A third-order topological invariant for three magnetic fields. / Mayer, Christoph; Hornig, Gunnar.
Tubes, sheets and singularities in fluid dynamics: proceedings of the NATO ARW, 2-7 September 2001, Zakopane, Poland. ed. / K. Bajer; H. K. Moffatt. Kluwer Academic, 2002. p. 151-156 (Fluid mechanics and its applications; 71(3)).Research output: Chapter in Book/Report/Conference proceeding › Chapter
}
TY - CHAP
T1 - A third-order topological invariant for three magnetic fields
A1 - Mayer,Christoph
A1 - Hornig,Gunnar
AU - Mayer,Christoph
AU - Hornig,Gunnar
PB - Kluwer Academic
PY - 2002
Y1 - 2002
N2 - The topology of divergence-free fields is important in many parts of physics, e. g. in magnetohydrodynamics, plasma physics, hydrodynamics, superfluids etc. With the focus on applications in magnetohydrodynamics, our principal aim is the characterisation of magnetic fields by the means of invariants. In this report an introduction to the problem of finding higher order invariants is given. Then a third-order link integral of three magnetic fields is presented, which can be shown to be a topological invariant and therefore an invariant in ideal magnetohydrodynamics. This integral generalises the known third-order link invariant derived from the Massey triple product, which could only be applied to isolated flux tubes. As an example three magnetic fields not confined to flux tubes are given that possess a third-order linkage.
AB - The topology of divergence-free fields is important in many parts of physics, e. g. in magnetohydrodynamics, plasma physics, hydrodynamics, superfluids etc. With the focus on applications in magnetohydrodynamics, our principal aim is the characterisation of magnetic fields by the means of invariants. In this report an introduction to the problem of finding higher order invariants is given. Then a third-order link integral of three magnetic fields is presented, which can be shown to be a topological invariant and therefore an invariant in ideal magnetohydrodynamics. This integral generalises the known third-order link invariant derived from the Massey triple product, which could only be applied to isolated flux tubes. As an example three magnetic fields not confined to flux tubes are given that possess a third-order linkage.
UR - http://library.dundee.ac.uk/F/?func=direct&local_base=DUN01&doc_number=000529364
U2 - 10.1007/0-306-48420-X_22
DO - 10.1007/0-306-48420-X_22
M1 - Chapter
SN - 9781402009808
SN - 1402009801
BT - Tubes, sheets and singularities in fluid dynamics: proceedings of the NATO ARW, 2-7 September 2001, Zakopane, Poland
T2 - Tubes, sheets and singularities in fluid dynamics: proceedings of the NATO ARW, 2-7 September 2001, Zakopane, Poland
A2 - Moffatt,H. K.
ED - Moffatt,H. K.
T3 - Fluid mechanics and its applications
T3 - en_GB
SP - 151
EP - 156
ER -