The Clebsch-Type Coordinate Systems

Abstract

The idea of a stream function (or flow function) is borrowed from hydrodynamic theory (see, e.g., Milne-Thomson (1968)). A stream function is any function that is constant along a stream line. In plasma physics, we are interested in stream functions for the magnetic field. Hence, in our context, a stream function is any function that is constant along afield line. In three-dimensional space, the equation Ф(u¹, u², u³) ≡ Ф(R) = constant represents a surface. A magnetic-field line can thus be identified with a curve lying at the intersection of two surfaces belonging to two different stream functions.