Resonance driving terms and tune spread with amplitude driven a beam-beam long range kick and a DC wire kick

TL;DR

This paper derives formulas for resonance driving terms and tune spread caused by beam-beam long-range interactions and DC wire compensators in cyclical machines, using the weak-strong approximation.

Contribution

It provides a detailed theoretical derivation of resonance and tune spread formulas specific to beam-beam and wire compensator effects in accelerators.

Findings

Derivation of formulas for resonance driving terms.

Analysis of tune spread with amplitude.

Application of weak-strong approximation in the derivation.

Abstract

This document presents in detail the derivation of the formulas that describe the resonance driving terms and the tune spread with amplitude generated by the beam-beam long range interactions and the DC wire compensators in cyclical machines. This analysis make use of the weak-strong approximation.