UPDATE ON DYNAMIC APERTURE SIMULATIONS

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


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


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


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


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


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.


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


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


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


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


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.


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.


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


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.


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


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


Analysis of the performance of the DA protocol: realisation dependence - I


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


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


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.


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

UPDATE ON DYNAMIC APERTURE SIMULATIONS

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