Update of the SPS transverse impedance model Benoit for the impedance team.
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Transcript of Update of the SPS transverse impedance model Benoit for the impedance team.
Update of the SPS transverse impedance model
Benoit for the impedance team
Status of the impedance model• Elements included in the database:
– 6.911 km beam pipe (Zotter/Metral analytical calculations for a round pipe including indirect space charge, transformed with Yokoya factor)
– 20 kickers (situation during 2006 run, analytical calculations with Tsutsui model)– 106 BPHs (CST 3D simulations)– 96 BPVs (CST 3D simulations)– 2 TW 200 MHz cavities (4 sections of 11 cells) without couplers (CST 3D simulations)– 2 TW 200 MHz cavities (5 sections of 11 cells) without couplers (CST 3D simulations)
• Some of the assumptions we need to make:– Ideal electromagnetic material properties (copper, ferrite)– Transverse kick is linear with transverse displacement– Simplified geometries:
kickerBeam pipeBPH
BPV
TW 200 MHz
Chosen elements : - 106 BPHs (CST 3D simulations) - 96 BPVs (CST 3D simulations) - 6.911 km beam pipe (Zotter/Metral analytical calculations for a round pipe including indirect space charge,
transformed with Yokoya factor) - 20 kickers (situation during 2006 run, analytical calculations with Tsutsui model) - 2 TW 200 MHz cavities (4 sections of 11 cells) without couplers (CST 3D simulations) - 2 TW 200 MHz cavities (5 sections of 11 cells) without couplers (CST 3D simulations)
Current SPS impedance Model: vertical plane
Additional assumptions:- all impedances lumped in one location- no space charge, no linear coupling, no chromaticity- no amplitude detuning- linear longitudinal restoring force
Mode spectrum as a function of bunch current
1st small instability:Nb=4 1010 p/b
2nd large instability:Nb=8 1010 p/b
stable unstablestable
unstable
Strongdamping
Current SPS impedance Model: horizontal plane
Mode spectrum as a function of bunch current
stable
Strongdamping
Chosen elements : - 106 BPHs (CST 3D simulations) - 96 BPVs (CST 3D simulations) - 6.911 km beam pipe (Zotter/Metral analytical calculations for a round pipe including indirect space charge,
transformed with Yokoya factor) - 2 TW 200 MHz cavities (4 sections of 11 cells) without couplers - 2 TW 200 MHz cavities (5 sections of 11 cells) without couplers
Current SPS impedance Model (no kicker): vertical plane
Additional assumptions:- all impedances lumped in one location- no space charge, no linear coupling, no chromaticity- no amplitude detuning- linear longitudinal restoring force
Instability threshold: Nb=9 1010 p/b
Conclusion• Without the kickers:
– the tune shift decreases significantly (Zeff decreases from 13 M/m to 4 M/m).
– the instability threshold remains around 8.5 1010 p/b.
• The TW 200 MHz RF cavities enhance the instability at 8 1011 p/b (modes -1 and -2).
Ongoing work
• Calculate growth rates to assess which instability (1st, 2nd or 3rd) is really critical for the SPS low longitudinal emittance bunch
• Thorough studies on the nominal longitudinal emittance bunch to assess the intensity limits with the current model
• Include the septa (ZS and MSE) in the model
Coherent tune shiftsH
oriz
on
tal t
un
e Q
x
BPH+BPV+pipe+TW200 Kickers+BPH+BPV+pipe+TW200
Ho
rizo
nta
l tu
ne
Qx
Wake functions for the current SPS model
Horizontalwakes
Verticalwakes
Dipolar contribution Quadrupolar contribution
Real impedance for the current SPS model(note: the simulated BPMs wake was optimized for HEADTAIL, and too short
to get an accurate impedance)
RealHorizontalimpedance
RealVertical
impedance
Dipolar contribution Quadrupolar contribution
Imaginary impedance for the current SPS model
ImaginaryHorizontalimpedance
ImaginaryVertical
impedance
Dipolar contribution Quadrupolar contribution
Dipolar wake “functions” imported into HEADTAIL
Conclusions:
- impedance and wakes have complicated shapes complicated beam dynamics
- negative horizontal impedance at low frequencies positive tune shift in the horizontal plane
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