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The motion of charged particles is studied numerically and analytically using a test particle approach. Acceleration near the X-type neutral line is described in terms of adiabatic invariants and separatrix crossings. The relation between regular and chaotic properties of the process is discussed for a realistic source in the plasma mantle.
It is shown that due to correlations between subsequent separatrix traversals the chaotic scattering of thermal ions and energetic electrons in the plasma sheet of the earth's magnetotail is modulated, oscillating in dependence on the strength of the magnetic field inhomogeneity and particle energy. Correlation-modulated chaotic scattering creates non-Maxwellian features of the magnetotail ion distribution both in the CPS and the PSBL. It also causes an oscillating latitudinal variation of the auroral ion precipitation.
It has been demonstrated in the past that single, 2D coronal arcades are very unlikely driven unstable by a simple shear of the photospheric footpoints of the magnetic field lines. By means of 2D, time-dependent MHD simulations, evidence is presented that a resistive instability can result if in addition to the footpoint shear a slow motion of the footpoints toward the photospheric neutral line is included. The photospheric footpoint velocity in this model is nonsingular and the shear dominates everywhere. Starting from a planar potential field geometry for the arcade, it is found that after some time a current sheet is formed which is unstable with respect to the tearing instability. The time of its onset scales with the logarithm of the magnetic diffusivity assumed in the calculation. In its nonlinear phase, a quasi-stationary situation arises in the vicinity of the x-line with an almost constant reconnection rate. The height of the x-line above the photosphere and the distance of the separatrix footpoints remain almost constant in this phase, while the helical flux tube, formed above the neutral line, continuously grows in size.
Analytic and numerical results on particle acceleration in 2D collisionless magnetic reconnection are presented. The particles are followed until they reach an outgoing flux surface at the same distance from the origin as the starting surface. The magnetic moment is not conserved for particles passing through the unmagnetized region around the X line at the origin. Other particles cross the separatrix without passing near the X line. The magnetic moment of the first class of outgoing particles is randomized, whereas it can be considered for the second class. The analytic model is based upon the observation of the final kinetic energy as a function of the initial conditions. Analytic results are shown to predict a Maxwellian tail for the distribution function in the perpendicular kinetic energy, with this energy much greater than the parallel kinetic energy. Numerical results showing that the predicted tail temperature agrees with the numerically computed temperature to within 10 percent over 4 orders of magnitude in the electric field are presented.
This is an investigation of stormtime particle transport that leads to formation of the ring current. Our method is to trace the guiding-center motion of representative ions (having selected first adiabatic invariants mu) in response to model substorm-associated impulses in the convection electric field. We compare our simulation results qualitatively with existing analytically tractable idealizations of particle transport (direct convective access and radial diffusion) in order to assess the limits of validity of these approximations. For mu approximately less than 10 MeV/G (E approximately less than 10 keV at L equivalent to 3) the ion drift period on the final (ring-current) drift shell of interest (L equivalent to 3) exceeds the duration of the main phase of our model storm, and we find that the transport of ions to this drift shell is appropriately idealized as direct convective access, typically from open drift paths. Ion transport to a final closed drift path from an open (plasma-sheet) drift trajectory is possible for those portions of that drift path that lie outside the mean stormtime separatrix between closed and open drift trajectories, For mu approximately 10-25 MeV/G (110 keV approximately less than E approximately less than 280 keV at L equivalent to 3) the drift period at L equivalent to 3 is comparable to the postulated 3-hr duration of the storm, and the mode of transport is transitional between direct convective access and transport that resembles radial diffusion. (This particle population is transitional between the ring current and radiation belt). For mu approximately greater than 25 MeV/G (radiation-belt ions having E approximately greater than 280 keV at L equivalent to 3) the ion drift period is considerably shorter than the main phase of a typical storm, and ions gain access to the ring-current region essentially via radial diffusion. By computing the mean and mean-square cumulative changes in 1/L among (in this case) 12 representative ions equally spaced in drift time around the steady-state drift shell of interest (L equivalent to 3), we have estimated (from both our forward and our time-reversed simulations) the time-integrated radial-diffusion coefficients D(sup sim)(sub LL) for particles having selected values of mu approximately greater than 15 MeV/G. The results agree surprisingly well with the predictions (D(sup ql)(sub LL)) of quasilinear radial diffusion theory, despite the rather brief duration (approximately 3 hrs) of our model storm and despite the extreme variability (with frequency) of the spectral-density function that characterizes the applied electric field during our model storm. As expected, the values of D(sup sim)(sub LL) deduced (respectively) from our forward and time-reversed simulations agree even better with each other and with D(sup sim)(sub LL) when the impulse amplitudes which characterize the individual substorms of our model storm are systematically reduced.
A generalization of the procedure to study shapes and stability of algebraic nuclear models introduced by Gilmore is presented. One calculates the expectation value of the Hamiltonian with respect to the coherent states of the algebraic structure of the system. Then equilibrium configurations of the resulting energy surface, which depends in general on state variables and a set of parameters, are classified through the Catastrophe theory. For one- and two-body interactions in the Hamiltonian of the interacting Boson model-1, the critical points are organized through the Cusp catastrophe. As an example, we apply this Separatrix to describe the energy surfaces associated to the Rutenium and Samarium isotopes.
Recently, the Convergin Flux Model has been proposed for X-ray bright points and cancelling magnetic features. The aim of this piece of work is to try and model theoretically specific X-ray bright points in the framework of the Converging Flux Model. The observational data used includes a magnetogram showing the normal component of the magnetic field at the photosphere and a high-resolution soft X-ray image from NIXT showing the brightenings in the lower solar corona. By approximating the flux concentrations in the magnetograms with poles of the appropriate sign and sense, the overlying three-dimensional potential field structure is calculated. Deduction of plausible motions of the flux sources are made which produce brightenings of the observed shape due to reconnection between neighbouring flux regions. Also the three-dimensional separatrix and separator structure and the way the magnetic field lines reconnect in three dimensions is deduced.
We propose that many features of the cusp and low-latitude boundary layer (LLBL) observed near noon MLT can be explained by interpreting the LLBL as being on open lines with an inner boundary at the separatrix between open and closed magnetic field lines. This interpretation places the poleward boundary of the LLBL and equatorward boundary of the cusp along the field line that bifurcates at the cusp neutral point. The interpretation accounts for the abrupt boundary of magnetosheath particles at the inner edge of the LLBL, a feature that is inconsistent with LLBL formation by diffusion onto closed field lines, and for the distribution of magnetosheath particles appearing more as one continuous region than as two distinct regions across the noon cusp/LLBL boundary. Furthermore, we can explain the existence of energetic radiation belt electrons and protons with differing pitch angle distributions within the LLBL and their abrupt cutoff at the poleward boundary of the LLBL. By modeling the LLBL and cusp region quantitatively, we can account for a hemispherical difference in the location of the equatorial boundary of the cusp that is observed to be dependent on the dipole tilt angle but not on the interplanetary magnetic field (IMF) x component. We also find important variations and hemispherical differences in that the size of the LLBL that should depend strongly upon the x component of the IMF. This prediction is observationally testable. Finally, we find that when the IMF is strongly northward, the LLBL may include a narrow region adjacent to the magnetopause where field lines are detached (i.e., have both ends connected to the IMF).
A technique was developed for the inclusion of large scale magnetospheric current systems in magnetic field models. The region 1 and 2 Birkeland current systems are included in the source surface model of the terrestrial magnetosphere. The region 1 and 2 Birkeland currents are placed in the model using a series of field aligned, infinitely thin wire segments. The normal component of the magnetic field from these currents is calculated on the surface of the magnetopause and shielded using image current carrying wires placed outside of the magnetosphere. It is found that the inclusion of the Birkeland currents in the model results in a northward magnetic field in the near-midnight tail, leading to the closure of previously open flux in the tail, and a southward magnetic field in the flanks. A sunward shift in the separatrix is observed.
It is found that the upper-bound limit for current collection in the case of strong magnetic field from the current is close to that given by the Parker-Murphy formula. This conclusion is consistent with the results obtained in laboratory experiments. This limit weakly depends on the shape of the wire. The adiabatic limit in this case will be easily surpassed due to strong magnetic field gradients near the separatrix. The calculations can be done using the kinetic equation in the drift approximation. Analytical results are obtained for the region where the Earth's magnetic field is dominant. The current collection can be calculated (neglecting scattering) using a particle simulation code. Dr. Singh has agreed to collaborate, allowing the use of his particle code. The code can be adapted for the case when the current magnetic field is strong. The needed dm for these modifications is 3-4 months. The analytical description and essential part of the program is prepared for the calculation of the current in the region where the adiabatic description can be used. This was completed with the collaboration of Drs. Khazanov and Liemohn. A scheme of measuring the end body position is also proposed. The scheme was discussed in the laboratory (with Dr. Stone) and it was concluded that it can be proposed for engineering analysis.
We compare electron densities measured at three different locations in solar flares: (1) in Soft X-Ray (SXR) loops, determined from SXR emission measures and loop diameters from Yohkoh Soft X-Ray Telescope maps (n(sub e, sup SXR) = (0.2-2.5) x 10(exp 11)/ cu cm); (2) in chromospheric evaporation upflows, inferred from plasma frequency cutoffs of decimetric radio bursts detected with the 0.1-3 GHz spectrometer Phoenix of ETH Zuerich (n(sub e, sup upflow) = (0.3-11) x 10(exp 10)/cu cm; and (3) in acceleration sites, inferred from the plasma frequency at the separatrix between upward-accelerated (type III bursts) and downward-accelerated (reverse-drift bursts) electron beams [n(sub e, sup acc) = (0.6-10) x 10(exp 9)/cu cm]. The comparison of these density measurements, obtained from 44 flare episodes (during 14 different flares), demonstrates the compatibility of flare plasma density diagnostics with SXR and radio methods. The density in the upflowing plasma is found to be somewhat lower than in the filled loops, having ratios in a range n(sub e, sup upflow)/n(sub e, sup SXR) = 0.02-1.3, and a factor of 3.6 higher behind the upflow front. The acceleration sites are found to have a much lower density than the SXR-bright flare loops, i.e., n(sub e, sup acc)/n(sub e, sup SXR) = 0.005- 0.13, and thus must be physically displaced from the SXR-bright flare loops. The scaling law between electron time-of-flight distances l' and loop half-lengths s, l'/s = 1.4 +/- 0.3, recently established by Aschwanden et al. suggests that the centroid of the acceleration region is located above the SXR-bright flare loop, as envisioned in cusp geometries (e.g., in magnetic reconnection models).
Historical satellite-derived sea surface temperature (SST) data are reanalyzed with a zebra color palette and a thermal separatrix method. The new results from this reanalysis are as follows: (a) Thirteen observational sequences of six rings from the Gulf Stream and the Brazil Current, which have historically been interpreted as solitary vortices or monopoles are shown to have a dipolar character; (b) some of these dipole rings have been observed in the open ocean, thereby eliminating the possibility that they are sustained by topographic interactions with the continental slope; (c) whether interacting with other features or evolving as isolated circulations, dipoles are seen to rotate within a relatively narrow range of approximately 4-8 deg/day (interacting) and 10-11 deg/day (isolated); and (d) feature tracking delineates energetic fluid in both vortices and eliminates the possibility of interpreting dipole rings as transient features produced by active monopoles and patches of entrained fluid.
This final report summarizes the development and application of the first ever method to measure a proxy of the global merging along the solar wind-Earth separatrix. The ultimate aim of the project is to quantify the reconnection potential in the magnetotail and the fraction of it that is due to bursty bulk flows (BBFs). To achieve this goal, we developed the first method that allows the measurement of the distribution of reconnection rate along the polar cap boundary. The method was then applied to substorms and steady magnetospheric convection (labeled as SMC or convection bay) periods in order to quantify the strength of reconnection and the fraction of it that is contributed by BBFs in each case. Results of this research were reported in two manuscripts submitted to the Journal of Geophysical Research and presented at three international conferences. This report is organized as follows. In Section 2 we discuss the conceptual framework that is the foundation of the method. In Section 3 we describe the details of the method. In Section 4 we describe the application of the technique to substorms and SMCs. In Section 5 we summarize the results of this investigation and provide references to the manuscripts and conference presentations that report on the results of this project.
The study of magnetic connectivity in the solar corona reveals a need to generalize the field line mapping technique to arbitrary geometry of the boundaries and systems of coordinates. Indeed, the global description of the connectivity in the corona requires the use of the photospheric and solar wind boundaries. Both are closed surfaces and therefore do not admit a global regular system of coordinates. At least two overlapping regular systems of coordinates for each of the boundaries are necessary in this case to avoid spherical-pole-like singularities in the coordinates of the footpoints. This implies that the basic characteristic of magnetic connectivity-the squashing degree or factor Q of elemental flux tubes, according to Titov and coworkers-must be rewritten in covariant form. Such a covariant expression of Q is derived in this work. The derived expression is very flexible and highly efficient for describing the global magnetic connectivity in the solar corona. In addition, a general expression for a new characteristic Q1, which defines a squashing of the flux tubes in the directions perpendicular to the field lines, is determined. This new quantity makes it possible to filter out the quasi-separatrix layers whose large values of Q are caused by a projection effect at the field lines nearly touching the photosphere. Thus, the value Q1 provides a much more precise description of the volumetric properties of the magnetic field structure. The difference between Q and Q1 is illustrated by comparing their distributions for two configurations, one of which is the Titov-Demoulin model of a twisted magnetic field.
W present the extension of the magnetic breakout model for CME initiation to a fully 3-dimensional, spherical geometry. Given the increased complexity of the dynamic magnetic field interactions in 3-dimensions, we first present a summary of the well known axisymmetric breakout scenario in terms of the topological evolution associated with the various phases of the eruptive process. In this context, we discuss the completely analogous topological evolution during the magnetic breakout CME initiation process in the simplest 3-dimensional multipolar system. We show that an extended bipolar active region embedded in an oppositely directed background dipole field has all the necessary topological features required for magnetic breakout, i.e. a fan separatrix surface between the two distinct flux systems, a pair of spine fieldlines, and a true 3-dimensional coronal null point at their intersection. We then present the results of a numerical MHD simulation of this 3-dimensional system where boundary shearing flows introduce free magnetic energy, eventually leading to a fast magnetic breakout CME. The eruptive flare reconnection facilitates the rapid conversion of this stored free magnetic energy into kinetic energy and the associated acceleration causes the erupting field and plasma structure to reach an asymptotic eruption velocity of greater than or approx. equal to 1100 km/s over an approx.15 minute time period. The simulation results are discussed using the topological insight developed to interpret the various phases of the eruption and the complex, dynamic, and interacting magnetic field structures.
We propose a model for the jetting activity that is commonly observed in the Sun's corona, especially in the open-field regions of polar coronal holes. Magnetic reconnection is the process driving the jets and a relevant magnetic configuration is the well-known null point and fan separatrix topology. The primary challenge in explaining the observations is that reconnection must occur in a short-duration energetic burst rather than quasi-continuously as is implied by the observations of long-lived structures in coronal holes, such as polar plumes, for example. The key idea underlying our model for jets is that reconnection is forbidden for an axisymmetric null-point topology. Consequently, by imposing a twisting motion that maintains the axisymmetry, magnetic stress can be built up to large levels until an ideal instability breaks the symmetry and leads to an explosive release of energy via reconnection. Using 3D MHD simulations we demonstrate that this mechanism does produce jets with high speed and mass, driven by nonlinear Alfven waves. We discuss the implications of our results for observations of the solar corona.
We report the multiwavelength investigations of an eruptive flare event that occurred on 2001 April 2 at about 11 UT. The manifestations associated with this flare event have been studied from the near-Sun region to about 0.5 AU. The H-alpha images from the Meudon Spectroheliograph reveal a fast spectacular eruption of plasmoids from the flare site to the west and a Moreton wave disturbance propagating toward the south, A bright, fast, wide coronal mass ejection (CME) associated with this eruptive event was imaged by SOHO/LASCO and the remote-sensing interplanetary scintillation technique. The timings and positions of the Type II radio bursts, H-alpha eruption, and CME onset as well as the magnetic field configuration suggest a release of energy at the null point. The results seem to support the "breakout" scenario proposed by Antiochos and coworkers, and they are also suggestive that the energy release is followed by magnetic reconnection between the low-lying loops near the separatrix and the loop system above them.
We investigate the effect of magnetic reconnection between open and closed fields, often referred to as interchange reconnection, on the dynamics and topology of coronal hole boundaries. The most important and most prevalent three-dimensional topology of the interchange process is that of a small-scale bipolar magnetic field interacting with a large-scale background field. We determine the evolution of such a magnetic topology by numerical solution of the fully three-dimensional MHD equations in spherical coordinates. First, we calculate the evolution of a small-scale bipole that initially is completely inside an open field region and then is driven across a coronal hole boundary by photospheric motions. Next the reverse situation is calculated in which the bipole is initially inside the closed region and driven toward the coronal hole boundary. In both cases, we find that the stress imparted by the photospheric motions results in deformation of the separatrix surface between the closed field of the bipole and the background field, leading to rapid current sheet formation and to efficient reconnection. When the bipole is inside the open field region, the reconnection is of the interchange type in that it exchanges open and closed fields. We examine, in detail, the topology of the field as the bipole moves across the coronal hole boundary and find that the field remains well connected throughout this process. Our results, therefore, provide essential support for the quasi-steady models of the open field, because in these models the open and closed flux are assumed to remain topologically distinct as the photosphere evolves. Our results also support the uniqueness hypothesis for open field regions as postulated by Antiochos et al. On the other hand, the results argue against models in which open flux is assumed to diffusively penetrate deeply inside the closed field region under a helmet streamer. We discuss the implications of this work for coronal observations.