5
Explosive Energy Conversion

We owe our earliest awareness of magnetized cosmic plasmas to their propensity to explode. Throughout prehistory, magnetically mediated solar explosions (today called coronal mass ejections) occasionally lit the skies at night with auroras over the caves of our ancestors. But it was not until relatively recently, in the mid-19th century, that Richard Carrington, a solar astronomer, first witnessed a solar precursor—a solar flare—to an auroral night. Even earlier in the 19th century, Alexander von Humboldt first identified a terrestrial type of magnetically mediated explosion, which, to emphasize its explosive nature, he named a magnetic storm. (Humboldt recognized the episodic and, so, storm-like character of localized terrestrial magnetic disturbances that occurred suddenly around midnight. Researchers now refer to this type of localized magnetic disturbance as a “substorm” and use the term “magnetic storm” to refer to a global disturbance.) Also in the early 1800s, explosive auroral storms, now known to be auroral counterparts of Humboldt’s localized magnetic storms, were recognized and described as “recurring fits.” During the century following Carrington, solar flares and magnetic storms—both manifestations of magnetically mediated explosions, as mentioned—were topics at the center of interest of a new discipline that became known as solar-terrestrial relations.

After Sputnik, “solar-terrestrial relations” became “space physics,” and space physicists, using data from spacecraft, began to expand their awareness of the explosive nature of magnetized cosmic plasmas. Terrestrial substorms, they found, are one of a hierarchy of explosive magnetospheric phenomena that begins with unnamed turbulence in the magnetotail, progresses through “bursty bulk flows” and “pseudo-breakups” to substorms and then to magnetic storms. It seems certain that the members of this hierarchy are related, but the relationships are unclear or controversial. Missions to planets other than Earth have added to the inventory of such phenomena. Mariner 10 recorded substorm-like events at Mercury, and Galileo in Jupiter’s magnetosphere has observed dynamical events that appear to be related to substorms. Data from spacecraft have also expanded the known types of explosive solar phenomena. Beyond optical solar flares, newly identified types include coronal bright spots and x-ray flares. But the solar eruptive phenomenon most directly related to magnetic storms is the coronal mass ejection (CME), discovered in the mid-1970s in Skylab measurements (Figure 5.1).



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Plasma Physics of the Local Cosmos 5 Explosive Energy Conversion We owe our earliest awareness of magnetized cosmic plasmas to their propensity to explode. Throughout prehistory, magnetically mediated solar explosions (today called coronal mass ejections) occasionally lit the skies at night with auroras over the caves of our ancestors. But it was not until relatively recently, in the mid-19th century, that Richard Carrington, a solar astronomer, first witnessed a solar precursor—a solar flare—to an auroral night. Even earlier in the 19th century, Alexander von Humboldt first identified a terrestrial type of magnetically mediated explosion, which, to emphasize its explosive nature, he named a magnetic storm. (Humboldt recognized the episodic and, so, storm-like character of localized terrestrial magnetic disturbances that occurred suddenly around midnight. Researchers now refer to this type of localized magnetic disturbance as a “substorm” and use the term “magnetic storm” to refer to a global disturbance.) Also in the early 1800s, explosive auroral storms, now known to be auroral counterparts of Humboldt’s localized magnetic storms, were recognized and described as “recurring fits.” During the century following Carrington, solar flares and magnetic storms—both manifestations of magnetically mediated explosions, as mentioned—were topics at the center of interest of a new discipline that became known as solar-terrestrial relations. After Sputnik, “solar-terrestrial relations” became “space physics,” and space physicists, using data from spacecraft, began to expand their awareness of the explosive nature of magnetized cosmic plasmas. Terrestrial substorms, they found, are one of a hierarchy of explosive magnetospheric phenomena that begins with unnamed turbulence in the magnetotail, progresses through “bursty bulk flows” and “pseudo-breakups” to substorms and then to magnetic storms. It seems certain that the members of this hierarchy are related, but the relationships are unclear or controversial. Missions to planets other than Earth have added to the inventory of such phenomena. Mariner 10 recorded substorm-like events at Mercury, and Galileo in Jupiter’s magnetosphere has observed dynamical events that appear to be related to substorms. Data from spacecraft have also expanded the known types of explosive solar phenomena. Beyond optical solar flares, newly identified types include coronal bright spots and x-ray flares. But the solar eruptive phenomenon most directly related to magnetic storms is the coronal mass ejection (CME), discovered in the mid-1970s in Skylab measurements (Figure 5.1).

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Plasma Physics of the Local Cosmos FIGURE 5.1 Large coronal mass ejection from November 6, 1997, as recorded by the LASCO C2 coronagraph at 12:36 universal time. The white inner circle represents the solar disk, which is hidden by the coronagraph’s occulting disk (dark circle). Courtesy of SOHO (ESA and NASA).

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Plasma Physics of the Local Cosmos These eruptive phenomena cover 13 orders of magnitude in energy and 5 orders of magnitude in time. Yet all are instances in which flow energy first converts gradually to magnetic energy and then explosively dissipates into kinetic energy and—in the case of flares—into electromagnetic radiation. A possible unifying concept that recurs in the following discussion is storage-release. That is, something stops magnetic energy from dissipating as fast as the flow generates it. So magnetic energy builds up until something causes the rapid dissipation of the stored energy to ensue. Most solar and magnetospheric theoretical research in this area concerns developing storing-and-releasing scenarios. The storage-release concept is deeply engrained in current thinking on explosive energy conversion, and much of the following discussion reflects its hegemony. STORAGE-RELEASE IN THE SUN’S CORONA A basic feature of the evolution leading to a solar explosive event such as a flare or coronal mass ejection is that magnetic energy is stored. The characteristic time scale for magnetic energy transfer through the solar surface, the photosphere, is much longer than the time scale for transfer through the corona. If the energy could be gradually released as it was introduced into the system, there would be no explosive energy release in the corona. The underlying source of energy for all coronal activity is the mass motion in the subphotospheric convection region. Both the plasma beta and the magnetic Reynolds number1 are much greater than unity in the photosphere and below and, consequently, the turbulent motions there tangle and stress magnetic field lines before and after the field emerges into the corona, so that the coronal field contains a large amount of free energy that can be released through magnetic reconnection processes that alter its topology. It is the free energy in these stressed coronal magnetic fields that powers (perhaps with intermediate steps) solar nonthermal emissions such as ultraviolet and x-ray radiation, solar wind outflows, and high-energy particles. Solar activity can be understood, therefore, as simply the transformation of the energy in mass motions in the Sun’s convection zone into the energy in nonthermal emissions from the Sun’s atmosphere, with the magnetic field acting as an intermediary. It is not immediately obvious, however, why this energy transfer can lead to explosive phenomena such as CMEs or flares. The problem is that the Alfvén speed in the photosphere (<1 km/s) is at least three orders of magnitude smaller than the speed in the corona (>1000 km/s), which implies that the corona can easily adjust to changes in photospheric driving via a quasi-steady evolution. Indeed, this is usually the case. The time scales (of the order of days) for slow variations in the emissions from active regions, quiet regions, and coronal holes are commensurate with the slow evolution of the underlying photospheric magnetic field. As discussed in Chapter 2, however, reconnection based on classical resistivity is not fast enough to explain even these slow variations, much less explosive solar flares. The magnetic gradients must become steep enough, and the current sheets must become sufficiently intense, before fast reconnection can be triggered. Thus because some threshold must be reached before fast reconnection can occur, magnetic free energy can build to substantial levels before release. Solar flares, and indeed perhaps coronal heating, are then naturally storage-release mechanisms. It is less clear what the storage mechanism for CMEs is. CME models can typically be sorted into three basic classes, using analogies to the dynamics of a spring (Figure 5.2). In the mass-loading model, chromospheric or coronal mass—for example, a prominence—weighs down a magnetic arcade or magnetic flux rope, stressing the magnetic spring. A CME occurs when the mass slips off, releasing the spring. Mass-loading models are concerned, in part, with specifying the slipping-off process. In the tether-release model a magnetic arcade, whose fields act like a set of tethers to constrain an underlying high-pressure magnetic configuration such as a flux rope, slowly weakens through magnetic reconnection. The final stage, before all magnetic tethers break, can occur

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Plasma Physics of the Local Cosmos FIGURE 5.2 Three classes of coronal mass ejection models. Image courtesy of J. Klimchuk (Naval Research Laboratory). Reprinted, with permission, from J.A. Klimchuk, Theory of coronal mass ejections, pp. 143-157 in Space Weather, Geophysical Monograph 125, P. Song, H.J. Singer, and G.L. Siscoe, eds., American Geophysical Union, Washington, D.C., 2000. Copyright 2000, American Geophysical Union.

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Plasma Physics of the Local Cosmos explosively, launching a CME. The third type of model, the tether-straining model, is a variation of the tether-release model. Here, the magnetic fields of an arcade are stressed through the growth of the underlying pressure. As in the case of tether release, the breaking of overlying magnetic fields through reconnection can occur explosively, releasing a CME. The mechanism for reconnection in the final phase, which gives the phenomenon its explosive character, is still a matter of conjecture. In every scenario that invokes some form of “tether cutting,” the fast phase occurs either because some threshold is passed where reconnection switches from dormant to active or because a current sheet where reconnection can occur is suddenly created. Since magnetic free energy powers all of these mechanisms, twisted or sheared magnetic field topologies, which can potentially change topology to release large amounts of energy, are required. The storage and release associated with CMEs can in fact be seen as a natural result of the conservation of magnetic helicity. Magnetic helicity is a property of the field related to its twist and linkage, and under coronal conditions the global helicity of a magnetic field is approximately conserved during reconnection. Thus reconnection by itself cannot release all of the free energy of a system, but only as much as can be released without altering the magnetic helicity of the system. In this manner, energy is built up in a twisted or sheared magnetic structure, until a mechanism such as those shown in Figure 5.2 leads to its eruption in a CME. The helicity of the structure is then bodily removed in the CME, and with its loss from the coronal system the rest of the stored energy can, in principle, be released.2 Outstanding Questions About Storage-Release in the Sun’s Corona How is magnetic free energy built up and stored in the corona? For example, does it arise primarily from photospheric motions, or from the emergence of an already-twisted magnetic field from the solar interior? How is this magnetic free energy then converted into heating in solar flares and/or kinetic energy in coronal mass ejections? How significant is mass to the CME system? What is the magnetic topology of the solar corona before, during, and after a CME? STORAGE-RELEASE IN EARTH’S MAGNETOTAIL As discussed in Chapter 2, the magnetospheric substorm is the primary mode of magnetic energy conversion in the nightside magnetosphere. Observations clearly indicate that, at substorm onset, the magnetosphere suddenly and radically changes its structure within localized regions, its convection state, and its dissipation rate. Why does the magnetosphere fail to change smoothly from a state of slow convection and low dissipation to a state of fast convection and high dissipation? A substorm has three main phases: a growth phase, during which magnetic energy is stored in the tail; an expansion phase, during which the stored energy is released; and a recovery phase, during which the magnetosphere returns to its pre-disturbance configuration (Figure 5.3). The growth phase begins when the interplanetary magnetic field (IMF) suddenly swings around to a southward orientation and reconnects abruptly with the northward geomagnetic field at the sunward magnetopause. As the open field lines are swept back into the magnetotail, magnetic flux is eroded from the dayside magnetopause and builds up rapidly in the northern and southern lobes of the magnetotail. The field intensity in the tail increases, and the plasma sheet (the reservoir of plasma between the tail lobes) thins. The growth phase continues until something triggers the explosive release of the accumulated magnetic energy in the expansion phase. In over half the substorms the expansion phase is triggered when the IMF turns northward again and dayside reconnection ceases.

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Plasma Physics of the Local Cosmos FIGURE 5.3 Schematic illustrating the three phases of a magnetospheric substorm, together with auroral images showing the auroral activity associated with each phase. The schematic is from W. Baumjohann and R.A. Treumann, Basic Space Plasma Physics, Imperial College Press, London, United Kingdom, 1996, and is reprinted by permission of the Imperial College Press. The auroral images were obtained with the IMAGE far-ultraviolet camera; IMAGE was located over the North Pole at an altitude of approximately 43,000 km. During the expansion phase, the stretched lobe field lines reconnect earthward of the distant neutral line, which is formed by the merging of open field lines during quiet conditions, and form a new neutral line in the mid-tail, between 20 and 35 Earth radii. The stored magnetic energy is thereby converted into heat and plasma kinetic energy in the form of enhanced plasma flows and energetic particle injections. The field lines earthward of the newly formed neutral line assume a dipolar configuration and flow around toward the dayside, replenishing the magnetic flux that had been stripped away by magnetopause reconnection. The reconnected field lines tailward of the new neutral line form a closed magnetic structure known as a plasmoid, which is ejected down the tail at a speed of several hundred kilometers per second. As the substorm enters the recovery phase, the neutral line retreats from its location in the mid-tail and propagates down the tail, eventually becoming a new distant neutral line. The basic substorm is quite a complicated transient affair, with specific auroral effects and magnetic fluctuations at the surface of Earth. In his pioneering paper on the auroral substorm,3 Syun-Ichi Akasofu described the global auroral signature of the magnetospheric substorm and identified the brightening of an auroral arc in the midnight sector of the auroral oval with the onset of the substorm expansion phase. Following onset, the aurora intensifies and emissions move poleward of the oval, sometimes filling half the area of the polar cap. During the recovery phase, auroral activity decreases and auroral forms characteristic of the recovery phase, such as the double oval and eastward-drifting omega bands, are observed. The details regarding how the stored magnetic energy in the tail lobes is transferred via tail reconnection to the plasma sheet and ultimately dissipated remain subjects for debate, and a number of different

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Plasma Physics of the Local Cosmos substorm models have been proposed. The two leading models are the near-Earth neutral-line (NENL) model, which is the one implicit in the substorm description above, and the current disruption model. In the NENL model, as the magnetic pressure and the currents intensify in the plasma sheet in the magnetotail, a threshold for the onset of rapid reconnection is exceeded, leading to explosive release of magnetic energy stored in the tail lobes and dipolarization of the tail magnetic configuration. In the current-disruption model, substorm breakup begins nearer Earth, at distances between 7 and 12 Earth radii, with the disruption of a very thin current sheet formed within the much thicker plasma sheet, while fast reconnection in the mid-tail develops later in the expansion phase. Observations have yielded conflicting evidence on whether the physical cause of breakup is in the near-Earth or mid-tail plasma sheet. Outstanding Questions About Explosive Energy Release in Earth’s Magnetosphere Why are substorms often triggered by a northward shift of the IMF after periods of southward IMF shift? What is the role of solar wind pressure changes? What is the nature of the threshold for the onset of rapid reconnection? What role does the ionosphere play in substorms? What are the nature and the importance of instabilities in the intense current layers in the near-Earth tail? UNIVERSALITY OF STORAGE-RELEASE MECHANISMS Solar active regions and planetary magnetospheres are typically driven by externally imposed forces that act over times that are long compared with the propagation time scale for magnetohydrodynamic waves. These systems then slowly evolve through a series of quasi-equilibrium states during which their magnetic field and plasma configurations are gradually driven far from possible minimum energy ground states. During this evolution, stress is accumulated as the system is prevented from returning to the ground state. Finally, these stressed configurations suddenly break, and the stored free energy is rapidly converted or dissipated into a variety of channels. Plasma systems typically possess a wide variety of spatial and temporal scales. Sudden energy transfer events in these systems may have their ultimate origin in this multiscale property. Short space-time scale dynamics can break the local connection to the global constraining and driving forces and thereby open new channels of energy rearrangement and dissipation. The resulting changes take the system far from its initial stressed state and allow it to evolve to a lower-energy configuration. Conceptually, the change might be bimodal, with microscale changes affecting the macroscale, or may involve an even more complex turbulent multiscale system. Thus the concept of storage and sudden release of energy is likely to be a universal one, naturally occurring in astrophysical systems possessing driving forces and multiple scales. Considered here in particular is how storage-release arises in magnetized plasmas, specifically in the context of the active Sun and the active magnetosphere of Earth. These solar system processes illustrate basic dynamical magnetic effects that occur throughout stellar systems, galaxies, and clusters of galaxies. We should be grateful for the simplicity of our local solar system laboratory, which has shown us so many effects but under conditions where their “simple” nature can be discerned. The Sun, for all its magnetic complexity, is, after all, a relatively pedestrian star. One can only guess at the magnetic complexity of a Wolf-Rayet star. Multiple star systems, each star with its time-dependent magnetic fields and stellar wind, suggest a whole new level of magnetic complications. We would also expect more activity from a young star—if one thinks back to the young Sun when it had a rotation period of 2 days, the interplanetary magnetic field must have been very tightly wound, which in combination with

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Plasma Physics of the Local Cosmos the massive wind of its youth would no doubt lead to extremes of violent interplanetary dynamics. These statements are not mere speculations: evidence is beginning to accumulate from stellar observations. For example, a huge stellar eruption has been observed in the very young binary system of XZ-Tauri AB.4 Eruptions have also been observed in a classic T-Tauri star and its stellar accretion disk that have been speculated to be akin to coronal mass ejections.5 Moreover, the M-dwarfs, with their monstrous flares (which can be hundreds of times brighter than the brightest solar flares) and equally monstrous starspots (covering more than half the stellar diameter) also represent extreme applications of the basic principles discussed in this section. Whatever goes on in distant stellar and galactic systems, it involves the violent interaction of fields and plasmas, within and around stars, galactic nuclei, and their surrounding spaces. NOTES 1.   The plasma beta (β) is the ratio of the plasma pressure to the magnetic pressure. As discussed in Chapter 2, the magnetic Reynolds number (Rm) is the ratio of the magnetic diffusion time to the plasma flow time. When the magnetic Reynolds number is large, the magnetic field is “frozen” in the flow and moves with it. 2.   B.C. Low, Solar activity and the corona, Solar Physics 167, 217, 1996. See also E.G. Blackman and A. Brandenburg, Doubly helical coronal ejections from dynamos and their role in sustaining the solar cycle, Astrophysical Journal 584, L99-L102, 2003. 3.   S.-I. Akasofu, The development of the auroral substorm, Planetary Space Science 12, 273-282, 1964. 4.   J.E. Krist, Hubble Space Telescope WFPC2 imaging of XZ Tauri: Time evolution of a Herbig-Haro bow shock, Astrophysical Journal Letters 515, L35-L38, 1999. 5.   J.M. Oliveira, B.H. Foing, J.Th. van Loon, and Y.C. Unruh, Magnetospheric accretion and winds on the T Tauri star SU Aurigae: Multi-spectral line variability and cross-correlation analysis, Astronomy and Astrophysics 362, 615-627, 2000.