Time-dependent pseudopotential and its application for description of the averaged motion of the charged particles. Part 2. General expression for time-dependent pseudopotentials

The series of publications describes a new method to control the movement of the charged particles by high frequency electric fields. This new class of high frequency electric fields is characterized by pseudopotentials slowly evolving in time. The paper considers the deriving of the basic expression for slowly evolving pseudopotentials. It is shown that the classical pseudopotential is just the leading term of decomposition of the true pseudo-Hamiltonian in a double series: with respect to a small parameter which characterizes the amplitude of the electric field, and with respect to the frequency of the electric field. The classical pseudopotential expression is generalized to include the case of high frequency electric fields which are characterized by "fast" and a "slow" characteristic time scales simultaneously.