Magnetostatic atmospheres possessing identical invariants of ideal magnetohydrodynamics

A physical analysis is presented of two distinct families of two-dimensiona l (2D) analytical solutions for isothermal periodic magnetostatic atmospher es in uniform gravity, one arrived at by Dungey and the other arrived at by Low and Manchester. It is demonstrated that particular members of the two families of 2D equilibria may be generated from the same planar state by pl asma displacements which move the system through continuous sequences of eq uilibria while ensuring flux freezing. The two families of solutions both p ossess undulating magnetic field lines but geometrically different flux sur faces. The Dungey solutions can be created from a planar state by an undula ting deformation whose spatial variation is along the field lines. By contr ast, the 2D plane of variation of the Low-Manchester solutions lies at an a ngle to the field lines of the planar state. As a result, a mixed mode of u ndulating, interchange and shearing displacements must be made to the plana r state to produce the more complex 2D state. Finally, the physical propert ies of these topologically equivalent states, including the magnetic and el ectrical helicities and the hydromagnetic potential energy, as introduced b y Mouschovias, are discussed in terms of the variational principles of Krus kal and Kulsrud. (C) 2000 American Institute of Physics. [S1070-664X(00)006 04-2].