Calculation of Coherent Synchrotron Radiation Impedance for a Beam Moving in a Curved Trajectory

Coherent synchrotron radiation (CSR) fields are generated when a bunched beam moves along a curved trajectory. A new code, named CSRZ, was developed using finite difference method to calculate the longitudinal CSR impedance for a beam moving along a curved chamber. The method adopted in the code was originated by Agoh and Yokoya [Phys. Rev. ST Accel. Beams 7 (2004) 054403]. It solves the parabolic equation in the frequency domain in a curvilinear coordinate system. The chamber considered has uniform rectangular cross-section along the beam trajectory. The code was used to investigate the properties of CSR impedance of a single or a series of bending magnets. The calculation results indicate that the shielding effect due to outer chamber wall can be well explained by a simple optical approximation model at high frequencies. The CSR fields reflected by the outer wall may interfere with each other along a series of bending magnets and lead to sharp narrow peaks in the CSR impedance. In a small storage ring, such interference effect can be significant and may cause microwave instability, according to a simple estimate of instability threshold.