Geometric Impedance of LHC Collimators O. Frasciello, S. Tomassini, M. Zobov LNF-INFN Frascati, Italy With contributions and help of N.Mounet (CERN), A.Grudiev (CERN), B.Salvant (CERN), E.Metral (CERN) Meeting on Beam Impedance Calculations for HiLumi LHC, CERN, 29 October 2013

The principal aim is: 1.To refine the existing LHC impedance model in view of the LHC HiLumi upgrade 2.To start simulations for modified collimators

A descreapancy was found between simulation results and measurements of the betatron tunes shifts with beam current and instability rise time Example from N. Mounet et al., “Beam Stability with Separated Beams at 6.5 TeV” LHC Beam Operation Workshop – Evian 2012

Very fine mesh is needed: 1.To reproduce in detail the long and complicated geometry 2.To overcome numerical problems when simulating long tapers 3.To perform simulations for very short bunches required for HEADTAIL modeling

LHC Secondary Collimator Design

Collimator GdfidL Model

From ABCI manual For our collimator taper and bunch length of 1 mm  z should be smaller than 0.05 mm…

Analytical Result Numerical Test

12 k  /m60 k  /m k  /m Factor of 2? 0.05 mm mm<0.2 mm

Low Frequency Broad-Band Transverse Impedance

It is better to compare kick factors since: 1.They are proportional to the effective imaginary impedance that directly enter in the formula for the betatron tune shift 2.It is possible to compare contributions of vacuum chamber components having impedances with different frequency dependence 3.Easily calculated by all numerical codes Betatron frequency shift Loss factor definition

Dipole Resistive Wall (Kick) Loss Factors Courtesy Nicolas Mounet

Comparison of Resistive Wall and Geometric Total Kick Factors Geometric

1mm half-gap, 2mm bunch length, 0.2mm mesh size Transverse Longitudinal

3mm half-gap, 2mm bunch length, 0.2mm mesh size

5mm half-gap, 2mm bunch length, 0.2mm mesh size

11.5mm half-gap, 2mm bunch length, 0.2mm mesh size

20mm half-gap, 2mm bunch length, 0.2mm mesh size CERN Computer Cluster Overcrowded No picture -> CERN Computer Cluster Overcrowded

From A.Grudiev, AB-Note RF

mesh=0.5 mm, sigma=3 cm, wake=50 m, half-gap= 1 mm

mesh=0.5 mm, sigma=3 cm, wake=50 m, half-gap= 5mm

mesh=0.5 mm, sigma=3 cm, wake=50 m, half-gap= 11.5 mm

mesh=0.5 mm, sigma=3 cm, wake=50 m, half-gap= 20 mm

With BPM cavityWithout BPM cavity Half gaps (mm)k T (V/Cm) · · · · · ·10 13 Impedance Increase due to BPM Cavity The transverse effective impedance is estimated to be about 20% higher

Transverse Impedance of Collimator

CONCLUSIONS 1.The analytical formula for a flat taper impedance can be used as the upper estimate of the low frequency collimator impedance (for small gaps) 2.Transverse loss (kick) factor evaluation allows comparing contributions of the resistive wall impedance and the geometric collimator impedances in single bunch dynamics. In particular it was shown that a) the effective geometric impedance dominates the effective resistive wall impedance of tungsten collimators almost for all collimator gaps b) the geometric impedance becomes comparable with the resistive wall contribution for the half-gaps > 10 mm even for CFC material 3. For single bunch transverse instability growth rate studies with HEADTAIL we have provided both the transverse dipole and the longitudinal wakes for 2 mm bunch length 4. For the new collimators the BPM cavity is estimated to increase the effective geometric impedance by 20-30%. 5. More work is needed to investigate the collimator HOMs, especially HOMs observed in simulations at very low frequencies.