Amplitude Dependent Closest Tune Approach Generated by Normal and Skew Octupoles

Amplitude dependent closest tune approach, an action dependent analogue of the $|Delta Q_{min}$ generated by linear coupling, was observed in the LHC in 2012. It restricts the accessible resonance free area of the tune diagram and by altering tune spread has the potential to impact upon Landau damping. A theoretical description of such behaviour, generated by normal octupoles and linear coupling was recently validated in the LHC. Simulation has also established that amplitude-dependent closest approach can be generated by a combination of normal and skew octupoles. This paper summarizes these simulation based observations.