Sources of collective effects include single or multiple inter-particle scattering and interaction with the vacuum chamber and other surroundings, formalized in terms of impedance.
In particular, a charged particle beam may be considered as a non-neutral plasma, and one may find mathematical methods in common with the study of stability or instabilities.
One may also find commonality with the field of fluid mechanics since the density of charged particles is often sufficient to be considered as flowing continuum.
Another important topic is the attempt to mitigate collective effects by use of single bunch or multi-bunch feedback systems.
The collective effects must typically be added in addition to the single particle dynamics, which may be modeled using a tracking code.