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Geometry and neoclassical theory in a quasi-isodynamic stellarator

We show that in perfectly quasi-isodynamic magnetic fields, which are generally non-quasisymmetric and which can approximate fields of experimental interest, neoclassical calculations can be carried out analytically more completely than in a general stellarator. Here, we define a quasi-isodynamic field to be one in which the longitudinal adiabatic invariant is a flux function and in which the constant-B contours close poloidally. We first derive several geometric relations among the magnetic field components and the field strength. Using these relations, the forms of the flow and current are obtained for arbitrary collisionality. The flow, radial electric field, and bootstrap current are also determined explicitly for the long-mean-free-path regime.