The Role of Nonlinear Magnetic Fields and Euler Potential in Dynamo Theory Revisited

Abstract

This chapter reexamines the role of Euler potentials (EP) in magnetic dynamo theory. There is a link between the cross-product of gradients of the EP and magnetic field lines in a moving media [1]. However, its role and importance are a subject of debate, partly because of the anti-dynamo theorem of Cowling [2] and the stringent constraints obtained in 2D- and 3D- simulations [3]. This raises questions about the utility of such potentials in the broader magneto-genesis and dynamo theories. We reexamine this question in this chapter and find that a reinterpretation of such potentials may offer a new understanding of EP’s role in the evolution of magnetic field lines.