The Code MBIM2 for the Calculation of the Arbitrary Multibunch Beams Longitudinal Coherent Oscillations Stability (In The Case of Long Bunches)

The presented code is an advanced version of the code MBIM1 also presented at this conference and dealing with short bunches. The code MBIM2 analyses the stability of longitudinal coherent motion for arbitrary multibunch beams in storage rings without limitations on the bunch length or RF cavities wavelength, which is especially important for higher types of multipole synchrotron oscillations. The code implies also the possibility to consider coupling between different types of multipole synchrotron oscillations and Landau damping. In considered approach, the problem reduces to the eigenvalue problem for the linear algebraic equation system. The order of this system is equal to the number of bunches times numbes of multipole types times approximation order wich appears to be small (a few units) in most cases.