Using the Klima-Bogolyubov-Zubarev method, the acceleration of charged particles (electrons) in moving intensity minima of interference laser fields was investigated. The electromagnetic field intensity threshold for an eventual slipping-through of the particle through the potential barrier is found both analytically and numerically. Millimetre and submillimetre electromagnetic waves should be emitted due to forced electron oscillations in potential wells. (author). 4 figs., 5 refs.