On the application of the boundary element method in coronal magnetic field reconstruction

Solar magnetic field is believed to play a central role in solar activities and flares, filament eruptions as well as CMEs are due to the magnetic field re-organization and the interaction between the plasma and the field. At present the reliable magnetic field measurements are still confined to a few lower levels like in photosphere and chromosphere. Although IR technique may be applied to observe the coronal field but the technique is not well-established yet. Radio techniques may be applied to diagnose the coronal field but assumptions on radiation mechanisms and propagations are needed. Therefore extrapolation from photospheric data upwards is still the primary method to reconstruction coronal field. Potential field has minimum energy content and a force-free field can provide the required excess energy for energy release like flares, etc. Linear models have undesirable properties and it is expected to consider non-constant-alpha force-free field model. As the recent result indicates that the plasma beta is sandwich-ed distributed above the solar surface (Gary, 2001), care must be taken in modeling the coronal field correctly. As the reconstruction of solar coronal magnetic fields is an open boundary problem, it is desired to apply some technique that can incorporate this property. The boundary element method is a well-established numerical techniques that has been applied to many fields including open-space problems. It has also been applied to solar magnetic field problems for potential, linear force-free field and non-constant-alpha force-free field problems. It may also be extended to consider the non-force-free field problem. Here we introduce the procedure of the boundary element method and show its applications in reconstruction of solar magnetic field problems. This revised version was published online in August 2006 with corrections to the Cover Date.     

Equivalent Electric Circuit Models of Coronal Magnetic Loops and Related Oscillatory Phenomena on the Sun

Coronal loops, which trace closed magnetic field lines, are the primary structural elements of the solar atmosphere. Complex dynamics of solar coronal magnetic loops, together with action of possible subphotospheric dynamo mechanisms, turn the majority of the coronal loops into current-carrying structures. In that connection none of the loops can be considered as isolated from the surroundings. The current-carrying loops moving relative to each other interact via the magnetic field and currents. One of the ways to take into account this interaction consists in application of the equivalent electric circuit models of coronal loops. According to these models, each loop is considered as an equivalent electric LCR-circuit with variable inductive coefficients L, capacitance C, and resistance R, which depend on shape, scale, position of the loop with respect to neighbouring loops, as well as on the plasma parameters in the magnetic tube. Such an approach enables to describe the process of electric current dynamics in the groups of coronal loops, as well as the related dynamical, energy release and radiation processes. In the present paper we describe the major principles of LCR-circuit models of coronal magnetic loops, and show their application for interpretation of the observed oscillatory phenomena in the loops and in the related radiation.     

Thermal cyclotron radiation from a hot coronal loop with helical magnetic field

The spectral and polarization properties of thermal cyclotron radio emission from a hot coronal loop with a current along the axis are computed. The magnetic field is supposed to have a component along the loop axis as well as a poloidal part due to the current, both components being of comparable magnitude. In this specific configuration a helical magnetic field is present with a remarkable minimum of its absolute value along the loop axis and a maximum at its periphery. The presence of one or two maxima of magnetic field value along the line of sight results in increasing optical thickness of the gyroresonance layers at appropriate frequencies in the microwave band and, therefore, in enhanced radio emission at those harmonics which are optically thin (for example,s=4). These cannot be observed in models with the commonly employed magnetic field configuration (longitudinal along the loop axis).We show that the frequency spectrum of thermal cyclotron radiation from a hot coronal loop with a helical magnetic field differs from that of the standards-component source (with smooth frequency characteristics and polarization corresponding toe-mode) in that plenty of fine structures (line-like features and cut-offs) are present and theo-mode is prevalent in some frequency intervals. The enhanced radio emission at high harmonics and the complicated form of frequency spectrum in the model considered imply that some microwave sources, which are poorly explained in traditional models of solar active regions, may be associated with helical magnetic fields in hot coronal loops. Computations allow one to indicate spectral and polarizational peculiarities of local sources testifying to the presence of a helical magnetic field.     

Microwave spectrum analysis as solar energy release diagnostics

The possibilities of using spectrographic observations of microwave radio emission as a solar flare plasma diagnostic are discussed. The spectral fine structure of the emission is interpreted in the context of plasma emission mechanisms. The balance equations for particles and plasma turbulence together with the transfer equations for electromagnetic waves in a plasma are solved for a model containing a diverging magnetic loop. As a result of the analysis of the blip-type spectral feature, the structure of energy release region and the unperturbed plasma concentration in the preflare loop are evaluated. The number of accelerated electrons and the intensity of the plasma turbulence in the source region are estimated using the properties of the weak continuum emission following the blip. Based on the degree of circular polarization of both the narrow band and the continuum emission, estimates for the external magnetic field strength and the angular width of the radiating plasma turbulence have been obtained.     

The Role of Magnetic Reconnection in CME Acceleration

Observations carried out from the coronagraphs on board space missions (LASCO/SOHO, Solar Maximum and Skylab) and ground-based facilities (HAO/Mauna Loa Observatory) show that coronal mass ejections (CMEs) can be classified into two classes based on their kinematics evolution. These two classes of CMEs are so-called fast and slow CMEs. The fast CME starts with a high initial speed that remains more or less constant; it is also called the constant-speed CME. On the other hand, the slow CME starts with a low initial speed, but shows a gradual acceleration; it is also called the accelerated and slow CME. Low and Zhang [Astrophys. J. 564, L53–L56, 2002] suggested that these two classes of CMEs could be a result of a difference in the initial topology of the magnetic fields associated with the underlying quiescent prominences. A normal prominence magnetic field topology will lead to a fast CME, while an inverse quiescent prominence results in a slow CME, because of the nature of the magnetic reconnection processes. In a recent study given by Wu et al. [Solar Phys. 225, 157–175, 2004], it was shown that an inverse quiescent prominence magnetic topology also could produce a fast CME. In this study, we perform a numerical MHD simulation for CMEs occurring in both normal and inverse quiescent prominence magnetic topology. This study demonstrates three major physical processes responsible for destabilization of these two types of prominence magnetic field topologies that can launch CMEs. These three initiation processes are identical to those used by Wu et al. [Solar Phys. 225, 157–175, 2004]. The simulations show that both fast and slow CMEs can be initiated from these two different types of magnetic topologies. However, the normal quiescent prominence magnetic topology does show the possibility for launching a reconnection island (or secondary O-line) that might be thought of as a “CME’’.     

Energy Release and Particle Acceleration in Flares: Summary and Future Prospects

RHESSI measurements relevant to the fundamental processes of energy release and particle acceleration in flares are summarized. RHESSI??s precise measurements of hard X-ray continuum spectra enable model-independent deconvolution to obtain the parent electron spectrum. Taking into account the effects of albedo, these show that the low energy cut-off to the electron power-law spectrum is typically ?tens of keV, confirming that the accelerated electrons contain a large fraction of the energy released in flares. RHESSI has detected a high coronal hard X-ray source that is filled with accelerated electrons whose energy density is comparable to the magnetic-field energy density. This suggests an efficient conversion of energy, previously stored in the magnetic field, into the bulk acceleration of electrons. A new, collisionless (Hall) magnetic reconnection process has been identified through theory and simulations, and directly observed in space and in the laboratory; it should occur in the solar corona as well, with a reconnection rate fast enough for the energy release in flares. The reconnection process could result in the formation of multiple elongated magnetic islands, that then collapse to bulk-accelerate the electrons, rapidly enough to produce the observed hard X-ray emissions. RHESSI??s pioneering ??-ray line imaging of energetic ions, revealing footpoints straddling a flare loop arcade, has provided strong evidence that ion acceleration is also related to magnetic reconnection. Flare particle acceleration is shown to have a close relationship to impulsive Solar Energetic Particle (SEP) events observed in the interplanetary medium, and also to both fast coronal mass ejections and gradual SEP events. New instrumentation to provide the high sensitivity and wide dynamic range hard X-ray and ??-ray measurements, plus energetic neutral atom (ENA) imaging of SEPs above ??2 R_??, will enable the next great leap forward in understanding particle acceleration and energy release is large solar eruptions??solar flares and associated fast coronal mass ejections (CMEs).     

Solar Drivers of 11-yr and Long-Term Cosmic Ray Modulation

In the current paradigm for the modulation of galactic cosmic rays (GCRs), diffusion is taken to be the dominant process during solar maxima while drift dominates at minima. Observations during the recent solar minimum challenge the pre-eminence of drift at such times. In 2009, the ～2 GV GCR intensity measured by the Newark neutron monitor increased by ～5% relative to its maximum value two cycles earlier even though the average tilt angle in 2009 was slightly larger than that in 1986 (～20° vs. ～14°), while solar wind B was significantly lower (～3.9 nT vs. ～5.4 nT). A decomposition of the solar wind into high-speed streams, slow solar wind, and coronal mass ejections (CMEs; including post-shock flows) reveals that the Sun transmits its message of changing magnetic field (diffusion coefficient) to the heliosphere primarily through CMEs at solar maximum and high-speed streams at solar minimum. Long-term reconstructions of solar wind B are in general agreement for the ～1900-present interval and can be used to reliably estimate GCR intensity over this period. For earlier epochs, however, a recent ¹⁰Be-based reconstruction covering the past ～10⁴ years shows nine abrupt and relatively short-lived drops of B to ?0 nT, with the first of these corresponding to the Spörer minimum. Such dips are at variance with the recent suggestion that B has a minimum or floor value of ～2.8 nT. A floor in solar wind B implies a ceiling in the GCR intensity (a permanent modulation of the local interstellar spectrum) at a given energy/rigidity. The 30–40% increase in the intensity of 2.5 GV electrons observed by Ulysses during the recent solar minimum raises an interesting paradox that will need to be resolved.     

The Effects of Transverse Magnetic Field and Density Variations on the Particle Energy Spectra in a Reconnecting 3D Current Sheet

Electron and proton acceleration by a super-Dreicer electric field is further investigated in a non-neutral reconnecting current sheet (RCS) with a variable plasma density. The tangential B _z and transverse magnetic field components B _x are assumed to vary with the distances x and z from the X nullpoint linearly and exponentially, respectively; the longitudinal component (a ‘guiding field’) is accepted constant. Particles are found to gain a bulk of their energy in a thin region close to the X nullpoint where the RCS density increases with z exponentially with the index λ and the tangential magnetic field B _x also increases with z exponentially with the index α. For the RCS with a constant density (λ = 0), the variations of the tangential magnetic field lead to particle power-law energy spectra with the spectral indices γ₁ being dependent on the exponent α as: for protons and for electrons in a strong guiding field (β > 10⁻²) and for electrons in a moderate or weak guiding field (β > 10⁻⁴). For the RCS with an exponential density increase in the vicinity of the X nullpoint (λ≥ 0) there is a further increase of the resulting spectral indices γ that depends on the density exponent index λ as for protons and for electrons in weaker guiding fields and as for electrons in stronger guiding fields. These dependencies can explain a wide variety (1.5–10) of particle spectral indices observed in solar flares by the variations of a magnetic field topology and physical conditions in a reconnecting region. This can be used as a diagnostic tool for the investigation of the RCS dynamics from the accelerated particle spectra found from hard X-ray and microwave emission.     

The Two Sources of Solar Energetic Particles

Evidence for two different physical mechanisms for acceleration of solar energetic particles (SEPs) arose 50 years ago with radio observations of type III bursts, produced by outward streaming electrons, and type II bursts from coronal and interplanetary shock waves. Since that time we have found that the former are related to “impulsive” SEP events from impulsive flares or jets. Here, resonant stochastic acceleration, related to magnetic reconnection involving open field lines, produces not only electrons but 1000-fold enhancements of ³He/⁴He and of (Z>50)/O. Alternatively, in “gradual” SEP events, shock waves, driven out from the Sun by coronal mass ejections (CMEs), more democratically sample ion abundances that are even used to measure the coronal abundances of the elements. Gradual events produce by far the highest SEP intensities near Earth. Sometimes residual impulsive suprathermal ions contribute to the seed population for shock acceleration, complicating the abundance picture, but this process has now been modeled theoretically. Initially, impulsive events define a point source on the Sun, selectively filling few magnetic flux tubes, while gradual events show extensive acceleration that can fill half of the inner heliosphere, beginning when the shock reaches ～2 solar radii. Shock acceleration occurs as ions are scattered back and forth across the shock by resonant Alfvén waves amplified by the accelerated protons themselves as they stream away. These waves also can produce a streaming-limited maximum SEP intensity and plateau region upstream of the shock. Behind the shock lies the large expanse of the “reservoir”, a spatially extensive trapped volume of uniform SEP intensities with invariant energy-spectral shapes where overall intensities decrease with time as the enclosing “magnetic bottle” expands adiabatically. These reservoirs now explain the slow intensity decrease that defines gradual events and was once erroneously attributed solely to slow outward diffusion of the particles. At times the reservoir from one event can contribute its abundances and even its spectra as a seed population for acceleration by a second CME-driven shock wave. Confinement of particles to magnetic flux tubes that thread their source early in events is balanced at late times by slow velocity-dependent migration through a tangled network produced by field-line random walk that is probed by SEPs from both impulsive and gradual events and even by anomalous cosmic rays from the outer heliosphere. As a practical consequence, high-energy protons from gradual SEP events can be a significant radiation hazard to astronauts and equipment in space and to the passengers of high-altitude aircraft flying polar routes.     

Extreme Ultraviolet Imager Observations of the Structure and Dynamics of the Plasmasphere

The IMAGE Extreme Ultraviolet Imager (EUV) provides our first global images of the plasmasphere by imaging the distribution of He⁺ in its 30.4-nm resonance line. The images reveal the details of a highly structured and dynamic entity. Comparing EUV images and selected in-situ observations has helped to validate the remote sensing measurements. The brightness in the EUV images is heavily weighted by the He⁺ density near the plane of the magnetic equator, but two lines of evidence emphasize that the features seen by EUV extend far from the equator, and in at least some cases reach the ionosphere. Certain features and behaviors, including shoulders, channels, notches, and plasma erosion events, appear frequently in the EUV images. These are keys to understanding the ways that electric fields in the inner magnetosphere affect the large and meso-scale distribution of plasma, and their study can elucidate the mechanisms by which the solar wind and interplanetary magnetic field couple to the inner magnetosphere.     

3He-Rich Solar Energetic Particle Events

³He-rich solar energetic particle (SEP) events show huge enrichments of ³He and association with kilovolt electrons and Type-III radio bursts. Observations from a new generation of high resolution instruments launched on the Wind, ACE, Yohkoh, SOHO, TRACE, and RHESSI spacecraft have revealed many new properties of these events: the particle energy spectra are found to be either power-law or curved in shape, with the ³He spectrum often being distinctly different from other species. Ultra-heavy nuclei up to >200 amu are found to be routinely present at average enrichments of >200 times solar-system abundances. The high ionization states previously observed near ∼1 MeV/nucleon have been found to decrease towards normal solar coronal values in these events. The source regions have been identified for many events, and are associated with X-ray jets and EUV flares that are associated with magnetic reconnection sites near active regions. This paper reviews the current experimental picture and theoretical models, with emphasis on the new insights found in the last few years.     

Modelling of the electromagnetic field in the interplanetary space and in the Earth's magnetosphere

A magnetohydrodynamic model of the solar wind flow is constructed using a kinematic approach. It is shown that a phenomenological conductivity of the solar wind plasma plays a key role in the forming of the interplanetary magnetic field (IMF) component normal to the ecliptic plane. This component is mostly important for the magnetospheric dynamics which is controlled by the solar wind electric field. A simple analytical solution for the problem of the solar wind flow past the magnetosphere is presented. In this approach the magnetopause and the Earth's bow shock are approximated by the paraboloids of revolution. Superposition of the effects of the bulk solar wind plasma motion and the magnetic field diffusion results in an incomplete screening of the IMF by the magnetopause. It is shown that the normal to the magnetopause component of the solar wind magnetic field and the tangential component of the electric field penetrated into the magnetosphere are determined by the quarter square of the magnetic Reynolds number. In final, a dynamic model of the magnetospheric magnetic field is constructed. This model can describe the magnetosphere in the course of the severe magnetic storm. The conditions under which the magnetospheric magnetic flux structure is unstable and can drive the magnetospheric substorm are discussed. The model calculations are compared with the observational data for September 24–26, 1998 magnetic storm (Dst _min=−205 nT) and substorm occurred at 02:30 UT on January 10, 1997. This revised version was published online in August 2006 with corrections to the Cover Date.     

Reconstructed 3-d magnetic field structure and hard X-ray two ribbons for 2000 Bastille-day event

The Bastille-day event in 2000 produced energetic 3B/X5.6 flare with a halo CME, which had great geo-effects consequently. This event has been studied extensively and it is considered that it follows the two-ribbon flare model. The flare/CME event was triggered by an erupting filament and TRACE observations showed formation of giant arcade structures during the flare process. Hard X-ray (HXR) two ribbons revealed for the first time in this flare event (Masuda et al., 2001). The reconstruction of 3-D coronal magnetic fields revealed a magnetic flux rope structure, for the first time, from extrapolation of observed photospheric vector magnetogram data and the flux rope structure was co-spatial with portion of the filament and a UV bright lane (Yan et al., 2001a, 2001b). Here we review some recent work related to the flux rope structure and the HXR two ribbons by comparing their locations and the flux temporal profiles during the flare process so as to understand the energy release and particle accelerations. It is proposed that the rope instability may have triggered the flare event, and reconnection may occur during this process. The drifting pulsation structure in the decimetric frequency range is considered to manifest the rope ejection, or the initial phase of the coronal mass ejection. The HXR two ribbons were distributed along the flux rope and the rope foot points coincide with HXR sources. The energy dissipation from IPS observations occurred within about 100 R _⋅ is consistent with the estimate for the flux rope system. This revised version was published online in August 2006 with corrections to the Cover Date.     

Fast Dust in the Heliosphere

The dynamics of dust particles in the solar system is dominated by solar gravity, by solar radiation pressure, or by electromagnetic interaction of charged dust grains with the interplanetary magnetic field. For micron-sized or bigger dust particles solar gravity leads to speeds of about 30 to 40 km s^–1 at the Earths distance. Smaller particles that are generated close to the Sun and for which radiation pressure is dominant (the ratio of radiation pressure force over gravity F _rad/F _grav is generally termed ) are driven out of the solar system on hyperbolic orbits. Such a flow of -meteoroids has been observed by the Pioneer 8, 9 and Ulysses spaceprobes. Dust particles in interplanetary space are electrically charged to typically +5 V by the photo effect from solar UV radiation. The dust detector on Cassini for the first time measured the dust charge directly. The dynamics of dust particles smaller than about 0.1 m is dominated by the electromagnetic interaction with the ambient magnetic field. Effects of the solar wind magnetic field on interstellar grains passing through the solar system have been observed. Nanometer sized dust stream particles have been found which were accelerated by Jupiters magnetic field to speeds of about 300 km s^–1.     

Variations of the magnetic fields in large solar flares

We present preliminary results from high resolution observations obtained with the Michelson Doppler Imager (MDI) instrument on the SOHO of two large solar flares of 14 July 2000 and 24 November 2000. We show that rapid variations of the line-of-sight magnetic field occured on a time scale of a few minutes during the flare explosions. The reversibility/irreversibility of the magnetic field of both active regions is a very good tool for understanding how the magnetic energy is released in these flares. The observed sharp increase of the magnetic energy density at the time of maximum of the solar flare could involve an unknown component which deposited supplementary energy into the system. This revised version was published online in August 2006 with corrections to the Cover Date.     

Radio Diagnostics of the Solar Flare Reconnection

First, high-frequency (HF) slowly drifting pulsating structures are interpreted as radio emissions of electron beams accelerated in the magnetic reconnection volume and injected into magnetic islands (plasmoids). Then, the time evolution of plasma parameters (density, magnetic field, etc.) in a 2-D MHD model of solar flare reconnection is computed numerically. Assuming plasma radio emission from locations where the “double-resonance’’ instability generates upper-hybrid (UH) waves due to unstable distribution function of suprathermal electrons, the radio spectra and spatial source structures in the reconnection region are modeled. By comparison of the modeled and observed spectra a remarkable similarity has been found between the computed narrow-band emission and the observed lace bursts. Finally, a new diagnostics of the reconnection process is proposed.     

Nonthermal Radiation Mechanisms

In this paper we review the possible radiation mechanisms for the observed non-thermal emission in clusters of galaxies, with a primary focus on the radio and hard X-ray emission. We show that the difficulty with the non-thermal, non-relativistic Bremsstrahlung model for the hard X-ray emission, first pointed out by Petrosian (Astrophys. J. 557, 560, 2001) using a cold target approximation, is somewhat alleviated when one treats the problem more exactly by including the fact that the background plasma particle energies are on average a factor of 10 below the energy of the non-thermal particles. This increases the lifetime of the non-thermal particles, and as a result decreases the extreme energy requirement, but at most by a factor of three. We then review the synchrotron and so-called inverse Compton emission by relativistic electrons, which when compared with observations can constrain the value of the magnetic field and energy of relativistic electrons. This model requires a low value of the magnetic field which is far from the equipartition value. We briefly review the possibilities of gamma-ray emission and prospects for GLAST observations. We also present a toy model of the non-thermal electron spectra that are produced by the acceleration mechanisms discussed in an accompanying paper Petrosian and Bykov (Space Sci. Rev., 2008, this issue, Chap. 11).     

Pulsar Wind Nebulae as Cosmic Pevatrons: A Current Sheet’s Tale

I outline, from a theoretical and somewhat personal perspective, significant features of Pulsar Wind Nebulae (PWNe) as Cosmic Accelerators. I pay special attention to the recently discovered gamma ray “flares” in the Crab Nebula’s emission, focusing on the possibility, raised by the observations, that the accelerating electric field exceeds the magnetic field, suggesting that reconnection in the persistent current layer (a “current sheet”) plays a significant role in the behavior of this well studied Pevatron. I address the present status of the termination shock model for the particle accelerator that converts the wind flow energy to the observed non-thermal particle spectra, concluding that it has a number of major difficulties related to the transverse magnetic geometry of the shock wave. I discuss recent work on the inferred pair outflow rates, which are in excess of those predicted by existing theories of pair creation, and use those results to point out that the consequent mass loading of the wind reduces the wind’s bulk flow 4-velocity to the point that dissipation of the magnetic field in a pulsar’s wind upstream of the termination shock is restored to life as a viable model for the solution of the “σ” problem. I discuss some suggestions that current starvation in the current flow supporting the structured (“striped”) upstream magnetic field perhaps induces a transition to superluminal wave propagation. I?show that current starvation probably does not occur, because those currents are carried in the current sheet separating the stripes rather than in the stripes themselves.