Differential Geometric and Topological methods with MHD and plasma physics

Abstract

Non-solitonic examples of the application of geometrical and topological methods in plasma physics and magnetohydrodynamics (MHD) are given. The first example considers the generalization of magnetic helicity to gravitational torsion loop. The second example considers also the application of this same torsion loop metric to some problems of helical fields in MHD dynamo theory. In the last example a Riemannian magnetic metric is given where the magnetic field itself is present in the diagonal time-independent metric. In this example the MHD equations are shown to be compatible to the geometrical Bianchi identity by making use of Cartan's differential calculus formalism. The Riemann curvature of the helical flow is also obtained.