We introduced briefly in Section 1.3.2 the idea of a current sheet as a narrow region across which the magnetic field changes rapidly. In this chapter we consider in detail the formation of such sheets in a medium where the magnetic field is frozen to the plasma (§1.4), and then in Chapter 4 we describe how they diffuse through the plasma.

There are several ways in which current sheets may form. One is by the collapse of an X-type neutral point (§2.1). Such a formation in two dimensions through a series of static potential field states may be described by complex variable theory, in which the sheet is treated as a branch cut in the complex plane (§2.2). Other techniques are required for three-dimensional axisymmetric fields (§2.2.5), force-free fields (§2.3.1) or more general magnetostatic fields (§2.3.2). The concept of magnetic relaxation as developed by Moffatt is described in Section 2.4, and a self-consistent theory for slow time–dependent formation is discussed in Section 2.5. Finally, two other ways of forming current sheets are described, namely by shearing a field with separatrices (§2.6) and by braiding (§2.7).

X-Point Collapse

As we shall discuss in detail in Section 7.1, an X-type neutral point in a magnetic configuration tends to be locally unstable, provided the sources of the field are free to move (Dungey, 1953).