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UPDATE ON DYNAMIC APERTURE SIMULATIONS. M. Giovannozzi For the AB/ABP-LHC Optics and Commissioning Section Protocol of DA computation and target Main studies: MQM and MQY MQX MQTL Analysis of the performance of the DA protocol Outlook Acknowledgements: S. Fartoukh. - PowerPoint PPT Presentation
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16/06/2006 M. Giovannozzi - XIX LHC MAC Meeting 1
UPDATE ON DYNAMIC APERTURE SIMULATIONS
M. GiovannozziFor the AB/ABP-LHC Optics and Commissioning Section
•Protocol of DA computation and target•Main studies:
–MQM and MQY
–MQX
–MQTL
•Analysis of the performance of the DA protocol•Outlook
Acknowledgements: S. Fartoukh
16/06/2006 M. Giovannozzi - XIX LHC MAC Meeting 2
Protocol of DA computation and target - I• Massive tracking of initial conditions for sufficient
number of turns to determine stability of initial condition.
• Conditions:– 105 turns– Initial conditions distributed along 5 directions in the
(x, y) phase space– 15 initial conditions (couples for Lyapounov exponent
evaluation)/beam sigma– Scan from 8-20 sigma – Momentum offset set to 0.75×10-3 -> ¾ of bucket
height– 60 realisations of the LHC lattice for random magnetic
errors
16/06/2006 M. Giovannozzi - XIX LHC MAC Meeting 3
Protocol of DA computation and target - II
• Machine model:– Optics version: V6.4 with nonlinear package
correctors in Q3 moved -> effectively V6.5 optics
– Magnetic errors: • Only nonlinear imperfections• Magnetic errors are derived from: magnetic models
and/or measurement
– Machine status: mainly injection
16/06/2006 M. Giovannozzi - XIX LHC MAC Meeting 4
Protocol of DA computation and target - III
• Recap of targets for DA value:– Injection: 12 sigma
• Margin from simulations at injection to reality: factor of 2
• Break down of contributions to DA uncertainty– Extrapolation to 107 turns 7 %– Finite mesh size in tracking 5 % – Amplitude ratio 5 %– Linear imperfections 5 %– Time-dependent effects 10 %– Ripple 10 %– Safety margin 20 %
CPU-time
16/06/2006 M. Giovannozzi - XIX LHC MAC Meeting 5
Aim of the studies
• Define target values of the field quality of the magnets.
• Magnet production/installation is in full swing, hence:– DA is used to provide feedback on the field
quality of the magnets with impact on the hardware, e.g. change of cross section -> main dipoles and quadrupoles
– DA is used to assess impact of field quality of magnet classes whenever this deviates from beam dynamic targets
16/06/2006 M. Giovannozzi - XIX LHC MAC Meeting 6
Main studies: MQM and MQY - I• MQM:
– Three types (MQM, MQMC, MQML) depending on length. – Used in the dispersion suppressor and matching sections
• MQY– Large aperture quadrupoles used in the matching sections
• Issues:– Wide range of powering values at injection -> hysteresis
effects cannot be neglected– Sometimes located in regions with high beta-values, e.g.
IR4/6.
• Approach:– Scan each multipole around the measured value of a given
mutipole to determine acceptable ranges.
16/06/2006 M. Giovannozzi - XIX LHC MAC Meeting 7
Main studies: MQM and MQY - IITypical values for the optical functions for MQY quadrupoles
0
100
200
300
400
500
600
700
MQY.4R
1
MQY.B
5L2
MQY.A
5L2
MQY.B
4L2
MQY.A
4L2
MQY.A
4R2
MQY.B
4R2
MQY.6L
4
MQY.5L
4
MQY.5R
4
MQY.6R
4
MQY.4L
5
MQY.4R
5
MQY.5L
6
MQY.4L
6
MQY.4R
6
MQY.5R
6
MQY.B
4L8
MQY.A
4L8
MQY.A
4R8
MQY.B
4R8
MQY.A
5R8
MQY.B
5R8
MQY.4L
1
Bet
a-fu
nct
ion
(m
)
Beta X
Beta YIR4
IR6
Values comparable with max beta-functions for MQM-like quadrupoles
16/06/2006 M. Giovannozzi - XIX LHC MAC Meeting 8
0
2
4
6
8
10
12
14
16
-1.5 -1.0 -0.5 0.0 0.5 1.0
b10 (units)
DA
(si
gm
a)
Minimum (angles) Average (seed)
15 deg.
30 deg.45 deg.
60 deg.
75 deg.
Main studies: MQM and MQY - IIIDA reduction at large angle
Systematic value of b10 for MQY
Scan over MQY multipoles
16/06/2006 M. Giovannozzi - XIX LHC MAC Meeting 9
Main studies: MQM and MQY - IV
0
2
4
6
8
10
12
14
16
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
a9 (units)
DA
(si
gm
a)
Minimum (angles) Average (seed)
15 deg.
30 deg.
45 deg.
60 deg.
75 deg.
DA reduction at small angle
Scan over MQY multipoles
16/06/2006 M. Giovannozzi - XIX LHC MAC Meeting 10
10.0
10.5
11.0
11.5
12.0
12.5
13.0
13.5
0 10 20 30 40 50 60 70 80
Angle (degrees)
Min
imu
m D
A (
sig
ma)
All Ds, MBs, MQs, MQWs, MQM, MQY
All Ds, MBs, MQs, MQWs(whole prod.), MQXA, MQXB, MQM, MQY
Main studies: MQXImpact of measured field quality of triplet quadrupoles at injection.
Impact on DA at small angles
16/06/2006 M. Giovannozzi - XIX LHC MAC Meeting 11
Main studies: MQTL - I
• Long trim quadrupoles used:– As correctors (i.e. combined with an MQ) in all
Q11 and Q10, Q9, Q8, Q7 in IR3/7– Main quadrupoles in Q6 assembly in IR3/7
• Field quality feature a large systematic b10 of about 15 units.
• Feed down effects due to vertical closed orbit, generating a9 (see impact on DA for MQY) were checked.
16/06/2006 M. Giovannozzi - XIX LHC MAC Meeting 12
10
11
12
13
14
15
16
17
0 10 20 30 40 50 60 70 80
Angle (degrees)
Min
imu
m D
A (
sig
ma
)
All Ds, MB, MQ, MQW (whole prod.), MQXA, MQXB, MQM, MQY
All Ds, MB, MQ, MQW (whole prod.), MQXA, MQXB, MQM, MQY, MQTL
All Ds, MB, MQ, MQW (whole prod.), MQXA, MQXB, MQM, MQY, MQTL - CO feeddown
Main studies: MQTL - II
No dramatic impact on DA
Magnetic errors computed as feed-down from the measured field quality of random orbit (4 mm) are used.
16/06/2006 M. Giovannozzi - XIX LHC MAC Meeting 13
9
10
11
12
13
14
15
16
17
0 10 20 30 40 50 60 70 80
Angle (degrees)
Min
imu
m D
A (
sig
ma)
All Ds, MBs, MQs
All Ds, MB, MQ, MQW (whole prod.), MQXA, MQXB, MQM, MQY,MQTL - CO feed down
All Ds, MB, MQ, MQW (whole prod.), MQXA, MQXB, MQM -hysteresis, MQY - hysteresis, MQTL - CO feed down
Summary of results - I
Minimum DA (over angles) decreased from 11.2 -> 10.4
All magnets, but MBs and MQs, reduce DA by 1 sigma
16/06/2006 M. Giovannozzi - XIX LHC MAC Meeting 14
10
11
12
13
14
15
16
17
18
19
20
0 10 20 30 40 50 60 70 80
Angle (degrees)
Ave
rag
e D
A (
sig
ma)
All Ds, MBs, MQs
All Ds, MB, MQ, MQW (whole prod.), MQXA, MQXB, MQM, MQY,MQTL - CO feed downAll Ds, MB, MQ, MQW (whole prod.), MQXA, MQXB, MQM -hysteresis, MQY - hysteresis, MQTL - CO feed down
Summary of results - II
Loss of DA visible also on average DA.
16/06/2006 M. Giovannozzi - XIX LHC MAC Meeting 15
Analysis of the performance of the DA protocol - I
• Detailed analysis of dependence of the DA estimate on:– Number of angles -> pushed up to 103 (for 60
realisations)– Number of realisations -> pushed up to 600 (for 5
angles)
• The model used is LHC, optics V6.4 (injection) with errors in– Main dipoles– Main quadrupoles– Cold separation dipoles
16/06/2006 M. Giovannozzi - XIX LHC MAC Meeting 16
Analysis of the performance of the DA protocol: angle dependence
Minimum DA (over realisations and angles) vs. # angles
This indicates that about 20-50 angles should be used
Nangles, i = 90° i /(Nangles +1), 1 < i < Nangles
~ 5% -> corresponding to the allocated budget
16/06/2006 M. Giovannozzi - XIX LHC MAC Meeting 17
Analysis of the performance of the DA protocol: realisation dependence - I
16/06/2006 M. Giovannozzi - XIX LHC MAC Meeting 18
10.0
10.5
11.0
11.5
12.0
12.5
13.0
13.5
14.0
0 100 200 300 400 500 600Number of realisations
Din
amic
ap
ertu
re a
t 15
deg
rees
(s )
Minimum Average Maximum
Standard LHC simulations
Analysis of the performance of the DA protocol: realisation dependence - II
This indicates that about 300 realisations should be used -> not feasible
This spread is much reduced for the most realistic LHC model -> this might mitigate the need for more realisations
16/06/2006 M. Giovannozzi - XIX LHC MAC Meeting 19
Outlook - I• Present status of DA studies:
– Minimum (over realisations and angles) DA is 10.4 sigma
– The model used is the most complete possible -> magnetic errors from simulations gradually replaced by those results from magnetic measurements and all classes of magnets are included
• Improvement of the model:– Move to the latest optics version V6.500
• Improvement of the protocol for DA computation– Increase number of angles and realisations
16/06/2006 M. Giovannozzi - XIX LHC MAC Meeting 20
Outlook - II• Next step
– Take into account slot assignment activity from Magnet Evaluation Board
– Take into account pre-assignment of magnets, e.g. all SSS are already pre-assigned
– Assign actual measured errors
• General comment:– The field quality of each individual is taken into
account in the slot allocation process, e.g.:• b2 for quadrupoles (beta-beating)
• b1, a2, b3 for dipoles (corrector strength, coupling, 3rd order driving term)
– The impact on DA is yet to be evaluated.
16/06/2006 M. Giovannozzi - XIX LHC MAC Meeting 21
Outlook - III• Tools
– Software tool developed by Colleagues in AT/MAS-MA to gather information from databases (magnetic and slot allocation)
– New routines to assign measured errors in MAD-X developed inside AB/ABP-LOC
– First result: beta-beating correction based on the best estimate of the distribution of b2 errors in the machine as-installed