A radio-frequency (RF) cavity apparatus for accelerating charged particles includes first and second cavity arms. The first and second cavity arms have respective first and second axes of rotational symmetry and each cavity arm includes at least one cell. The first and second cavity arms are connected by a resonance coupler. The cell(s) of the first cavity arm have an axial dimensional parameter that is equal to a corresponding axial dimensional parameter of the cell(s) of the second cavity arm, and the cell(s) of the first cavity arm have at least one non-axial dimensional parameter that differs from corresponding non-axial dimensional parameter(s) of the cell(s) of the second cavity arm.