This study presents 2D approximated expressions for eddy currents in the Ti-coated layer of a nonlinear kicker and compares them with numerical simulations. Nonlinear kicker-based injection schemes have be-come popular in recent years and are used at several facilities. Eddy currents, which depend on both the applied magnetic field and the chamber’s geometry, can create unwanted field components. The proposed approximations offer a fast and practical way to esti-mate the effects of these eddy currents.

Our studies indicate that parametric instabilities except the envelope instability are unlikely to be observed in actual linear accelerators unless waterbag or KV distributions are generated. Furthermore our studies and previous literatures indicate the dominance of particle resonances over parametric instabilities in high-intensity linear accelerators. Any counter evidence has not been found yet. We propose a way to overcome the previous design rule to avoid the zero-current phase advance > 90° for the high-intensity linac.

Higher harmonic cavities (HHCs) play a critical role in storage rings by extending the bunch length, thus mitigating beam instability and increasing the beam lifetime. This study investigates the influence of Robinson instability on the bunch lengthening performance for both active and passive HHCs. A detailed comparison is conducted to analyze the Robinson instability thresholds* and the parameters of the HHCs** that govern the onset of instability. Simulation results and theoretical analysis are combined to provide guidelines for optimizing HHCs configurations to balance effective bunch lengthening with stability requirements. As illustrative examples, we consider an active normal-conducting HHC for Korea-4GSR , and a passive superconduting HHCs for PLS-II.