Fast Failures of
LHC Crab Cavities
Tobias Baer
4th LHC Crab Cavity Workshop
16th December 2010
Thanks to: R. Calaga, R. de Maria, J. Tückmantel, J. Wenninger, K. Fuchsberger
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Content
1.
Introduction and Semi-Analytical Approach
2.
Tracking Studies (MAD-X)
3.
Mitigation Strategy
4.
Conclusion
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Content
1.
Introduction and Semi-Analytical Approach
2.
Tracking Studies (MAD-X)
3.
Mitigation Strategy
4.
Conclusion
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KEK Crab Cavity Quench
• Full decay of crab cavity in ≈100µs.
• Oscillations of Crab Cavity phase (up to 50° in 50µs).
100µs
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K. Nakanishi et al., Beam
Behaviour due to Crab Cavity
Breakdown, Proceedings of
IPAC’10, Kyoto
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Analytical Approach
• Horizontal kick by crab cavity:
q V
z

p x ,cc ( z )  
 sin   

E
c 

q
E
V
Φ
Ѳ
φ
ω
z
c
optimal voltage (local scheme, IP5):
V
c  E  tan( 2 )
q     *   cc  sin(  )
= particle charge
= particle Energy (7 TeV)
= voltage of crab cavity
= phase of crab cavity
= full crossing angle (580/285 µrad)
= phase advance CC ->IP (≈ π/2)
= angular frequency of CC (2 π∙400 MHz)
= longitudinal position of particle
= speed of light
maximal displacement:
xcc ( z )
x
c  tan( 2 )
z


 sin   

   x , IP  sin(  )
c 

= 3.98 (1.02 for nominal optics)
Maximal kick by crab cavity:
x≈
For z = 7.55cm (= 1∙σz): xcc(z = 7.55cm) ≈
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Upgrade optics
Nominal optics
4σx
1σx
2.36σx
0.60σx
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Analytical Approach
Beamloss approximation with simple Monte Carlo (upgrade optics):
• Failure of single cavity (V -> 0): Scaling factor (≈ 1.12)
Particle is lost if |x + xcc(z) ∙ k(ΔφCC->TCP)| > 5.7 ∙ σx
1. Gaussian
Distribution
2. Gaussian
Distribution
-> expected loss: (0.88 ± 0.06)%
• Phase error of single cavity (Φ -> π/2):
Particle is lost if |x + xcc(z, Φ = π/2)∙k - xcc(z, Φ = 0)∙k| > 5.7σx
CC with
failure
CC without
failure
-> expected loss: (24.8 ± 0.3)%
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Content
1.
Introduction and Semi-Analytical Approach
2.
MAD-X Tracking Studies
• Fast Voltage Decay
• Phase Error
3.
Mitigation Strategy
4.
Conclusion and Outlook
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Failure of CRAB.R5.B1
Voltage of Crab.R5.B1 = 0.
Total beam loss: 1.3% in 2 turns (2% in first 10 turns), mainly at TCP.C6L7.B1.
IP1
IP5
Losses
CC failure
Upgrade optics SLHCV3.0
4444_thin, IP1/5: β* = 0.15m,
Θ=580μrad, CC Local scheme
IP5, 400/10,000 particles
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Failure of CRAB.R5.B1
Bunchshape at TCP.C6L7.B1 directly after failure.
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Failure of CRAB.R5.B1
Bunchshape at TCP.C6L7.B1, 1 turn after failure.
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Failure of CRAB.R5.B1
Bunchshape at TCP.C6L7.B1, 2 turns after failure.
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Failure of CRAB.R5.B1
Bunchshape at TCP.C6L7.B1, 3 turns after failure.
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Failure of CRAB.R5.B1
Bunchshape at TCP.C6L7.B1, 4 turns after failure.
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Content
1.
Introduction and Semi-Analytical Approach
2.
MAD-X Tracking Studies
• Fast Voltage Decay
• Phase Error
3.
Mitigation Strategy
3.
Conclusion and Outlook
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Phase Error of CRAB.L5.B1
Upgrade Optics, Phase of Crab.L5.B1 = -π/2.
Total beam loss: 15% - 35% in 2 turns, mainly at TCP.C6L7.B1
IP1
IP5
Losses
CC failure
Upgrade optics SLHCV3.0
4444_thin, IP1/5: β* = 0.15m,
Θ=580μrad, CC Local scheme
IP5, 400/10,000 particles
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Beam Losses
Failure
Most beam losses occur one turn after the failure.
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Phase Error of CRAB.L5.B1
Bunchshape at TCP.C6L7.B1 directly after failure.
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Phase Error of CRAB.L5.B1
Bunchshape at TCP.C6L7.B1, 1 turn after failure.
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Content
1.
Introduction and Semi-Analytical Approach
2.
Tracking Studies (MAD-X)
3.
Mitigation Strategy
4.
Conclusion
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Mitigation strategy
xcc ( z )
x
c  tan( 2 )
z


 sin   

   x , IP  sin(  )
c 

ω = angular frequency of crab cavity
β* = beta function at IP
NCC = number of independent crab cavities
on each side of IP
1

   *  N CC
Maximal displacement by single CC
(local scheme IP5)
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Beam losses for 90⁰ phase shift of single CC
(local scheme IP5)
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Content
1.
Introduction and Semi-Analytical Approach
2.
Tracking Studies (MAD-X)
3.
Mitigation Strategy
4.
Conclusion
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Conclusion
• Upgrade optics:
• Fast voltage decay: Losses of 1-2% in first turns.
• Phase error: Losses of up to 15-35% in first turns.
(assuming instantaneous, constant phase shift by 90°)
• Nominal LHC optics -> see R. Calaga‘s slides for halo losses.
• Losses mainly at primary collimators one turn after the failure.
• Mitigation options:
•
•
•
•
Larger β* (>30cm).
Higher frequency.
Crab kick by several INDEPENDENT crab cavities.
Hollow electron lens against beam halo.
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Thank you
for your Attention
Tobias Baer
CERN BE/OP
[email protected]
Office: +41 22 76 75379
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Backup slides
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Analysis Conditions
• Optics:
• SLHCV3.0 4444_thin, β* = 0.15m (IP1/5), β* = 10.0m (IP2/8)
• Nominal optics, β* = 0.55m (IP1/5), β* = 10.0m (IP2/8)
• Crab cavity local scheme IP5, CCs at Q4
• Abrupt failure at defined turn
• Tracking of 400 – 10,000 particles for ≈20 turns.
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Bunchshape at IP5
Bunchshape at IP5 in nominal operation (Horizontal)
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Bunchshape at IP5
Bunchshape at IP5 in nominal operation (Vertical)
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Phase Error of CRAB.L5.B1
Bunchshape at TCP.C6L7.B1, 2 turns after failure.
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Phase Error of CRAB.L5.B1
Bunchshape at TCP.C6L7.B1, 3 turns after failure.
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Phase Error of CRAB.L5.B1
Bunchshape at TCP.C6L7.B1, 4 turns after failure.
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Next steps
• Improve simulation
• Time dependent failures (based on KEK measurements)
• Realistic model of tail population
• Other failure scenarios
• Failure crab cavities IP1
• Beam 2
• Global Crab Cavity scheme
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Collimation 3.5TeV, β*=3.5m
TCSG.4R6.B1
TCSG.6R7.B1
TCSG.B4L7.B1
TCP.C6L7.B1
12.1σ
TCSG.D5R7.B1
TCSG.A4R7.B1
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TCSG.D4L7.B1
TCP.D6L7.B1
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