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A nonlinear self-consistent theory of excitation of an axially asymmetric wakefield by relativistic electron bunches in cylindrical dielectric resonator with a vacuum channel for the charged particles transportation through the resonator is constructed. An excited fields are presented in the form of superposition solenoidal and potential fields. The solenoidal electromagnetic fields are presented by an expansion of the required fields into solenoidal fields of the empty dielectric resonator. The potential field is presented by the eigenfunction expansion method. The dispersion equation for determination of eigenfrequencies and the equation for eigenvalues are obtained, eigenwaves, eigenfunctions and their norms are found. For an excited fields the analytical expressions, that take into account both longitudinal and transverse dynamics of bunch particles are derived. Along with the equations of motion they provide a self-consistent description of the dynamics of generated fields and bunches. The formulated nonlinear theory allows investigating numerically the nonlinear effects such as increasing of the transverse bunch size, and head-tail beam breakup instability, which occurs if the electron bunch in the structure is misaligned.
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