TRANSVERSE IMPEDANCE OF LHC COLLIMATORS

Transcription

1 Contributed talk WEOAC03 ( min, 14 slides) TRANSVERSE IMPEDANCE OF LHC COLLIMATORS Elias Métral Work in collaboration with G. Arduini,, R. Assmann,, A. Boccardi,, T. Bohl, F. Caspers,, M. Gasior,, O.R. Jones, K.K. Kasinski,, T. Kroyer,, S. Redaelli, G. Robert-Demolaize Demolaize,, G. Rumolo,, R. Steinhagen,, T. Weiler,, F. Zimmermann, C. Bracco,, B. Salvant,, F. Roncarolo Elias Métral, PAC07, Albuquerque, New Mexico, USA, June 25-29, /14

2 CONTENTS THEORY Zotter2005 s formula Case of a LHC collimator MEASUREMENTS Coherent tune shift from a LHC (horizontal) prototype at the SPS in 2004 & 2006 Coupled-bunch instability with 72 bunches in the SPS in 2006 STABILITY DIAGRAM Nominal case at injection and top energy (after the squeeze) Scans in gap of the collimators & resistivity of the secondary collimators CONCLUSION Elias Métral, PAC07, Albuquerque, New Mexico, USA, June 25-29, /14

3 ZOTTER2005 S THEORY (1/2) Valid for a circular beam pipe of infinite length Any number of layers Any beam velocity Any frequency Unification of 3 regimes: low, intermediate and high Any σ (conductivity), ε (permittivity) and μ (permeability) Zotter2005 s formula compared to Burov-Lebedev2002 Tsutsui2003 (theory + HFSS simulations but only above 1 MHz!) Vos2003 Al-Khateeb_et_al.2006 Bane1991 (high-frequency) Henry-Napoly1991 î Similar results obtained in the low-frequency regime Elias Métral, PAC07, Albuquerque, New Mexico, USA, June 25-29, /14

4 ZOTTER2005 S THEORY (2/2) 1. μ meter long round LHC collimator 1. μ 10 6 Z ê md d C = 100 Im H >0 L Im H <0 L Re ρ C b = 2 mm =10 μωm μ μ μ f Hz Elias Métral, PAC07, Albuquerque, New Mexico, USA, June 25-29, /14

5 MEASUREMENT 1 (1/2) Coherent tune shift from a LHC prototype collimator at the SPS (single bunch at 270 GeV/c) in 2004 Zimmermann et al., EPAC06 Elias Métral, PAC07, Albuquerque, New Mexico, USA, June 25-29, /14

6 MEASUREMENT 1 (2/2) Nonlinear correction vs. gap (round beam) LHC collimators settings 6 s Courtesy F. Zimmermann b/σ Elias Métral, PAC07, Albuquerque, New Mexico, USA, June 25-29, /14

7 MEASUREMENT 2 (1/2) Coherent tune shift from a LHC prototype collimator at the SPS (single bunch at 270 GeV/c) in Tune [(Q x )*10-4 ] Beam current [10 10 p/b] RMS bunch length [10-10 s] Collimator jaws position [mm] :25:00 04:30:00 04:35:00 04:40:00 04:45:00 time (hh:mm:ss) Elias Métral, PAC07, Albuquerque, New Mexico, USA, June 25-29, /14

8 MEASUREMENT 2 (2/2) Comparison between 2004 and Doing this the classical thickwall formula for the RW impedance is assumed Courtesy R. Steinhagen Elias Métral, PAC07, Albuquerque, New Mexico, USA, June 25-29, /14

9 Rise -time turns MEASUREMENT 3 (1/2) Predicted instability rise-time with a batch of 72 nominal bunches in the SPS at 270 GeV/c SPS RW HIBL + coll HIBL SPS RW HTWL + coll HTWL SPS RW HIBL SPS RW HTWL With Inductive- Bypass = low-frequency regime Half gap b mm Classical Thick-Wall impedance Elias Métral, PAC07, Albuquerque, New Mexico, USA, June 25-29, /14

10 MEASUREMENT 3 (2/2) Collimator OUT (± 30 mm) Collimator IN (± 2 mm) Vertical centroid position envelope [a.u.] Horizontal centroid position envelope [a.u.] Beam current [10 10 p/b] Relative chromaticity [x10] t x ª 35 ms Left jaw position [mm] Right jaw position [mm] Beam current [10 10 p/b] Horizontal centroid position envelope [a.u.] Vertical centroid position envelope [a.u.] Relative chromaticity [*10] :58:55 04:58:56 time (hh:mm:ss) s 07:57:01 time (hh:mm:ss) SPS T rev 23 μs t x e [12, 32 ms] Elias Métral, PAC07, Albuquerque, New Mexico, USA, June 25-29, /14

11 - I m H DQ L ê STABILITY DIAGRAM (1/3) Nominal case (25 ns bunch spacing and nominal intensity) INJECTION Rise time of 50 ms (= 565 turns) - I m H DQ L ê TOP ENERGY Rise time of 185 ms (= 2083 turns) Re H DQ L ê Re H DQ L ê 10-4 From nonlinearities + space charge (2D) LHC T rev 89 μs From Landau octupoles at max. î Will be damped by feedback î Only ~ 50% of nominal beam intensity is stable Elias Métral, PAC07, Albuquerque, New Mexico, USA, June 25-29, /14

12 Scan of the gap of the collimators (top energy) - I m H DQ L ê STABILITY DIAGRAM (2/3) Nominal collimator gap â 1.2 â 1.5 â 2 From Landau octupoles at max. â 3 â 10 No collimator Re H DQ L ê 10-4 Elias Métral, PAC07, Albuquerque, New Mexico, USA, June 25-29, /14

13 Scan of the resistivity of the secondary collimators - I m H DQ L ê STABILITY DIAGRAM (3/3) 10-5 Ωm (nominal) Ωm (copper) From Landau octupoles at max Ωm No secondary collimator Re H DQ L ê 10-4 Elias Métral, PAC07, Albuquerque, New Mexico, USA, June 25-29, /14

14 CONCLUSION Measurements performed so far are in agreement with our theoretical predictions but are not a proof of the low-frequency regime ( ~ 1 MHz), which to our knowledge has neither been measured nor simulated Collimator bench measurements near 8 khz are planned at CERN for the second half of the year Coupled-bunch instability in the LHC induced by the collimators At injection Will be damped by a transverse feedback At top energy Planned to be damped by Landau octupoles (ongoing studies) Estimated max. stable intensity < 50% of the nominal one A good control of the tunes and chromaticities will be needed to increase the intensity Elias Métral, PAC07, Albuquerque, New Mexico, USA, June 25-29, /14