Abstract
An expression for a third-order link integral of three magnetic fields is presented. It is a topological invariant and therefore an invariant of ideal magnetohydrodynamics. The integral generalizes existing expressions for third-order invariants which are obtained from the Massey triple product, where the three fields are restricted to isolated flux tubes. The derivation and interpretation of the invariant show a close relationship with the well-known magnetic helicity, which is a second-order topological invariant. Using gauge fields with an SU(2) symmetry, helicity and the new third-order invariant originate from the same identity, an identity which relates the second Chern class and the Chern–Simons 3-form. We present an explicit example of three magnetic fields with non-disjunct support. These fields, derived from a vacuum Yang–Mills field with a non-vanishing winding number, possess a third-order linkage detected by our invariant.
Original language | English |
---|---|
Pages (from-to) | 3945-3959 |
Number of pages | 15 |
Journal | Journal of Physics A: Mathematical and General |
Volume | 35 |
Issue number | 17 |
DOIs | |
Publication status | Published - 2002 |
Keywords
- Magnetohydrodynamics (MHD)
- Topological invariants
- MHD