Abstract
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.
Highlights
When dealing with the study of high intensity beam dynamics, we must take into account, in a self-consistent way and in addition to the external guiding fields, the effects of the self-induced electromagnetic fields, called wakefields [1]
In this paper we present a novel simulation code for the longitudinal beam dynamics in a circular machine, which uses an alternative approach with respect to the previously mentioned codes, allowing one to simulate, simultaneously, the effects of short and long range wakefields without the necessity to distinguish between the two, and avoiding the issues related to the use of wakefield and convolution sum
In this paper we have presented a novel algorithm which exploits an alternative approach to the currently used convolution sum for wakefield simulations, and developed a tracking code, MUSIC, which simulates the longitudinal beam dynamics in a circular accelerator in presence of multibunch with intrabunch motions
Summary
When dealing with the study of high intensity beam dynamics, we must take into account, in a self-consistent way and in addition to the external guiding fields, the effects of the self-induced electromagnetic fields, called wakefields [1]. There exist several simulation codes specialized in circular accelerators for the single bunch longitudinal [10,11,12] and transverse [13,14] beam dynamics, and for multibunch [15,16], which have been proved to be reliable tools in the comprehension of the wakefield effects. In this paper we present a novel simulation code for the longitudinal beam dynamics in a circular machine, which uses an alternative approach with respect to the previously mentioned codes, allowing one to simulate, simultaneously, the effects of short and long range wakefields without the necessity to distinguish between the two, and avoiding the issues related to the use of wakefield and convolution sum.
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