Abstract

The new approach to calculating gyroinvariant drift velocities, recently published [Phys. Fluids B 2, 11 (1990)], is generalized to the case of nonuniform and time variable electric and magnetic fields. As before, a continuous averaging is done over a suitable quasiperiodic function. However, now the nonanalytic complex functions are related to a rotating frame. Successive integration by parts is done as before to obtain higher-order drift velocities, in contrast to the Hamiltonian or Lagrangian treatment of Littlejohn [J. Math. Phys. 20, 2445 (1979)] and other authors. The results in this paper are gyroinvariant as in the earlier treatment and the second-order drift velocities found are more compact and simpler than previous ones. The guiding center position is also determined to second order using algebraic procedures.