Numerical Calculation of Beam Coupling Impedances in the Frequency Domain using FIT

The transverse impedance of kicker magnets is considered to be one of the main beam instability sources in the projected SIS-100 at FAIR and also in the SPS at CERN. The longitudinal impedance can contribute to the heat load, which is especially a concern in the cold sections of SIS-100 and LHC. In the high frequency range, commercially available time domain codes like CST Particle Studio serve to calculate the impedance but they are inapplicable at medium and low frequencies which become more important for larger size synchrotrons. We present the ongoing work of developing a Finite Integration Technique (FIT) solver in frequency domain which is based on the Parallel and Extensible Toolkit for Scientific computing (PETSc) framework in C++. Proper beam adapted boundary conditions are important to validate the concept. The code is applied to an inductive insert used to compensate the longitudinal space charge impedance in low energy machines. Another application focuses on the impedance contribution of a ferrite kicker with inductively coupled pulse forming network (PFN).