A force-free field with constant alpha in an oblate
cylinder: A generalization of the Lundquist solution

Vandas, M.; Romashets, E.

doi:10.1051/0004-6361:20021691

Cited by 71 publications

(57 citation statements)

References 10 publications

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“…We quantify this property so that b can be estimated from the magnetic data collected across a MC. We also confirm the results of Vandas & Romashets (2003) who derived an analytical solution of a linear force-free field contained inside an elliptical boundary. We find that the configuration of the core inherits the oblate shape of the boundary but with a significantly lower aspect ratio, in agreement with previous observations (e.g., Dasso et al 2005a;Liu et al 2008;Möstl et al 2009).…”

Section: Discussionsupporting

confidence: 87%

“…A third analytical solution for a linear force-free field with an elliptical boundary (particular case of Eq. (4) with a = 0) was found by Vandas & Romashets (2003). Equation (6) was solved with elliptic cylindrical coordinates, one of the few coordinates system where Eq.…”

Section: Analytical Solutionsmentioning

confidence: 99%

“…It was, and is still, widely used to fit the magnetic field observed in MCs and to derive global quantities such as the magnetic flux and helicity (e.g., Burlaga 1988;Lepping et al 1990;Dasso et al 2003;Lynch et al 2003;Dasso et al 2005b;Mandrini et al 2005;Dasso et al 2006;Leitner et al 2007). An extension of this model to an elliptical boundary was realized by Vandas & Romashets (2003). They derived analytical solutions for any value of the aspect ratio (ratio of the ellipse sizes).…”

Section: Introductionmentioning

confidence: 99%

“…Still, the Lundquist solution is known to have difficulties in fitting the magnetic field strength, in particular it was found that it frequently overestimates the axial component of the field near the flux-rope axis (e.g., Gulisano et al 2005). The elliptical model of Vandas & Romashets (2003) provides a better fit to observed MCs having a field strength more uniform than in the Lundquist solution. This indicates the existence of some flat flux ropes .…”

Section: Introductionmentioning

confidence: 99%

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Magnetic cloud models with bent and oblate cross-section boundaries

Démoulin¹,

Dasso

2009

A&A

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Context. Magnetic clouds (MCs) are formed by magnetic flux ropes that are ejected from the Sun as coronal mass ejections. These structures generally have low plasma beta and travel through the interplanetary medium interacting with the surrounding solar wind. Thus, the dynamical evolution of the internal magnetic structure of a MC is a consequence of both the conditions of its environment and of its own dynamical laws, which are mainly dominated by magnetic forces. Aims. With in-situ observations the magnetic field is only measured along the trajectory of the spacecraft across the MC. Therefore, a magnetic model is needed to reconstruct the magnetic configuration of the encountered MC. The main aim of the present work is to extend the widely used cylindrical model to arbitrary cross-section shapes. Methods. The flux rope boundary is parametrized to account for a broad range of shapes. Then, the internal structure of the flux rope is computed by expressing the magnetic field as a series of modes of a linear force-free field. Results. We analyze the magnetic field profile along straight cuts through the flux rope, in order to simulate the spacecraft crossing through a MC. We find that the magnetic field orientation is only weakly affected by the shape of the MC boundary. Therefore, the MC axis can approximately be found by the typical methods previously used (e.g., minimum variance). The boundary shape affects the magnetic field strength most. The measurement of how much the field strength peaks along the crossing provides an estimation of the aspect ratio of the flux-rope cross-section. The asymmetry of the field strength between the front and the back of the MC, after correcting for the time evolution (i.e., its aging during the observation of the MC), provides an estimation of the cross-section global bending. A flat or/and bent cross-section requires a large anisotropy of the total pressure imposed at the MC boundary by the surrounding medium. Conclusions. The new theoretical model developed here relaxes the cylindrical symmetry hypothesis. It is designed to estimate the cross-section shape of the flux rope using the in-situ data of one spacecraft. This allows a more accurate determination of the global quantities, such as magnetic fluxes and helicity. These quantities are especially important for both linking an observed MC to its solar source and for understanding the corresponding evolution.

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Section: Discussionsupporting

confidence: 87%

Section: Analytical Solutionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Magnetic cloud models with bent and oblate cross-section boundaries

Démoulin¹,

Dasso

2009

A&A

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“…(f) Marubashi and Lepping (2007) include curvature into the classic model. rope (Owens, Merkin, and Riley, 2006;Vandas and Romashets, 2003;Vandas et al, 2006;Démoulin and Dasso, 2009); non-cylindrical flux rope fitting (Mulligan and Russell, 2001;Owens et al, 2012); torus fitting Marubashi and Lepping, 2007). The Grad-Shafranov reconstruction technique (Hu and Sonnerup, 2002;) assumes a structure in magneto-hydrostatic (MHS) equilibrium with an invariant direction, and uses the Grad-Shafranov equation to describe the magnetic field in the structure.…”

Section: Introductionmentioning

confidence: 99%

Magnetic Field Configuration Models and Reconstruction Methods for Interplanetary Coronal Mass Ejections

et al. 2013

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This study aims to provide a reference to different magnetic field models and reconstruction methods for interplanetary coronal mass ejections (ICMEs). In order to understand the differences in the outputs of those models and codes, we analyze 59 events from the Coordinated Data Analysis Workshop (CDAW) list, using four different magnetic field models and reconstruction techniques; force-free fitting (Goldstein, 1983; Burlaga, 1988;Lepping, Burlaga, and Jones, 1990), magnetostatic reconstruction using a numerical solution to the Grad-Shafranov equation (Hu and Sonnerup, 2001), fitting to a self-similarly expanding cylindrical configuration (Marubashi and Lepping, 2007) and elliptical, non-force free fitting (Hidalgo, 2003). The resulting parameters of the reconstructions for the 59 events are compared statistically, as well as in selected case studies. The ability of a method to fit or reconstruct an event is found to vary greatly: the Grad-Shafranov reconstruction is successful for most magnetic clouds (MCs) but for less than 10% of the non-MC ICMEs; the other three Al-Haddad et al methods provide a successful fit for more than 65% of all events. The differences between the reconstruction and fitting methods are discussed, and suggestions are proposed as to how to reduce them. We find that the magnitude of the axial field is relatively consistent across models but not the orientation of the axis of the ejecta. We also find that there are a few cases for which different signs of the magnetic helicity are found for the same event when we do not fix the boundaries, illustrating that this simplest of parameters is not necessarily always well constrained by fitting and reconstruction models. Finally, we look at three unique cases in depth to provide a comprehensive idea of the different aspects of how the fitting and reconstruction codes work.

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Investigating plasma motion of magnetic clouds at 1 AU through a velocity‐modified cylindrical force‐free flux rope model

et al. 2015

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(2015), Investigating plasma motion of magnetic clouds at 1 AU through a velocity-modified cylindrical force-free flux rope model, J. Geophys. Res. Space Physics, 120, 1543-1565, doi:10.1002 and usually modeled by a flux rope. By assuming the quasi-steady evolution and self-similar expansion, we introduce three types of global motion into a cylindrical force-free flux rope model and developed a new velocity-modified model for MCs. The three types of the global motion are the linear propagating motion away from the Sun, the expanding, and the poloidal motion with respect to the axis of the MC. The model is applied to 72 MCs observed by Wind spacecraft to investigate the properties of the plasma motion of MCs. First, we find that some MCs had a significant propagation velocity perpendicular to the radial direction, suggesting the direct evidence of the CME's deflected propagation and/or rotation in interplanetary space. Second, we confirm the previous results that the expansion speed is correlated with the radial propagation speed and most MCs did not expand self-similarly at 1 AU. In our statistics, about 62%/17% of MCs underwent a underexpansion/overexpansion at 1 AU and the expansion rate is about 0.6 on average. Third, most interestingly, we find that a significant poloidal motion did exist in some MCs. Three speculations about the cause of the poloidal motion are therefore proposed. These findings advance our understanding of the MC's properties at 1 AU and the dynamic evolution of CMEs from the Sun to interplanetary space.

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A force-free field with constant alpha in an oblate cylinder: A generalization of the Lundquist solution

Cited by 71 publications

References 10 publications

Magnetic cloud models with bent and oblate cross-section boundaries

Magnetic cloud models with bent and oblate cross-section boundaries

Magnetic Field Configuration Models and Reconstruction Methods for Interplanetary Coronal Mass Ejections

Investigating plasma motion of magnetic clouds at 1 AU through a velocity‐modified cylindrical force‐free flux rope model

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