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2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón
Studies of Machine protection for a Crab Cavity in the LHC
Bruce Yee Rendón
Departamento de FísicaCentro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional Unidad Zacatenco
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2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón
Scheme
Introduction.Machine protection studies.Results.Future work.
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2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón
Introduction
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2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón
LHC
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2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón
In Table 1 shown relevant optics parameter for the Nominal and Upgrade scheme in the LHC.
Table 1. Optics parameters for the Nominal and Upgrade (ATS scheme [1]) under study.
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Parameter Symbol Nominal Scheme Upgrade Scheme
Energy E [TeV] 7 7
Protons per bunch Nb[1011] 1.15 1.7
rms bunch length σz[cm] 7.55 7.55
Beta function at IP5/IP1
β*[cm] 50 15
Emittance ε[10-6 mrad] 3.75 3.75
Full crossing angle θ[μrad] 285 580
LHC parameters
2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón
Luminosity
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The Luminosity in the nominal LHC is 1034 cm-2 s-1.
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21
21
1
4
x
syx
bfNNNL
Figure 1: The Crossing angle scheme.
2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón
Crab Cavities
A device called “crab cavity” (CC) applies a tiny sideways kick to each particle bunch, in order to changed its dynamics to achieve a head-on collision at the IP.
For the HL-LHC the luminosity will increase by factor of 5 (with respect to the nominal) [2].
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IP5
Left CCs Right CCs Figure 3: The CC´s effect in the beam at collision point in the LCC scheme.
Figure 2 : The CC scheme at IP5 for the Upgrade.
2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón
Machine protection studies
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2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón
LHC safe operation
• The Stored energy in the LHC beam at 7 TeV is 350 MJ [3].
• 5% of a single beam can quench the superconducting magnets [3].
• The safe beam extraction is in 3 turns [4].
• The CC ´s effect in the beam loss, when the CC presents or not a failure [5].
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2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón
Collimation´s tools
• SixTrack simulates the track of large numbers of particles, taking in account the interaction of beam with the collimators [6].
• Local Loss Maps shows the particles losses (in the collimators, cold and warm magnets) around the lattice [7].
• Absorbed particles in the collimators.
• Lost particles around the ring (not in the collimators).
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2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón
Beam distribution
• In general, halos distributions are using to made collimation studies.
• A double and triple Gaussian distributions were used in order to simulate a more realistic beam profile [8,9,10].
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Figure 4 : The typical beam distribution using for machine protection studies.
2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón
Double Gaussian distribution
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Tails. Core.
Around 2 millions of particles generated.
Figure 5 : The beam profile obtained by using the CMS measurements. The sigma of the tails is 1.8 times than the core [8].
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10-1
10-2
10-3
10-4
10-5
2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón
Triple Gaussian distribution
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Figure 6 : The beam profile obtained by apply Abel transformation to the scrapping measurements of collimation team at injection energy at LHC [9,10].
Core.A1=0.53σ1=0.66
Tails.Around 1 millions of particles generated.
A2=0.16σ2=1.32
A3=0.005σ3=1.996
2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón
Simulation cases
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2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón
Free turns
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Turns
Voltage
Phase
Figure 7 : Here we show the way that the amplitude of voltage and phase are change as a function of the number of the turns. In the Free turns (FT) the voltage and phase of the CC remain zero.
V
0
t1
T1
ϕinicial
2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón
Normal operation
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Turns
Turns
Voltage
Adiabatic Ramping up
Phase
Figure 8 : In the Normal operation (NO) represent the ideal performance of the CC.
2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón
Voltage failure
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Turns
Turns
Voltage
Adiabatic Ramping up
Phase
establish “steady-state”conditions with crab cavity and collimator before simulating a crab-cavity failure
Figure 9 : In the Voltage failure (VF) just the voltage drops to zero, in contrast the phase remains like in the normal operation scheme [5, 9,10].
2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón
Phase failure
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Turns
Voltage
Adiabatic Ramping up
PhaseTurns
establish “steady-state”conditions with crab cavity and collimator before simulating a crab-cavity failure
Figure 10 : In analogy with the VF case, in the Phase failure (PF) case just the phase change 90 degrees with respect to its initial phase [5, 11,12].
2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón
Results
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2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón
Distribution of the turns in the simulation
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Case Free turns Ramping upturns
Plateau turns
Ramping down turns
Final valuevoltage
Final valuephase
FT 200 0 0 0 Remains equals
Remains equals
NO 1 10 189 0 Remains equals
Remains equals
VF 1 10 169 1,3 or 5 0 Remains equals
PF 1 10 169 1,3 or 5 Remainsequals
π/2
The numbers of turns for the tracking are 200 turns. The collimators are turn on in since the first turn.
Table 2. This Table illustrates the distribution of the turns for the different case and shows the finals value of voltage and phase.
2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón
Nominal
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2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón
LLM for the Nominal LHC
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Figure 11 : The LLM for a phase failure of 90° in 5 turns, for a simple and double Gaussian distribution increase the beam size by factor of three to overpopulated the tails.
2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón
Absorbed particle in the Nominal LHC
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Figure 12 : The percentage of the particle absorbed for the failures in voltage and phase using a double Gaussian (beam size increase by a factor of 1.5).
( 1x106 particles, double Gaussian with 1.5 σx,y)
2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón
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Lost particle in the PF case at Nominal LHC
( 1x106 particles, double Gaussian with 1.5 σx,y)
Figure 13 : The percentage of the particle total for the failures in phase using a double Gaussian (beam size increase by a factor of 1.5).
2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón
ATS
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2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón
Results with out CC in the ATS scheme
Here is presents the percentage of lost and absorbed particles using a Double Gaussian (Table 3).
Table 3. The percentage of particles lost, absorbed and impact real for the ATS lattice, without CC. The total of particles generated around 1 million.
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Distribution Lost particles [%] Absorbed Particles [%]
Double Gaussian ( 1.0 σx,y) 0.17 1.81
Double Gaussian ( 1.5 σx,y) 1.1 13.66
2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón
CC voltage correctors
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The equation of the CC left voltage:
(1)
The equation of the right CC voltage: (2)
where δ is the kick of the correctors, Es is the beam energy, q charge of particle, c is the speed of the light, ω is the frequency of the CC, σt is the rms bunch length and ncc the number of CC.
ccz
srightCCkickrightCC
nq
EcV
ccz
sleftCCkickleftCC
nq
EcV
2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón
CC voltage analytic formula
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The equation of the CC left voltage:
(3)
The equation of the right CC voltage [12]:
(4)
(5.1) with (5.2)
where β* is the beta function at IP, βleft/right cc is the beta function in the left/right cc, Θ crossing angel, Δφleft/right is the difference of phase advance between the IP and the CCleft/right, Δφcc is the difference of phase advance between the left and right CC and R2,2 is the element (2,2) of the transport matrix from left and right CC.
ccleftleftCC
sleftCC
nq
EcV
)sin(
)tan(*
2
ccoleftCC
sleftCC
nq
EcV
)sin(
)tan(*
2
leftCCrightCC VRV 22 )( CCrightCC
leftCC CosR
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2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón
Voltage
Here is presents the value of voltage using de formulas (1) to (5.2).
Table 4. The value of voltage for a CC of 400 MHz for the ATS lattice.
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Voltage of Corrector (MeV) Analytic Voltage (MeV)
VleftCC=9.3465 VleftCC=10.129
VrightCC=10.867 a) VrightCC=11.782*
b) VrightCC= 11.778**
*Equation (4).**Equations (5.1) & (5.2).
2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón
X Orbit
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Figure 14 : The superposition of the Orbit X, using the voltage of the orbit corrector and the two initial formula in the region from S.DS.L5.B1/E.DS.R5.B1. .
6E-5
4E-5
2E-5
0.0
-2E-5
-4E-5
-6E-5
X(m
)
X Orbit
IP5
3CCs
6117 6317 6517 6717 6917 7117
Ct(m)
2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón
X orbit
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Figure 15 : The Orbit X using the voltage calculate by formulas 3 and 4 from S.DS.L5.B1/E.DS.R5.B1.
2.5
2.0
1.5
1.0
0.5
0.0
-0.5
X(σ
)
6117 6317 6517 6717 6917 7117
Ct(m)
X Orbit
IP5 3CCs
2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón
X-Ct Voltage Failure
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IP5Right CCLeft CC
IP5Free turns
Linear fit
Effect of the ramping up
Figure 16 : The effect of the CC in the X coordinate close to IP5 is shown for a tracking of one particle 200 turns. The plots consists in the superposition of the CC´s operation cases, failures in voltage, and a linear fit w.r.t. the normal operation case. The fit give us a slope of 274 μ rad, close to the half of the crossing angle.
.
2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón
X-Ct Voltage Failure
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IP5Right CCLeft CC
Free turns
Linear fit
Effect of the ramping up
Free turns
Normal operation
Failure starts
Figure 17: A close up when the failure starts of the Figure16. The effect of the voltage failure for the different cases are shown and compare between them.
2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón
X-Ct Phase Failure
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Figure 18: In analogy with the voltage failure (Figure 17) , the effect of the phase failure for the different cases are shown and compare between them.
Normal operation
Failure starts
Free turns
Failure starts
Free turns
Normal operation
2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón
X-Ct Voltage and Phase Failure
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Figure 19 : The superposition between the failures of voltage and phase in five turns, using the free turns and normal operation case like baseline. The effect produces for the phase change is larger than the voltage. The square of the voltage failure cover the circles of the phase failures before the failures appears.
Failure starts
Free turns
Normal operation
2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón
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Figure 20 : The LLM for a phase failure of 90° in 5 turns, for a double Gaussian distribution increase the beam size by factor of 1.5 to overpopulated the tails.
( 1 million particles)
LLM for the ATS LHC
2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón
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Figure 21 : The LLM for a phase failure of 90° in 5 turns, for a double Gaussian distribution increase the beam size by factor of 1.5 in the Nominal and ATS scheme..
( 1 million particles)
Comparisons
2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón
Future Work
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2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón
Activities
• Implement the correct aperture model of the full ring and settings for the ATS lattice (Collimation team help).
• Consider different distributions which can describe better the tails (using a Triple Gaussian from halo scraping measurements)
• Study more realistic case of failure in voltage and phase (the way that voltage or phase change).
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2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón
Acknowledgements
I want to say thank to A. Marsili, F. Burkart, R. de Maria, T. Baer, R. Tomas, J. Barranco, R. Calaga, F. Zimmermann, R. Lopez; US-LARP, CONACYT.
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2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón
References
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[1] R. De Maria et al, “A proposal for the optics and layout of the HL-LHC with Crab-cavities”, IPAC´11, THPZ013, 2011.
[2] O. Brunning et al., “The Large Hadron Collider”, Progress in Particle and Nuclear Physics,2012.
[3] R. Schmidt et al., PAC07, 2007.
[4] J. Wenninger, “Machine Protection Specifications”, LHC-CC10, 2010.
[5] T. Baer et al, “Beam losses due to abrupt Crab Cavities failures in the LHC”, IPAC´11, TUPZ009, 2011.
[6] F. Schmidt. “SixTrack, User’s Reference Manual”. CERN SL/94-56 AP.�
2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón
References
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[7] LHC Collimation Project, http://lhc-collimation-project.web.cern.ch/lhc-collimation-project/code-tracking-2009.htm
[8] The CMS Collaboration, “Absolute Calibration of the CMS Luminosity”, CMS PAS EWK-11-001, 2011.
[9] F. Burkart et al, “Absolute Calibration of the CMS Luminosity”, IPAC´11, THPZ030, 2011.
[10] B. Yee Rendon, “Abel transformation report”, personal note, 2012.
[11] R. Calaga et al., “Beam Losses due to Abrupt Crab Cavity Failures in the LHC, PAC´11, MOODN4,2011.
[12] Y. Sun et al, “Beam Dynamics aspects of Crab Cavities in the CERN Large Hadron Collider”, Phys. Rev. ST Accel. Beams, vol 12, no.10, 2009.
2nd Hi-Lumi LHC-LARP Frascati 14/11/2012 B. Yee Rendón
Thanks for your attention
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