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Regularized Biot-Savart Laws for Modeling Magnetic Flux Ropes  

Viacheslav S. Titov   Submitted: 2017-12-22 13:47

Many existing models assume that magnetic flux ropes play a key role in solar flares and coronal mass ejections (CMEs). It is therefore important to develop efficient methods for constructing flux-rope configurations constrained by observed magnetic data and the morphology of the pre-eruptive source region. For this purpose, we have derived and implemented a compact analytical form that represents the magnetic field of a thin flux rope with an axis of arbitrary shape and circular cross-sections. This form implies that the flux rope carries axial current I and axial flux F, so that the respective magnetic field is the curl of the sum of axial and azimuthal vector potentials proportional to I and F, respectively. We expressed the vector potentials in terms of modified Biot-Savart laws whose kernels are regularized at the axis in such a way that, when the axis is straight, these laws define a cylindrical force-free flux rope with a parabolic profile for the axial current density. For the cases we have studied so far, we determined the shape of the rope axis by following the polarity inversion line of the eruptions' source region, using observed magnetograms. The height variation along the axis and other flux-rope parameters are estimated by means of potential field extrapolations. Using this heuristic approach, we were able to construct pre-eruption configurations for the 2009 February 13 and 2011 October 1 CME events. These applications demonstrate the flexibility and efficiency of our new method for energizing pre-eruptive configurations in simulations of CMEs.

Authors: Viacheslav S. Titov, Cooper Downs, Zoran Mikić, Tibor Török, Jon A. Linker and Ronald M. Caplan
Projects: None

Publication Status: Accepted for publication in ApJL.
Last Modified: 2017-12-24 20:47
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2010 August 1-2 sympathetic eruptions: II. Magnetic topology of the MHD background field  

Viacheslav S. Titov   Submitted: 2017-07-26 19:20

Using a potential field source surface (PFSS) model, we recently analyzed the global topology of the background coronal magnetic field for a sequence of coronal mass ejections (CMEs) that occurred on 2010 August 1-2. Here we repeat this analysis for the background field reproduced by a magnetohydrodynamic (MHD) model that incorporates plasma thermodynamics. As for the PFSS model, we find that all three CME source regions contain a coronal hole that is separated from neighboring coronal holes by topologically very similar pseudo-streamer structures. However, the two models yield very different results for the size, shape, and flux of the coronal holes. We find that the helmet-streamer cusp line, which corresponds to a source-surface null line in the PFSS model, is structurally unstable and does not form in the MHD model. Our analysis indicates that generally, in MHD configurations, this line rather consists of a multiple-null separator passing along the edge of disconnected flux regions. Some of these regions are transient and may be the origin of so-called streamer blobs. We show that the core topological structure of such blobs is a three-dimensional "plasmoid", consisting of two conjoined flux ropes of opposite handedness, which connect at a spiral null point of the magnetic field. Our analysis reveals that such plasmoids appear also in pseudo-streamers on much smaller scales. These new insights into the coronal magnetic topology provide some intriguing implications for solar energetic particle events and for the properties of the slow solar wind.

Authors: Viacheslav S. Titov, Zoran Mikic, Tibor Torok, Jon A. Linker, and Olga Panasenco
Projects: None

Publication Status: accepted for publication in ApJ.
Last Modified: 2017-07-31 11:05
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Generalized Squashing Factors for Covariant Description of Magnetic Connectivity in the Solar Corona  

Viacheslav S. Titov   Submitted: 2007-03-27 10:49

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 (Titov et al., 2002) - 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 Q_perp 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 Q_perp provides a much more precise description of the volumetric properties of the magnetic field structure. The difference between Q and Q_perp is illustrated by comparing their distributions for two configurations, one of which is the Titov-Demoulin (1999) model of a twisted magnetic field.

Authors: V. S. Titov
Projects: None

Publication Status: ApJ (in press, est. Vol. 660, No. 1, 2007 May 1)
Last Modified: 2007-03-27 12:33
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Abstracts by Author
Regularized Biot-Savart Laws for Modeling Magnetic Flux Ropes
2010 August 1-2 sympathetic eruptions: II. Magnetic topology of the MHD background field
Generalized Squashing Factors for Covariant Description of Magnetic Connectivity in the Solar Corona

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