Discussions on the Cancellation Effect on a Circular Orbit

As remarked in Ref. [2], when the self-consistent dynamics is treated with both the transverse and longitudinal interactions taken into account, the canonical formu lation, which explicitly reveals the cancellation effect, is completely equivalent to the Lorentz force approach with the cancellation implicitly taken care of. Here Trafic⁴is a good example that one does not need the cancellation effect to solve realistic problems [1]. However, in the CSR study, due to the complexity of the problem, sometimes one effect (such as the head-tail part of F⊥) is emphasized without taking into account the other effect (such as the head-tail part of eΦ(t)/r) which is strongly correlated to the former one). Viewing the interaction process from a different an gle may sometimes be instructive in this regard, which also allows further analysis [12] and simulations. The cancella tion theory shows that the transverse emittance is related to the change of kinetic energy and the transverse force. Since the time dependent parts of the singular local contributions to these two terms are oppositely correlated, after reduc tion, only the effective forces have impact on the transverse emittance growth.