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Corrigendum: Quasi-separatrix layer reconnection for nonlinear line-tied collisionless tearing modes (2014 Plasma Phys. Control. Fusion 56 064013)
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 Plasma Phys. Control. Fusion 56 099502 (http://iopscience.iop.org/0741-3335/56/9/099502) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 98.221.53.71 This content was downloaded on 02/03/2015 at 01:00
Please note that terms and conditions apply.
Plasma Physics and Controlled Fusion Plasma Phys. Control. Fusion 56 (2014) 099502 (2pp)
doi:10.1088/0741-3335/56/9/099502
Corrigendum: Quasi-separatrix layer reconnection for nonlinear line-tied collisionless tearing modes (2014 Plasma Phys. Control. Fusion 56 064013) J M Finn1 , Z Billey2 , W Daughton1 and E Zweibel2 1 2
Los Alamos National Laboratory, Los Alamos, NM 87545, USA Department of Physics, University of Wisconsin, Madison, WI 53706, USA
Received 9 July 2014 Accepted for publication 9 July 2014 Published 30 July 2014 This is a correction to a reference error in our paper ‘Quasi-separatrix layer reconnection for nonlinear line-tied collisionless tearing modes’, which appeared in the special issue ‘Self-organization in Magnetic Flux Ropes Cluster’ in Plasma Physics and Controlled Fusion earlier in 2014.
In our recent paper ‘Quasi-separatrix layer reconnection for nonlinear line-tied collisionless tearing modes’ [1], we referred to the development of the concept of a quasi-separatrix layer (QSL) and the squashing degree Q used to detect a QSL. For our purposes here we describe the situation in terms of the special case of reference [1], in which field lines enter the region of interest at y = 0 and exit at y = L. In the presence of a magnetic null or closed field line, the field line mapping from y = 0 to y = L can be singular; without these structures a QSL is said to be present if the field line mapping, while not singular, shows a great deal of stretching. We correctly referred to [3] as having developed the QSL concept but mistakenly credited [3] with introducing the squashing degree Q. In [3] this stretching of field lines was quantified in terms of the gradient of the field line linkage, i.e. in terms of field line Jacobian matrix Jij =
the sum of squares of the matrix elements. Equivalently, this quantity is the trace of J T J , and the quantity N is the Frobenius norm of the matrix J . In a series of papers [4–6], Titov and co-workers introduced the squashing degree Q, a modification to the quantity N which, in its most general form, takes into account the expansion of the flux tube between the footpoints and, in more general cases, the geometry of the two footpoint surfaces. The quantity Q can be found by integrating a small circle of field lines on the entering footpoint plane y = 0 to the footpoints at y = L and computing the ratio of the major and minor axes of the ellipse formed by the intersection of the flux tube with the plane y = L. This quantity is related to the ratio of the maximum to minimum eigenvalues of J T J or to the ratio of the maximum to minimum singular values of J . This process removes the overall expansion or contraction of the flux tube and the effect of projection of field lines at the footpoint surfaces, effects considered unimportant for magnetic reconnection. The development of these ideas is explained in more detail in these original sources and in the recently published book in [2].
∂Xi . ∂xj
The components (x1 , x2 ) and (X1 , X2 ) represent positions of field line footpoints at y = 0 and y = L, respectively. Specifically, it was suggested in [3] that the stretching of tubes of magnetic flux between the footpoints be quantified in terms of the quantity N , where N = 2
Jij2
ij
0741-3335/14/099502+02$33.00
=
∂Xi 2 ij
∂xj
References [1] Finn J M, Billey Z, Daughton W and Zweibel E 2014 Quasi-separatrix layer reconnection for nonlinear line-tied collisionless tearing modes Plasma Phys. Control. Fusion 56 064013
,
1
© 2014 IOP Publishing Ltd Printed in the UK
Plasma Phys. Control. Fusion 56 (2014) 099502
Corrigendum
[5] Titov V S, Demoulin P and Hornig G 1999 Quasi-separatrix layers: refined theory and its application to solar flares Magnetic Fields and Solar Processes (Astron. Nachr. Suppl. vol 324) ed A Wilson et al (Noordwijk: ESA) p 17 ESA SP-448 (arXiv:astro-ph/9909392) [6] Titov V S, Hornig G and Demoulin P 2002 Theory of magnetic connectivity in the solar corona J. Geophys. Res. 107 1164
[2] Priest E R 2014 Magnetohydrodynamics of the Sun (New York: Cambridge University Press) [3] Priest E R and Demoulin P 1995 Three-dimensional magnetic reconnection without null points. 1: Basic theory of magnetic flipping J. Geophys. Res. 100 23443 [4] Titov V S 2007 Generalized squashing factors for covariant description of magnetic connectivity in the solar corona Astrophys. J. 660 863
2
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About
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My IOPscience
Corrigendum: Quasi-separatrix layer reconnection for nonlinear line-tied collisionless tearing modes (2014 Plasma Phys. Control. Fusion 56 064013)
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 Plasma Phys. Control. Fusion 56 099502 (http://iopscience.iop.org/0741-3335/56/9/099502) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 98.221.53.71 This content was downloaded on 02/03/2015 at 01:00
Please note that terms and conditions apply.
Plasma Physics and Controlled Fusion Plasma Phys. Control. Fusion 56 (2014) 099502 (2pp)
doi:10.1088/0741-3335/56/9/099502
Corrigendum: Quasi-separatrix layer reconnection for nonlinear line-tied collisionless tearing modes (2014 Plasma Phys. Control. Fusion 56 064013) J M Finn1 , Z Billey2 , W Daughton1 and E Zweibel2 1 2
Los Alamos National Laboratory, Los Alamos, NM 87545, USA Department of Physics, University of Wisconsin, Madison, WI 53706, USA
Received 9 July 2014 Accepted for publication 9 July 2014 Published 30 July 2014 This is a correction to a reference error in our paper ‘Quasi-separatrix layer reconnection for nonlinear line-tied collisionless tearing modes’, which appeared in the special issue ‘Self-organization in Magnetic Flux Ropes Cluster’ in Plasma Physics and Controlled Fusion earlier in 2014.
In our recent paper ‘Quasi-separatrix layer reconnection for nonlinear line-tied collisionless tearing modes’ [1], we referred to the development of the concept of a quasi-separatrix layer (QSL) and the squashing degree Q used to detect a QSL. For our purposes here we describe the situation in terms of the special case of reference [1], in which field lines enter the region of interest at y = 0 and exit at y = L. In the presence of a magnetic null or closed field line, the field line mapping from y = 0 to y = L can be singular; without these structures a QSL is said to be present if the field line mapping, while not singular, shows a great deal of stretching. We correctly referred to [3] as having developed the QSL concept but mistakenly credited [3] with introducing the squashing degree Q. In [3] this stretching of field lines was quantified in terms of the gradient of the field line linkage, i.e. in terms of field line Jacobian matrix Jij =
the sum of squares of the matrix elements. Equivalently, this quantity is the trace of J T J , and the quantity N is the Frobenius norm of the matrix J . In a series of papers [4–6], Titov and co-workers introduced the squashing degree Q, a modification to the quantity N which, in its most general form, takes into account the expansion of the flux tube between the footpoints and, in more general cases, the geometry of the two footpoint surfaces. The quantity Q can be found by integrating a small circle of field lines on the entering footpoint plane y = 0 to the footpoints at y = L and computing the ratio of the major and minor axes of the ellipse formed by the intersection of the flux tube with the plane y = L. This quantity is related to the ratio of the maximum to minimum eigenvalues of J T J or to the ratio of the maximum to minimum singular values of J . This process removes the overall expansion or contraction of the flux tube and the effect of projection of field lines at the footpoint surfaces, effects considered unimportant for magnetic reconnection. The development of these ideas is explained in more detail in these original sources and in the recently published book in [2].
∂Xi . ∂xj
The components (x1 , x2 ) and (X1 , X2 ) represent positions of field line footpoints at y = 0 and y = L, respectively. Specifically, it was suggested in [3] that the stretching of tubes of magnetic flux between the footpoints be quantified in terms of the quantity N , where N = 2
Jij2
ij
0741-3335/14/099502+02$33.00
=
∂Xi 2 ij
∂xj
References [1] Finn J M, Billey Z, Daughton W and Zweibel E 2014 Quasi-separatrix layer reconnection for nonlinear line-tied collisionless tearing modes Plasma Phys. Control. Fusion 56 064013
,
1
© 2014 IOP Publishing Ltd Printed in the UK
Plasma Phys. Control. Fusion 56 (2014) 099502
Corrigendum
[5] Titov V S, Demoulin P and Hornig G 1999 Quasi-separatrix layers: refined theory and its application to solar flares Magnetic Fields and Solar Processes (Astron. Nachr. Suppl. vol 324) ed A Wilson et al (Noordwijk: ESA) p 17 ESA SP-448 (arXiv:astro-ph/9909392) [6] Titov V S, Hornig G and Demoulin P 2002 Theory of magnetic connectivity in the solar corona J. Geophys. Res. 107 1164
[2] Priest E R 2014 Magnetohydrodynamics of the Sun (New York: Cambridge University Press) [3] Priest E R and Demoulin P 1995 Three-dimensional magnetic reconnection without null points. 1: Basic theory of magnetic flipping J. Geophys. Res. 100 23443 [4] Titov V S 2007 Generalized squashing factors for covariant description of magnetic connectivity in the solar corona Astrophys. J. 660 863
2
