Alfven and fast wave forces, affecting ions in magnetic traps with closed magnetic surfaces

General expressions for time- and surface-averaged radio frequency forces, affecting ions in closed toroidal devices, are obtained in this paper. Toro idal effects are included in these forces. These effects can, for example, be important to calculate Alfven or fast wave forces in stellarators, spher omaks, or for toroidicity induced Alfven wave eigenmodes (TAE) in axially s ymmetric tokamaks. The further simplification of obtained expressions shoul d be fulfilled for the proper kind of rf waves and toroidal devices. It is hoped that these rf force expressions can, for example, be useful for the c omputer simulations of the transport barrier formation by Alfven and fast w aves in toroidal devices. (C) 1999 American Institute of Physics. [S1070-66 4X(99)04004-5].