J un 2 00 7 A trilinear method for finding null points in a 3 D vector space

Null points are important locations in vector fields, such as a magnetic field. A new technique (a trilinear method for finding null points) is presented for finding null points over a large grid of points, such as those derived from a numerical experiment. The method was designed so that the null points found would agree with any field lines traced using the commonly used trilinear interpolation. It is split into three parts: reduction, analysis, and positioning, which, when combined, provide an efficient means of locating null points to a user-defined subgrid accuracy. We compare the results of the trilinear method with that of a method based on the Poincare index, and discuss the accuracy and limitations of both methods.

[1]  A. Hood,et al.  MHD Wave Propagation in the Neighbourhood of Two Null Points , 2005, 0712.1809.

[2]  Jun Zhang,et al.  A New Method of Identifying 3D Null Points in Solar Vector Magnetic Fields , 2005 .

[3]  K. Nishikawa,et al.  Magnetotail field topology in a three-dimensional global particle simulation , 2006 .

[4]  In situ evidence for the structure of the magnetic null in a 3D reconnection event in the Earth's magnetotail , 2006, physics/0606014.

[5]  E. Priest,et al.  The 3D topology and interaction of complex magnetic flux systems , 1997 .

[6]  M. J. Murray,et al.  Simple emergence structures from complex magnetic fields , 2007 .

[7]  John M. Greene,et al.  Locating three-dimensional roots by a bisection method , 1992 .

[8]  E. Priest,et al.  Magnetic reconnection at three-dimensional null points , 1996, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[9]  C. Schrijver,et al.  The topology of a mixed-polarity potential field, and inferences for the heating of the quiet solar corona , 2002 .

[10]  D. Pontin,et al.  Current sheet formation and nonideal behavior at three-dimensional magnetic null points , 2007, astro-ph/0701462.

[11]  R. Lüst.  Stellar and solar magnetic fields , 1965 .

[12]  A. Hood,et al.  MHD mode coupling in the neighbourhood of a 2D null point , 2006, 0712.2402.

[13]  E. Priest,et al.  Basic topological elements of coronal magnetic fields. , 1996 .

[14]  R. Stenzel,et al.  A new laboratory experiment on magnetic reconnection , 2002 .

[15]  J. M. Smith,et al.  The structure of three‐dimensional magnetic neutral points , 1996 .

[16]  I. Craig,et al.  Current singularities at finitely compressible three-dimensional magnetic null points , 2005 .

[17]  A. Bhattacharjee,et al.  Separator reconnection at Earth's dayside magnetopause under generic northward interplanetary magnetic field conditions , 2007 .