Total LHC Impedance

LTC 08.12.2004. The LHC design report quotes a vertical resistive wall impedance at top energy of 103 + 26j MOhm/m at 8kHz (slow wave) and 5 +8j MOhm/m at 20 MHz (slow wave). The resistive wall impedance is lightly smaller (factor 2 to 1) at injection energy. The effective impedances of the LHC design report are a factor 28 (16) larger at 7 TeV (injection) than the usual normalized effective impedance estimates. The total broad band impedance is estimated at 0.070 Ohm (0.076 Ohm) at injection (squeezed optics) in the longitudinal plane and 1.34 MOhm/m (2.67 MOhm/m) for the transverse impedance. 50% of the nominal LHC intensity should just be at the border of stability for the squeezed optics with the Phase 1 collimator jaws. The Phase 1 collimation system is thus compatible with the initial intensity limitations imposed by the phased installation of the beam abort dilution kicker system. Due to the inductive bypass of the collimator impedance the imaginary part of the effective resistive wall impedance, and thus the real part of the tune shift, has only a weak dependence on the bunch spacing.  The real part of the resistive wall impedance still depends strongly on the bunch spacing. Elias Metral finishes his presentation by stating that an analysis of the higher order modes in the collimator tanks is still ongoing and that the impedance estimates for 'unconventional impedance sources' is also still ongoing. Talk by Elias Metral at LTC 08.12. 2004.

Transverse Impedance

Broadband

Resistive Wall

HOM

Collimator

Longitudinal Impedance

Broadband

HOM

Nonlinear & Incoherent Impedances