Axisymmetry is symmetry under rotation over the toroidal (i.e., cylindrical) angle φ over an arbitrary value, i.e. rotation about the cylindrical axis - see toroidal coordinates.
Axisymmetry is the basic assumption underlying the Grad-Shafranov Equation for the calculation of tokamak equilibria. With this assumption, the solution space of the MHD equilibrium problem is reduced from three to two dimensions. In actual magnetic confinement devices, this symmetry can only apply in an approximate fashion due to the fact that the external field coils are always discrete.