Total SPS Impedance

LTC 08.12.2004: A report by Luc Vos, published in 2003 (CERN-AB-2003-088) projected a longitudinal impedance of Z/n = 8.5 Ohm in the SPS in 2005 and a transverse impedance of 8.4-10 MOhm/m in 2002 (without MKE kicker elements). Nine MKE kicker elements will be installed in the SPS between 2003 and 2005 and more detailed impedance estimates are required for these elements. Simulations for the TMCI instability (Head Tail code and MOSES) indicate that the instability threshold increases with the impedance resonance frequency (broad band resonator -> Q approx 1) and the longitudinal emittance. Depending on the chosen ferrite inside the MKE the simulations predict a peak impedance value between 0.6 and 0.8 MOhm/m per MKE element. Combined with the SPS broad band impedance model one thus obtains for 9 MKE elements a resonance frequency of 1.6 GHz, a quality factor of Q = 0.8 and a total peak impedance of 13 MOhm/m. The MOSES simulations indicate for this impedance a TMCI threshold current below 1.2 10¹¹ particles for the LHC beam type with zero chromaticity and after RF capture at 2 MV (bunch length of 0.75 ns and Qs = 0.006). One should therefore be capable of measuring the TMCI instability in the SPS provided the instability is not masked by other effects (e.g. electron cloud instability).  This impedance estimate is consistent with measurements in the SPS done in 2003. However, the detailed effect depends on a large set of other parameters (e.g. vacuum chamber geometry, space charge and chromaticity values) and the detailed analysis including these contributions still needs to be done. Talk by Elias Metral at LTC 08.12.2004.

Transverse Impedance

Broadband

Resistive Wall

HOM

Collimator

Longitudinal Impedance

Broadband

HOM

Nonlinear & Incoherent Impedances