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In this paper, we provide an analytical description for transverse coupling impedances with dipole high order modes (HOMs) and beam breakup (BBU) instability suppression of relativistic, high-current beams undergoing strong acceleration, such as those typically produced by rf photoinjectors. The model adopted is based on the accepted theory of coupling impedances extended to the case of beams characterized by a fast transition due to strong acceleration, from the nonrelativistic to the relativistic regime in which a bunch trajectory may not be rigidly directed parallel to the axis of the electric field. The trajectory oscillations in a dipole HOM field in the transverse plane are effective in perturbing the bunch energy, which causes an increase of the coupling impedance up to the BBU instability. This BBU instability analysis is based on equations obtained by Volkov [Phys. Rev. ST Accel. Beams 12, 011301 (2009)PRABFM1098-440210.1103/PhysRevSTAB.12.011301] in which external focusing due to both the applied transverse electric (TE) HOM and the accelerating fundamental mode as well as dipole HOM damping by external loads are investigated. This analysis is valid in the limit in which the weak nonlinearity of applied fields near the axis may be neglected. The solution suggests a means of enhancing the BBU threshold current. The possibility of obtaining BBU instability suppression in a long, integrated photoinjector and linac structure, such as the superconducting rf source at Forschungs Zentrum Dresden (FZD), are numerically examined. New designs of photoinjectors that provide BBU instability suppression of all dipole HOMs to enhance the threshold currents are suggested

Beam breakup instability suppression in multicell superconducting rf guns