Plasma corners. I: Constant toroidal current density

If a toroidal plasma–vacuum interface has a corner, then it contains a stagnation point of the poloidal magnetic field, thus being part of a separatrix. Plasma corners are studied in magnetohydrostatic equilibria with plane symmetry (the large‐aspect‐ratio limit of axially symmetric ones) and constant axial current density. Their structure depends only on the multiplicity n of the stagnation point (defined such that the separatrix divides a neighborhood into 2n sectors) and on the relative orientation of the axial current density and the poloidal magnetic field nearby (termed ‘‘ordinary’’ or ‘‘extraordinary,’’ depending on whether the latter can be viewed as being generated by the former): Simple (i.e., n=2) ordinary corners resemble simple X points in vacuum fields in that all four sectors are right angled, but differ in that, for small distances r from the X point, the poloidal magnetic field is O(r log r−1) rather than O(r), and in that the curvature of the separatrix is O(r−1) rather than O(1). Degene...