The breaking of up-down symmetry of trapped particle orbits by a toroidal electric field

A breaking of the up-down symmetry due to the inductive electric field E(phi) is analyzed in detail for particles describing quasibanana orbits in the large aspect ratio approximation. Time-independent and time-dependent electric fields are considered. In the first case it is proved that the classical del B drift and the breaking of up-down symmetry due to E(phi) lead to a net inward radial drift, which agrees with the well-known Ware pinch formula. The weak points of previous treatments of the Ware pinch, e.g. taking only leading terms in the Taylor expansion of A(phi), are discussed. Yet the results obtained here lead to the same pinch formula, even for banana orbits with a large amplitude of poloidal angle and for more general conditions than previously considered. A more general formula for a time-dependent E(phi) has also been found. Our results show from a very general basis that the corresponding polarization type of drift does not play any role in the inward pinch; however, the second time derivative of the inductive electric field E(phi) could significantly increase or decrease the usual Ware pinch. (C) 1996 American Institute of Physics.