Explanation of Sextupole Instability in CERN PS Booster

Dual harmonic RF systems have been discussed for many years: to promote Landau damping, to reduce transverse space-charge, and to improve Touschek lifetime. Since its introduction into the CPS booster in 1982, the dual harmonic acceleration process suffered from an unexplained longitudinal instability occurring when the 2nd harmonic cavity is anti-phased and controlled by the 1st harmonic gap signa l. The instability does not occur when the beam fundamental is used as reference, nor when the RF harmonics are in-phase. The impetus for the present study arises from the conversion from harmonic num bers h=5 and 10 to h=1 and 2 for LHC operation. The instability has recently been diagnosed as a sextupole mode. In this paper, which is a synopsis of two laboratory notes [3,4], are presented experim ental results from machine development (MD) periods, and a detailed theoretical explanation for the instability (and its correction) that considers feedback from the beam versus the cavity fundamental .