Quasi-optical accelerating structure operated with a superposition of synchronized modes

A quasi-optical accelerating structure for future electron-positron linear colliders of TeV-level of particle´s energies is suggested. In order to achieve high accelerating gradient, it is supposed to operate simultaneously with several equidistant eigen modes, which allow field steering inside the structure with a difference frequency to be proportional a distance between nearest moving bunches of particles. This principle increases an achievable accelerating field. Methods of rf feeding for such structures are discussed.