Magnetic and Drift Surfaces using a New Stellarator Expansion

A new stellarator expansion has been devised, wherein the depths of the helical and toroidal field modulations are comparable and the total rotational transform is finite. To accomplish this, we define λ = ρ/R ≪ 1 (R is the major radius, ρ is the minor radius) and choose p, the number of helical periods, to be of order λ−2/3. Detailed calculations of vacuum magnetic field properties have been carried out, including the magnetic surfaces, V″, shear, etc. For the particle surface calculations, the ratio of ion gyroradius to major radius of the torus, ε = RL/R, is chosen to be of order λ3/2. Using the same methods as for the vacuum field calculations, analytic solutions are obtained for particle drift surfaces in stellarators with finite departures from axial symmetry. These surfaces, derived from perturbation techniques, are obtained for four particle classes that are, for the first time, precisely categorized according to trapping state. Transitions between classes are interpreted. Numerical calculation of integrals is carried out for comparison with approximate results.