication can occur across the various spatial scales. In the following sections, the various plasma coupling phenomena are described briefly and some of their universal aspects are noted. Throughout there are close connections to material addressed, for example, in Chapters 2, 3, and 5. ELECTROMAGNETIC INTERACTIONS The coupling of different spatial domains along extended magnetic field lines can occur via field-aligned particle flows, electric fields, currents, and parallel propagating waves. At Earth, the most important manifestation of this process is the strong electromagnetic coupling that occurs between the magnetosphere and the ionosphere. This coupling includes plasma circulation, plasma escape along field lines, field-aligned particle acceleration, and parallel (to B) currents. The current density along magnetic field lines is provided by electrons from the ionosphere (the downward currents) and the much more tenuous magnetosphere (the upward currents). Since the magnetospheric densities are low (a few per cubic centimeter at most at Earth), intense upward currents require field-aligned electric fields, which accelerate magnetospheric electrons down into the atmosphere to produce the required current and, in the process, create bright auroral forms. Figure 4.1 shows a view of Earth’s northern aurora from a spacecraft high overhead. The aurora consists of two components: the diffuse aurora, which covers a broad latitude range and is relatively structureless, and the highly structured and dynamic discrete aurora, whose bright forms are easily seen from the ground. The diffuse aurora is produced by particles precipitated from the near-Earth plasma sheet by wave-particle interactions, while the discrete auroral emissions are excited by beams of energetic electrons from the outer magnetosphere that have been accelerated in field-aligned electric fields and, in particularly dynamic situations or regions, by high-powered Alfvén waves (cf. Chapter 6). The processes that drive field-aligned currents into ionospheric plasmas also generate electric fields transverse to the magnetic field, the strength and location of which are strongly influenced by the properties of the ionospheric plasma. A two-way coupling between such regimes is set up in response to the driving field-aligned currents. These transverse electric fields drive ionospheric circulation and, through ion-neutral collisions, the motion of the neutral atmospheric gas. Similarly, the ionospheric feedback electric fields map upward along the magnetic fields, affecting processes in the overlying regions. In the terrestrial environs, the development of a disturbance ring current drives strong electric fields in regions of low ionospheric conductivity. These, in turn, affect both the planet’s thermal plasma envelope and the further development of the energetic-plasma ring current. The electromagnetic coupling processes in the magnetosphere-ionosphere systems of other planets are much less well understood than Earth’s, but they offer an elegant array of plasma dynamical processes. Jupiter’s magnetosphere is an especially rich environment for testing theories about electromagnetic coupling. In contrast to Earth’s magnetosphere, where the dynamics are driven by energy extracted from the solar wind interaction, the jovian magnetosphere is powered by the planet’s rotational energy that is transferred to the magnetosphere by field-aligned currents that couple the ionosphere with the magnetospheric plasma and set the plasma into corotational motion. Jupiter is of special astrophysical interest
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Plasma Physics of the Local Cosmos FIGURE 4.1 Earth’s northern aurora, as viewed with the far-ultraviolet camera on the IMAGE spacecraft. Auroral emissions can be seen extending to high latitudes on the nightside. Also evident are the terminator (the boundary between the dayside and the nightside) and, at the right of the image, bright ultraviolet dayglow emissions from the sunlit hemisphere. Courtesy of NASA and the IMAGE Far-Ultraviolet Imaging Team. because the transfer of torque through the electromagnetic coupling of the planet to the magnetosphere is a close analogue to the shedding of angular momentum from a central body to a surrounding nebula by means of magnetic fields and field-aligned currents thought to occur in other astrophysical environments (see sidebar, “The Formation of Stellar and Planetary Systems”).
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Plasma Physics of the Local Cosmos FIGURE 4.2 Jupiter’s northern aurora, as viewed at ultraviolet wavelengths with the Hubble Space Telescope. The image shows the main auroral oval, diffuse polar cap emissions, and auroral emissions at the magnetic footprints of Io (I), Ganymede (G), and Europa (E). Image courtesy of J. Clarke (Boston University). Reprinted, with permission, from J.T. Clarke et al., Ultraviolet emissions from the magnetic footprints of Io, Ganymede and Europa on Jupiter, Nature 415 997-1000, 2002. Copyright 2002, Macmillan Publishers Ltd. A distinctive feature of Jupiter’s magnetosphere-ionosphere system is the fact that the interaction of the Galilean moons with the magnetospheric plasma generates electrical currents that couple the moons to Jupiter’s ionosphere. The electrodynamical interaction between Jupiter and Io has been known for some time and is evidenced by radio emissions and auroral emissions at the foot of the flux tube linking the planet to the satellite. Recent Hubble Space Telescope observations of similar localized emissions at the magnetic footpoints of Ganymede and Europa are evidence that these moons, too, are electrically coupled by field-aligned currents with the jovian ionosphere (Figure 4.2). FLOW-OBJECT INTERACTIONS When a flowing magnetized plasma encounters an obstacle, such as another magnetized or a nonmagnetized plasma, relatively sharp boundaries tend to form that act to separate the plasmas. In the case of the supersonic solar wind encountering a planetary obstacle, the outermost boundary is a bow shock (discussed in Chapter 3), which heats and slows down the solar wind so that it can flow around the obstacle. If the planet is strongly magnetized, the solar wind is separated from the planetary plasma environment by a boundary known as a magnetopause. Magnetopauses exist at Earth, Jupiter, Saturn, Uranus, Neptune, and Mercury. The volume of space inside the magnetopause is dominated by the plasma and magnetic field associated with the planet, while outside the magnetopause the solar wind’s plasma and magnetic field dominate. A magnetopause also exists at the jovian moon Ganymede, whose intrinsic magnetic field was discovered in 1996; in this case, however, the ambient plasma is that of the jovian magnetosphere rather than the solar wind. The separation of solar wind and magnetospheric plasmas is not perfect, owing to a dissipation of the magnetopause current, allowing plasma and electric fields to penetrate the magnetopause. At Earth, this interaction produces a dynamic response that depends to a certain extent on the properties of the upper atmosphere, producing heat and auroral light emissions. Since Mercury, the only other terrestrial planet with a significant global magnetic field, has no atmosphere, but only a tenuous exosphere of sodium and
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Plasma Physics of the Local Cosmos THE FORMATION OF STELLAR AND PLANETARY SYSTEMS Angular momentum shedding from a centralized spinning region to a surrounding nebula is thought to happen, for example, in the early phases of stellar and planetary system formation. The process of stellar collapse can be summarized through the following paradigm:1 A protostellar core collapses inside out, and the initial angular momentum of the system produces an accretion disk. This disk transfers mass onto the central protostar while angular momentum is transferred outward. In general, it appears that the formation of a jet combined with an accretion disk is a crucial element of angular momentum shedding. These processes (in particular for high-mass stars) are poorly understood, since an adequate description of viscosity in hydromagnetic disks is still lacking. Nevertheless, the presence of a disk, as well as jets, has been observed and provides a mechanism for the formation of planetary bodies. Many such mysteries surround the early phases of the formation of stellar and planetary systems. Among these are the following (see figure, p. 51): What processes control the collapse of molecular cloud cores during the earliest phases of stellar system formation? Strong coupling between the neutral gas and dust components and the magnetized plasma components is thought to play a major role. The process of ambipolar diffusion that allows these components to separate is not well understood. That process has close analogues with the plasma-neutral interactions (see discussion in this chapter) occurring near the heliospheric boundaries, the plasma-neutral coupling occurring in planetary upper atmospheres, and the plasma-netural-dust interactions occurring in the neighborhood of comets. Solar system plasma physics has much to contribute to this topic. A related question is, What role does hydromagnetic turbulence play in the initial cloud-core collapse? Similar issues of turbulent transport processes surround the solar-system analogues to this problem already mentioned in Chapter 3. Other questions include: How do protostars shed > 98 percent of their angular momentum as they collapse into stellar and planetary systems? How are bipolar jets created and maintained? 1 Cf. F.J. Shu et al., The collapse of clouds and the formation and evolution of stars and disks, in Protostars and Planets III, University of Arizona Press, Tucson, 1993. potassium, its magnetosphere probably responds in a fundamentally different way from Earth’s magnetosphere to solar-wind variations. In fact, the role of the ionosphere in planetary magnetospheres can perhaps best be understood by exploring a magnetosphere, such as Mercury’s, that has no ionosphere. The NASA Messenger mission, now under development, will take this important next step. The solar wind most certainly breaches, by magnetic reconnection, the magnetopauses of Jupiter and the other gas giants as well, but the extent of the contribution of the resulting energy transfer to magnetospheric dynamics at these planets is not known.1 In the case of nonmagnetized bodies, such as Venus, Mars, and comets, it is the planetary or cometary ionosphere, not a strong intrinsic magnetic field, that is the obstacle to the solar wind. The boundary that separates the solar wind plasma from the ionospheric plasma is called the ionopause (Figure 4.3). Unlike the ionospheric plasma, the body’s neutral atmosphere is not confined by this boundary and extends beyond it into the solar wind-dominated region. Here, some of the neutral atoms or molecules are converted by photoionization, impact ionization, and charge exchange into ions, which are then picked up by the solar wind’s motional electric field, mass loading the solar wind and slowing its flow. In addition to the thermal pressure of the ionosphere against the solar wind, the solar wind is also opposed by a magnetic barrier that
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Plasma Physics of the Local Cosmos Some researchers have developed models of angular momentum shedding where the shedding occurs via magnetic field torquing. Magnetic field forcing also plays a central role in some theories of bipolar jet formation, which further aids the shedding of angular momentum. The physics involved in all of these applications is fundamentally similar to the physics in processes ongoing in solar system plasmas. Bipolar outflows and the shedding of angular momentum during star formation. (a) Sketch illustrating the stage in stellar formation when matter from the molecular cloud core continues to accrete on the circumstellar disk while collimated jets have formed from both poles. (b) A Hubble Space Telescope image of the young stellar object HH 30 showing the bipolar outflows and the circumstellar dust disk. (c) A sketch of a protostar viewed in the equatorial plane illustrating the interaction between the protostellar magnetic field and the surrounding accretion disk by means of which angular momentum is transferred outward. Panel (a) is reprinted by permission from F.H. Shu et al., Star formation in molecular clouds: Observation and theory, Annual Review of Astronomy and Astrophysics 25, 23-81, 1987. Copyright 1987, Annual Reviews www.annualreviews.org. Panel (b) is courtesy of C. Burrows (Space Telescope Science Institute and the European Space Agency), the WFPC 2 Investigation Definition Team, and NASA. Panel (c) is reprinted, with permission, from J.R. Najita and F.H. Shu, Magnetocentrifugally driven flows from young stars and disks. III. Numerical solution of the sub-Alfvénic region, Astrophysical Journal 429, 808-825. Copyright by the American Astronomical Society. forms because of the piling up of solar wind magnetic field lines at the ionopause as the solar wind plasma is slowed and compressed by the encounter with the ionospheric obstacle. As in the case of magnetized bodies, the separation of the solar wind plasma and the planetary or cometary plasma is not perfect, and at times of high solar wind dynamic pressure, the solar wind magnetic field may penetrate into the ionosphere. Of the various heliospheric plasma interactions, the one between the solar wind and Earth’s magnetospheric/ionospheric system has the most relevance for human activities and is by far the best studied. From a wide range of observations, it has been concluded that a small fraction of the solar wind mass, energy, and momentum incident upon Earth’s magnetosphere is allowed to penetrate the magnetopause. Once inside the magnetosphere, this solar wind energy powers high-latitude ionospheric convection, generates field-aligned currents into and out of the ionosphere, initiates geomagnetic storms and substorms, produces the ring current, and drives auroral displays. All of these phenomena intensify during periods of southward interplanetary magnetic field (IMF) orientation. Many mechanisms, including diffusion, impulsive penetration, and the Kelvin-Helmholtz instability, have been proposed to account for the interaction of the solar wind with the terrestrial magnetosphere. Only one, magnetic merging (or reconnection), predicts the observed relationships between the IMF
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Plasma Physics of the Local Cosmos FIGURE 4.3 Schematic illustrating the interaction of the solar wind with Venus. Reprinted, with permission, from T.E. Cravens, The solar wind interaction with non-magnetic bodies and the role of small-scale structures, pp. 353-366 in Solar System Plasma Physics, Geophysical Monograph 54, J.H. Waite, Jr., J.L. Burch, and R.L. Moore, eds., American Geophysical Union, Washington, D.C., 1989. Copyright 1989, American Geophysical Union. orientation and ionospheric and magnetospheric phenomena. However, there are many models for magnetic merging on Earth’s magnetopause. Some models propose that merging always occurs in the vicinity of the subsolar point on the magnetopause, others that its location depends on the IMF orientation. Some models propose that it occurs steadily, others that it takes place in bursts. Some models suggest that bursty merging occurs in response to varying solar wind conditions, others that it occurs in response to intrinsic magnetopause instabilities. Some models require that it occurs along an extended line, others that it takes place in patches.2 In situ measurements over the past 20 years have revealed convincing evidence for merging at the magnetopause, namely, mixed magnetosheath and magnetospheric plasmas, accelerated plasma flows, magnetic field components normal to the nominal magnetopause, and streaming electron populations. Because almost all of these studies were based on single-point measurements during transient magnetopause crossings, they could not determine the extent of merging, its duration, whether it was more rapid in the subsolar region or elsewhere, or whether it was triggered by varying solar wind conditions. Recent imaging of the proton aurora by the NASA IMAGE satellite, which can identify protons accelerated by the reconnection electric field as they bombard the dayside upper atmosphere, has shown that magnetic reconnection occurs continuously at the magnetopause, changing location in response to variations in the direction of the solar-wind magnetic field. In situ measurements by the four-spacecraft Cluster II mission have confirmed that the reconnection regions connect to the proton aurora emission regions.3
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Plasma Physics of the Local Cosmos PLASMA-NEUTRAL INTERACTIONS Plasma-neutral interactions involve the transfer of charge, momentum, and energy in ion-neutral and electron-neutral collisions. Important examples are the resonant charge exchange interaction between an ion and its parent neutral (H+ + H ⇔ H + H+) and the accidentally resonant charge exchange reaction O+ + H ⇔ H+ + O. In planets with radiation belts, the trapped energetic H+ and O+ ions can charge exchange with the background hydrogen gas, and in this way an energetic trapped ion becomes an energetic escaping neutral atom (Figure 4.4). Such energetic neutral atoms, which retain the energy and velocity of the parent ions, can be detected remotely to produce global images of the magnetospheric ion populations. Near ionopauses, the relatively hot solar wind ions can exchange charge with planetary neutrals, thereby affecting the plasma populations there. Exchange of charge with solar wind protons is one of the mechanisms by which inflowing interstellar neutrals are converted to ions within the heliosphere. (The other mechanism is photoionization by solar ultraviolet radiation.) The ions newly created by charge exchange and photoionization are picked up by the solar wind and transported outward, toward the termination shock, where some of them are accelerated to extremely high energies. These return to the inner heliosphere as anomalous cosmic rays. Charge exchange also plays a major role in establishing the structure of, and FIGURE 4.4 The creation of an energetic neutral atom through charge exchange. An oxygen ion trapped in the geomagnetic field captures an electron from a hydrogen atom in Earth’s extended neutral atmosphere (exosphere) (A). The resulting energetic neutral oxygen atom is no longer trapped and can travel in a line-of-sight path away from the source population (B). The detection of such energetic neutral atoms by a remote imager allows global images to be made of magnetospheric plasmas, which are invisible to standard astronomical observing techniques.
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Plasma Physics of the Local Cosmos populations within, the boundary regions of our heliosphere. It is, for example, responsible for the neutral hydrogen wall between the termination shock and the heliopause. In addition to charge exchange, other ion-neutral collisional processes can affect the momentum and energy transfer between different spatial domains, such as between ionospheres and magnetospheres. In the upper atmosphere of planets or comets where significant neutrals exist, plasma dynamics both drives and responds to the neutral circulation, leading to coupling and feedback between these regions. In the case of Earth’s ionosphere, ion convection driven by the interaction with the solar wind is generally faster than the motion of the ambient neutral gases. Neutrals are driven to move in the same direction as the ions due to ion drag or Ampere’s force. When the reconnection rate at the dayside magnetopause is significantly reduced—for example, when the IMF suddenly turns from southward to northward—the magnetospheric driver of the ion motion is quickly reduced, whereas the neutrals tend to maintain their original inertial motion, forming a so-called fly-wheel effect. Under such circumstances, neutrals transfer energy and momentum to the ions, thus providing a mechanical and electromagnetic coupling from the thermosphere to the ionosphere and the magnetosphere. RADIATION-PLASMA INTERACTIONS Most of the information researchers have about astronomical objects comes from electromagnetic waves that are generated in and modified by the objects’ dynamic gaseous envelopes or atmospheres. While radiative transfer in dynamic gaseous media is a well-developed discipline, the importance of the interaction between electromagnetic radiation and matter in the plasma state has only recently been recognized and analyzed. The Sun’s chromosphere, photosphere, and corona represent a unique laboratory for studies of the production, transport, and absorption of electromagnetic radiation in a plasma. The results of such studies are relevant to our understanding of radiation-plasma coupling in other astrophysical systems and to the interpretation of electromagnetic emissions from remote astrophysical objects. The atmospheric layers of the Sun are affected strongly by radiation-plasma coupling. The optical surface of the Sun, the photosphere, is an approximately 6000°C black body. Subsurface acoustic, gravity, and magnetohydrodynamic waves propagate upward from the photosphere and steepen into shocks as they rise through the overlying 20,000°C chromosphere (see Figure 4.5) because the gas and plasma densities decrease rapidly with altitude. The interaction of these waves and shocks with the chromospheric gas produces heat and ionization. At the same time, high-energy radiation in the form of ultraviolet and x-rays from the million-degree corona propagates downward through the transition region and into the chromosphere, producing additional ionization. These radiation-plasma interactions produce a temperature-altitude profile that is quite different from the profile predicted by the standard quasi-static models.4 The ionization profiles produced by the high-energy coronal radiation determine which particles are picked up most easily into the solar or stellar wind, and there is a well-known fractionation of solar and some stellar atmospheres in which elements with low first ionization potential (<10 eV) are enhanced over those with high first ionization potential. By the relative ion abundances in the solar wind it should be possible in principle to identify the source region of the wind, for example, in the chromosphere and to obtain information on heating mechanisms and magnetic topology in the source region.5 This information will in turn provide a context for the interpretation of observations of other stellar coronas. SUMMARY Plasmas throughout the universe are strongly affected by the presence of magnetic fields and the currents that flow in response to any stresses placed on the magnetic field. Magnetized plasmas can
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Plasma Physics of the Local Cosmos FIGURE 4.5 Cutaway drawing of the Sun showing some of its major regions and features. Courtesy of Steele Hill/NASA. interact with their local environment, producing phenomena such as angular momentum shedding, which is considered to be an important mechanism for astrophysical processes such as protostar collapse, formation of accretion disks, and formation of planets. Plasma coupling can also occur over vast distances among completely different plasma environments. For example, the Sun is magnetically coupled to the planets and moons in the solar system; and some planets, such as Jupiter, are magnetically coupled to their moons. Magnetic fields provide the connection between different plasma environments that acts to intro-
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Plasma Physics of the Local Cosmos duce nonlocal characteristics into a local plasma environment. When the interacting plasmas do not represent hard obstacles to each other, the coupling along magnetic field lines is gradual and is characterized by large spatial scales. But if a flowing magnetized plasma encounters an obstacle, such as a planet with a strong intrinsic magnetic field, relatively sharp boundaries tend to form and in this case the magnetic coupling is characterized by small spatial scales. Such small-scale coupling occurs at bow shocks, magnetopauses, and ionopauses. At sharp boundaries, like these, a host of microphysical plasma processes can occur, including magnetic reconnection, particle acceleration, wave excitation, and the generation of parallel electric fields. Phenomena associated with plasma-neutral interactions and radiation-plasma interactions mediate plasma coupling and can even represent controlling factors in the formation of plasma boundaries and the generation of stellar winds. It is fair to say that the wide range of plasma interactions that occur in solar system and astrophysical settings is appreciated but not very well understood. Phenomena such as magnetic reconnection are known to be crucial, but the underlying mechanisms have not been experimentally verified. The list of outstanding questions concerning plasma interactions is quite long, but the prospects for their resolution have improved greatly because of the rapid development of numerical modeling techniques and the advances in the remote sensing and multipoint measurements of plasmas. Outstanding Questions About Plasma Interactions How does the solar wind interact with a magnetized planet or moon that does not contain an ionosphere? Where, when, and how does magnetic reconnection occur at Earth’s magnetopause? What is the source region of the solar wind in the chromosphere, and what are the source region heating mechanisms and magnetic topology? What is the ultimate cause of solar wind fractionation, and why are high first-ionization-potential ions more prevalent in the slow solar wind? What is the role of charge exchange in the coupling of the solar wind with magnetized and unmagnetized solar system bodies? What is the role of fluid turbulence in transporting mass and momentum across plasma boundary layers? How does micro-turbulence couple into mesoscale plasma dynamics? NOTES 1. The most thoroughly studied of the outer-planet magnetospheres, Jupiter’s, is powered primarily by planetary rotation. However, changes in solar wind ram pressure have been shown to modulate magnetospheric activity and magnetosphere-ionosphere coupling, and theoretical arguments have been put forward to explain certain auroral features as the ionospheric signatures of reconnection at Jupiter’s dayside magnetopause (see S.W.H. Cowley, E.J. Bunce, and J.D. Nichols, Origins of Jupiter’s main oval auroral emissions, Journal of Geophysical Research 108(A4), 8002, 2003; and S.W.H. Cowley, E.J. Bunce, T.S. Stallard, and S. Miller, Jupiter’s polar ionospheric flows: Theoretical interpretation, Geophysical Research Letters 30(5), 1220, 2003). 2. Cf. the more detailed discussion in Chapter 2 of reconnection in Earth’s magnetosphere. 3. T. Phan, H.U. Frey, S. Frey, L. Peticolas, S. Fuselier, C. Carlson, H. Rème, J.-M. Bosqued, A. Balogh, M. Dunlop, L. Kistler, C. Mouikis, I. Dandouras, J.-A. Sauvaud, S. Mende, J. McFadden, G. Parks, E. Moebius, B. Klecker, G. Paschmann, M. Fujimoto, S. Petrinec, M.F. Marcucci, A. Korth, and R. Lundin, Simultaneous Cluster and IMAGE observations of cusp reconnection and auroral proton spot for northward IMF, Geophysical Research Letters 30(10), 1509, 2003. 4. See, for example, M. Carlsson and R.F. Stein, Does a non-magnetic solar chromosphere exist?, Astrophysical Journal Letters 440, L29, 1995. 5. H. Peter, Element fractionation in the solar chromosphere driven by ionization-diffusion processes, Astronomy and Astrophysics 335, 691-702, 1998.
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