Multibunch and multiparticle simulation code with an alternative approach to wakefield effects

The simulation of beam dynamics in the presence of collective effects requires a strong computational effort to take into account, in a self-consistent way, the wakefield acting on a given charge and produced by all the others. Generally this is done by means of a convolution integral or sum. Moreover, if the electromagnetic fields consist of resonant modes with high quality factors, responsible, for example, for coupled bunch instabilities, a charge is also affected by itself in previous turns, and a very long record of wakefield must be properly taken into account. In this paper we present a new simulation code for the longitudinal beam dynamics in a circular accelerator, which exploits an alternative approach to the currently used convolution sum, reducing the computing time and avoiding the issues related to the length of wakefield for coupled bunch instabilities. With this approach it is possible to simulate, without the need for large computing power, simultaneously, the single and multibunch beam dynamics including intrabunch motion. Moreover, for a given machine, generally both the coupling impedance and the wake potential of a short Gaussian bunch are known. However, a classical simulation code needs in input the so- called “Green” function, that is the wakefield produced by a point charge, making necessary some manipulations to use the wake potential instead of the Green function. The method that we propose does not need the wakefield as input, but a particular fitting of the coupling impedance requiring the use of the resonator impedance model, thus avoiding issues related to the knowledge of the Green function. The same approach can also be applied to the transverse case and to linear accelerators as well.