Lower and upper bounds on the energy of braided magnetic fields

摘要

Let B be a class of topologically equivalent regular magnetic fields occupying a cylindrical domain of axis Oz and produced by ideal MHD deformations of the uniform field B_0z, and let B_(ff) ? B be constituted of the fields of B which are force-free. We derive topological lower and upper bounds on the energy of the fields in B and in B_(ff) , respectively. We also establish new formulae for the field line helicity and the relative magnetic helicity of the fields in B, and give a sufficient criterion of ideal MHD linear stability for the fields in B_(ff) .