HiLumi LHC FP7 High Luminosity Large Hadron Collider Design Study - - PDF document

CERN-ACC-SLIDES-2014-0075

HiLumi LHC

FP7 High Luminosity Large Hadron Collider Design Study

Presentation Field quality requirements from dynamic aperture: including matching section

Nosochkov, Y (CERN)

12 November 2013

The HiLumi LHC Design Study is included in the High Luminosity LHC project and is partly funded by the European Commission within the Framework Programme 7 Capacities Specific Programme, Grant Agreement 284404. This work is part of HiLumi LHC Work Package 2: Accelerator Physics & Performance.

The electronic version of this HiLumi LHC Publication is available via the HiLumi LHC web site <http://hilumilhc.web.cern.ch> or on the CERN Document Server at the following URL: <http://cds.cern.ch/search?p=CERN-ACC-SLIDES-2014-0075>

CERN-ACC-SLIDES-2014-0075

The HiLumi LHC Design Study is included in the High Luminosity LHC project and is partly funded by the European Commission within the Framework Programme 7 Capacities Specific Programme, Grant Agreement 284404. Work supported by the US LHC Accelerator Research Program (LARP) through US Department of Energy contracts DE-AC02-07CH11359, DE-AC02-98CH10886, DE-AC02-05CH11231, and DE- AC02-76SF00515.

Field Quality Requirements for Separation Dipoles and Matching Quadrupoles at Collision Energy Based on Dynamic Aperture

Yuri Nosochkov (SLAC)

• Y. Cai, M.-H. Wang (SLAC)
• S. Fartoukh, M. Giovannozzi, R. de Maria, E. McIntosh (CERN)

3rd Joint HiLumi LHC—LARP Meeting 11—15 November 2013, Daresbury, UK

Introduction

• New large aperture magnets are planned for the HL-LHC lattice: superconducting

150 mm D1 and 105 mm D2 separation dipoles, 90 mm Q4 and 70 mm Q5 matching quadrupoles near IP1 and IP5.

• High beta functions in these magnets enhance sensitivity to their field errors

causing reduction of dynamic aperture (DA).

• Field quality in these magnets needs to be evaluated and optimized to satisfy two

conflicting requirements: the field errors must be small enough to provide a sufficient DA (~10s), but large enough to be realistically achievable.

• Estimates of field quality obtained from measured data and magnetic field

calculations are used as a starting point for evaluation and optimization.

• Impact of the field errors on DA is determined in tracking simulations using

SixTrack.

• Lattice: SLHCV3.1b with b*=15/15 cm at IP1 and IP5, SC IT quadrupoles with 150

mm coil diameter and 150 T/m gradient, 7 TeV beam energy.

Beta functions

High b-functions in the D1, D2, Q4, Q5 enhance beam sensitivity to their field errors. Field correctors for the IT also compensate the low order D1 field errors (n=3-6) since the two beams share the D1 aperture. 2-in-1 D2 and Q4, Q5 magnets do not have local correctors.

D1 D2 Q4 Q5 D1 D2 Q4 Q5 ≈180°

IT field quality specifications at r0 = 50 mm (“IT_errortable_v66”)

These IT specifications is the result of previous optimization studies. In this study, the IT specification errors are always included.

skew mean uncertainty random normal mean uncertainty random a3 0.800 0.800 b3 0.820 0.820 a4 0.650 0.650 b4 0.570 0.570 a5 0.430 0.430 b5 0.420 0.420 a6 0.310 0.310 b6 0.800 0.550 0.550 a7 0.152 0.095 b7 0.095 0.095 a8 0.088 0.055 b8 0.065 0.065 a9 0.064 0.040 b9 0.035 0.035 a10 0.040 0.032 b10 0.075 0.100 0.100 a11 0.026 0.0208 b11 0.0208 0.0208 a12 0.014 0.014 b12 0.0144 0.0144 a13 0.010 0.010 b13 0.0072 0.0072 a14 0.005 0.005 b14

• 0.020

0.0115 0.0115

 

1 1 4

) ( 10

   

    



n n n n ref x y

r iy x ia b B iB B

Q4 field errors at r0 = 30 mm (“Q4_errortable_v1”)

skew mean uncertainty random normal mean uncertainty random a3 0.682 1.227 b3 1.282 1.500 a4 0.428 0.893 b4 0.483 0.465 a5 0.177 0.406 b5 0.203 0.431 a6 0.484 0.277 b6 5.187 1.487 a7 0.094 0.189 b7 0.094 0.189 a8 0.193 0.257 b8 0.193 0.257 a9 0.088 0.088 b9 0.088 0.088 a10 0.120 0.120 b10 3.587 0.956 a11 0.326 0.489 b11 0.326 0.489 a12 0.445 0.222 b12 0.445 0.222 a13 0.606 0.303 b13 0.606 0.303 a14 0.827 0.413 b14 2.067 0.413 a15 1.127 0.564 b15 1.127 0.564

Estimate is based on scaling from the measured field of existing MQY quadrupole with 70 mm aperture and applied to 90 mm Q4. This estimate is expected to be updated.

Q5 expected field quality at r0 = 17 mm (“Q5_errortable_v0”)

skew mean uncertainty random normal mean uncertainty random a3 0.500 0.900 b3 0.940 1.100 a4 0.230 0.480 b4 0.260 0.250 a5 0.070 0.160 b5 0.080 0.170 a6 0.140 0.080 b6 1.500 0.430 a7 0.020 0.040 b7 0.020 0.040 a8 0.030 0.040 b8 0.030 0.040 a9 0.010 0.010 b9 0.010 0.010 a10 0.010 0.010 b10 0.300 0.080 a11 0.020 0.030 b11 0.020 0.030 a12 0.020 0.010 b12 0.020 0.010 a13 0.020 0.010 b13 0.020 0.010 a14 0.020 0.010 b14 0.050 0.010 a15 0.020 0.010 b15 0.020 0.010

Estimate is based on the measured field of existing MQY quadrupole with 70 mm aperture which is of the same type as Q5.

D1 expected field quality at r0 = 50 mm (“D1_errortable_v1”)

skew mean uncertainty random normal mean uncertainty random a2 0.679 0.679 b2 0.200 0.200 a3 0.282 0.282 b3

• 0.9

0.727 0.727 a4 0.444 0.444 b4 0.126 0.126 a5 0.152 0.152 b5 0.365 0.365 a6 0.176 0.176 b6 0.060 0.060 a7 0.057 0.057 b7 0.4 0.165 0.165 a8 0.061 0.061 b8 0.027 0.027 a9 0.020 0.020 b9

• 0.59

0.065 0.065 a10 0.025 0.025 b10 0.008 0.008 a11 0.007 0.007 b11 0.47 0.019 0.019 a12 0.008 0.008 b12 0.003 0.003 a13 0.002 0.002 b13 0.006 0.006 a14 0.003 0.003 b14 0.001 0.001 a15 0.001 0.001 b15

• 0.04

0.002 0.002

Estimate is based on magnetic field calculations for 160 mm aperture D1 magnet (T. Nakamoto, E. Todesco, CERN-ACC-2013-002).

D2 field errors at r0 = 35 mm (“D2_errortable_v3”)

skew mean uncertainty random normal mean uncertainty random a2 0.679 0.6790 b2 ±65 3.0 3.0 a3 0.282 0.2820 b3

• 30

5.0 5.0 a4 0.444 0.4440 b4 ±25 1.0 1.0 a5 0.152 0.152 b5

• 4.0

1.0 1.0 a6 0.176 0.176 b6 0.060 0.060 a7 0.057 0.057 b7

• 0.2

0.165 0.165 a8 0.061 0.061 b8 0.027 0.027 a9 0.020 0.020 b9 0.09 0.065 0.065 a10 0.025 0.025 b10 0.008 0.008 a11 0.007 0.007 b11 0.03 0.019 0.019 a12 0.008 0.008 b12 0.003 0.003 a13 0.002 0.002 b13 0.006 0.006 a14 0.003 0.003 b14 0.001 0.001 a15 0.001 0.001 b15 0.002 0.002 Estimate is based on magnetic field calculations for 2-in-1 D2 dipole (E. Todesco 01-Jan-2013). These values were obtained for a shorter magnet, therefore they may be potentially reduced for the longer D2. The large values of b2, b3, b4, b5 terms are due to field saturation.

Latest D2 field estimate at r0 = 35 mm (“D2_errortable_v4”)

skew mean uncertainty random normal mean uncertainty random a2 0.679 0.6790 b2 ±65→±25 3.0→2.5 3.0→2.5 a3 0.282 0.2820 b3

• 30→3.0

5.0→1.5 5.0→1.5 a4 0.444 0.4440 b4 ±25→±2.0 1.0→0.2 1.0→0.2 a5 0.152 0.152 b5

• 4.0→-1.0

1.0→0.5 1.0→0.5 a6 0.176 0.176 b6 0.060 0.060 a7 0.057 0.057 b7

• 0.2

0.165 0.165 a8 0.061 0.061 b8 0.027 0.027 a9 0.020 0.020 b9 0.09 0.065 0.065 a10 0.025 0.025 b10 0.008 0.008 a11 0.007 0.007 b11 0.03 0.019 0.019 a12 0.008 0.008 b12 0.003 0.003 a13 0.002 0.002 b13 0.006 0.006 a14 0.003 0.003 b14 0.001 0.001 a15 0.001 0.001 b15 0.002 0.002 The recent optimization of iron geometry and coil in D2 (E. Todesco) resulted in significant reduction of b2, b3, b4, b5 terms at collision energy (D2_errortable_v4). It also significantly reduced the mean values of b3 (95.8→3.8) and b5 (15→3.0) at injection energy. However, for most of this study, the D2_errortable_v3 was used as a reference table.

Typical set-up for SixTrack tracking

• 100,000 turns
• 60 random error seeds
• 30 particle pairs per amplitude step (2s
• 11 angles
• 7 TeV beam energy
• Initial Dp/p = 2.7e-4
• Tune = 62.31, 60.32
• Normalized emittance = 3.75 mm-rad
• Arc errors and correction are included
• IT local correctors to compensate an, bn errors of order n=3-6 in IT quads and D1

dipoles are included

DA without D1, D2, Q4, Q5 errors

This is our starting DA with only IT and arc errors included. The goal is to optimize D1, D2, Q4, Q5 errors in order to keep minimum DA near 10s.

Kicks due to an, bn terms in D1, D2 at x=10sx

x n x n x

r b x b  s  b  / / 10 10 /

1 4

) (

 

  

(and similar for y’ from an)

Largest kicks are produced by b2m, b3m, b4m in D2_v3 table. They are further amplified by ≈180° phase between left and right side D2 magnets around IP, and by the fact that mean bn terms of even order are

• f opposite sign in the

left and right D2. These kicks are substantially reduced in the D2_v4 error table.

Impact of large b2 in D2_v3 on DA

Large b2 terms in D2_v3 table affect beta functions by increasing b* and reducing peak b in the

• IT. This reduces impact of IT, D1, D2 errors resulting in a larger DA.

For comparison, bKL focusing strength from b2m=65 in one D2 is equivalent to ¼ of a regular arc quad or 7% of Q4. Beta perturbation from left side D2 is amplified by the right side D2. To maintain luminosity, this perturbation will be compensated in operation. To simulate such compensation and avoid too optimistic DA, we set b2=0 in D2 in all simulations.

Example of beta perturbation due to b2 in D2_v3

b2=0 b2×1/8 b2×2/8 b2×3/8 b2×3/8 b2×2/8 b2×1/8 b2=0

IT peak beta IP beta

X X Y Y

Feed-down due to orbit in D1, D2

Beam trajectory in D1, D2 is, on average, horizontally offset relative to magnet axis resulting in lower order feed-down bn, an terms. Example for D2_v3 table: b4m=25 creates an average feed-down term <b3m>=3.6 (12% of main b3m), and b5m=-4 creates feed-down <b4m>=-0.77 (3% of main b4m). Feed-down effect on DA will be verified in tracking.

Relative impact of Q4_v1, Q5_v0, D1_v1, D2_v3 errors

Q4, Q5 errors have minimal effect on DA, hence are acceptable. D2 errors without b2, b3, b4, b5 are acceptable. D1 errors should be optimized.

D2_v3

Impact of bn in D1_v1 with D2 errors off

Large DA reduction due to b7m, b9m. Consider b7m, b9m reduction by a factor of 2. D1 errors for n ≤ 6 are compensated using local IT correctors. 7th order resonances 3rd, 6th, 9th order resonances

Scan of b5 in D2_v3

Effect of b5 in D2_v3 on DA is small. Minor effect from feed-down.

Scan of b4 in D2_v3

Strong impact on DA requires a factor of 10 reduction of b4 relative to D2_v3 table. Feed-down has minor impact at reduced b4.

Scan of b3 in D2_v3

Strong DA reduction requires a factor of 10 reduction of b3 relative to D2_v3 table. Feed-down effect is small.

Sensitivity to b3, b4 uncertainty and random terms

b3u,r should be reduced at least a factor of 2 relative to D2_v3 table. b4u,r impact is small.

Scan of D2 b3m and b4m with other errors close to D2_v4 table

Consider reducing b3m by a factor of 20 relative to D2_v3 (i.e. factor of 2 relative to D2_v4).

D2_v4 value

Recommended target for D1 field quality

skew mean uncertainty random normal mean uncertainty random a2 0.679 0.6790 b2 0.200 0.200 a3 0.282 0.2820 b3

• 0.9

0.727 0.727 a4 0.444 0.4440 b4 0.126 0.126 a5 0.152 0.152 b5 0.365 0.365 a6 0.176 0.176 b6 0.060 0.060 a7 0.057 0.057 b7 0.4→0.2 0.165 0.165 a8 0.061 0.061 b8 0.027 0.027 a9 0.020 0.020 b9

• 0.59→-0.295

0.065 0.065 a10 0.025 0.025 b10 0.008 0.008 a11 0.007 0.007 b11 0.47 0.019 0.019 a12 0.008 0.008 b12 0.003 0.003 a13 0.002 0.002 b13 0.006 0.006 a14 0.003 0.003 b14 0.001 0.001 a15 0.001 0.001 b15

• 0.04

0.002 0.002

Reduce b7m and b9m a factor of 2 relative to D1_errortable_v1.

Recommended target for D2 field quality

skew mean uncertainty random normal mean uncertainty random a2 0.679 0.6790 b2 ±25 2.5 2.5 a3 0.282 0.2820 b3 3.0→1.5 1.5 1.5 a4 0.444 0.4440 b4 ±2.0 0.2 0.2 a5 0.152 0.152 b5

• 1.0

0.5 0.5 a6 0.176 0.176 b6 0.060 0.060 a7 0.057 0.057 b7

• 0.2

0.165 0.165 a8 0.061 0.061 b8 0.027 0.027 a9 0.020 0.020 b9 0.09 0.065 0.065 a10 0.025 0.025 b10 0.008 0.008 a11 0.007 0.007 b11 0.03 0.019 0.019 a12 0.008 0.008 b12 0.003 0.003 a13 0.002 0.002 b13 0.006 0.006 a14 0.003 0.003 b14 0.001 0.001 a15 0.001 0.001 b15 0.002 0.002 1) Use D2_errortable_v4 and further reduce b3m a factor of 2. 2) Minimize the b2 term or compensate its impact on beta function. Correction options are not yet decided, but may include adjustment of Q4 gradient or D2 spool-piece correctors.

DA with Q4_v1, Q5_v0 and target D1, D2 errors

Minimum DA is 9.9s dominated by vertical DA.

DA with target D1, D2 errors versus original D1_v1, D2_v4

Most improvement is near the vertical plane: +0.5s for DAmin and +0.7s for DAave. Further increase of vertical DA may be possible by optimizing vertical phase advance between IP1 and IP5 (in SLHCV3.1b it is integer x 2p causing amplification of systematic error effects in vertical plane in the IP1 and IP5 magnets).

Summary

• Impact on DA from estimated field errors in the large aperture D1, D2 separation dipoles

and Q4, Q5 matching quadrupoles in the SLHCV3.1b lattice has been evaluated.

• The Q4, Q5 field errors were found to be acceptable.
• Field error terms – b7m, b9m in D1, and b3m in D2 – were identified as having the most

impact on the DA. In order to obtain the minimum DA near 10s, these three terms were reduced a factor of 2 relative to D1_errortable_v1 and D2_errortable_v4, respectively.

• It is also critical to minimize the large D2 term b2 or compensate its impact on beta
• function. Correction options are not yet decided, but may include adjustment of Q4

strength or implementation of D2 spool-piece correctors.

• The feed-down effect due to offset orbit in the D1, D2 was found to be small.
• In summary, the evolution of minimum DA in optimization is as follows:
• With the IT errors and without D1, D2, Q4, Q5 errors the starting DAmin is 10.38s.
• With the IT, Q4, Q5 errors and D1_v1, D2_v3 error tables the DA would be extremely

small.

• With the IT, Q4, Q5 errors and D1_v1, D2_v4 error tables before optimization DAmin is

9.36s.

• With the IT, Q4, Q5 errors and optimized D1, D2 errors DAmin is 9.90s.
• Further improvement of the minimum DA may be possible by optimizing vertical phase

advance between IP1 and IP5.