CSR IMPEDANCE DUE TO A BEND MAGNET OF FINITE LENGTH WITH A VACUUM CHAMBER OF RECTANGULAR CROSS SECTION

Abstract

We study the impedance due to coherent synchrotron radiation (CSR) generated by a short bunch of charged particles passing through a dipole magnet of finite length in a vacuum chamber of a given cross section. Our method represents a further development of the previous studies: we decompose the electromagnetic field of the beam over the eigenmodes of the toroidal chamber and derive a system of equations for the expansion coefficients in the series. We illustrate our general method by calculating the CSR impedance of a beam moving in a toroidal vacuum chamber of rectangular cross section