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Localized particle orbits in a toroidal stellarator

The magnetic field strength in a toroidal stellarator with ℓ field periods in the poloidal direction is written in co-ordinates which characterize a field line. The result is a variation proportional to r̄m sin (mθ̄ + pϕ), m ≡ ℓ−1, as well as r̄ℓ sin (ℓθ̄ + pϕ). The extra term can be the principal helical contribution to the field strength for parameters relevant to present-day experiments. Criteria for the formation of magnetic wells are derived. Drift surfaces and transition curves are calculated and examples are presented for W VII-A parameters, both allowing for and neglecting the above effect. The region of phase space occupied by localized particles is considerably increased in the former case and the drift surfaces are somewhat modified. Simple consequences for transport processes associated with localized particles are indicated.