E. Todesco

MQXA: DECAY AND FIELD HARMONICS

E. TodescoMagnets, Superconductors and Cryostats Group

Technology Department, CERN

FiDeL meeting, 30 March 2009

E. Todesco 30th March 2009 – Decay and harmonics in MQXA- 2

CONTENTS

Decay

Field harmonicsAllowedNot allowed

E. Todesco 30th March 2009 – Decay and harmonics in MQXA- 3

DECAY

Measurements:Rotating coil, 600 mm long, In one central position, Measurements taken every ~3.7 minutes for up to 6 hoursOne close to injection (390 A) and one at high field (7149 A, i.e. ~ 7.3 TeV)

E. Todesco 30th March 2009 – Decay and harmonics in MQXA- 4

TRANSFER FUNCTION DECAY

Decay from 1 to -4 units after 20 minutes, from 2 to -8 units after 200 minutesWe propose to neglect this effect in FiDeL

-10

-8

-6

-4

-2

0

2

4

6

0 25 50 75 100 125 150 175 200 225 250

db2

(uni

ts)

Time (minutes)

1918171615141312111098765432

E. Todesco 30th March 2009 – Decay and harmonics in MQXA- 5

B6 DECAY

Decay from 0.2 to 0.8 units after 20 minutes, from 0.4 to 1.3 units after 200 minutes

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 25 50 75 100 125 150 175 200 225 250

db6

(uni

ts)

Time (minutes)

1918171615141312111098765432

E. Todesco 30th March 2009 – Decay and harmonics in MQXA- 6

B6 decay

The double exp fit works well

Time constants of about 500 sMagnet t (s) d c err

2 480 0.71 0.82 0.0093 420 0.69 0.86 0.0104 900 0.68 0.48 0.0045 480 0.85 0.69 0.0106 300 0.55 0.88 0.0067 420 0.68 0.91 0.0098 420 0.65 0.98 0.0159 480 0.55 1.30 0.013

10 480 0.50 1.29 0.01511 420 0.53 1.20 0.01012 480 0.56 1.09 0.00813 360 0.37 1.11 0.01714 480 0.65 0.88 0.00715 480 0.71 0.66 0.00916 540 0.60 0.62 0.00717 540 0.60 0.90 0.01118 540 0.86 0.69 0.01019 480 0.69 0.87 0.010

E. Todesco 30th March 2009 – Decay and harmonics in MQXA- 7

Decay OTHER HARMONICS

Other multipolesAll other multipoles are neglectedThere is an unexplained systematic decay in a4

b 3 a 3 b 4 a 4 b 5 a 5 b 6 a 6 b 7 a 7 b 8 a 8 b 9 a 9 b 10

Ave -0.01 -0.02 -0.02 -0.57 0.02 0.00 0.58 0.01 0.00 0.00 0.00 0.00 0.00 0.00 -0.02

Stdev 0.40 0.32 0.09 0.53 0.13 0.11 0.13 0.03 0.01 0.01 0.01 0.01 0.00 0.00 0.00

Min -0.79 -0.74 -0.23 -1.61 -0.26 -0.24 0.26 -0.07 -0.02 -0.02 -0.02 -0.02 -0.01 -0.01 -0.03

Max 0.87 0.49 0.10 0.50 0.24 0.23 0.79 0.05 0.04 0.02 0.01 0.01 0.01 0.01 -0.01

Ave 0.12 -0.08 0.01 -0.66 0.01 0.00 0.88 0.01 0.01 -0.01 0.00 -0.01 0.00 0.00 -0.04

Stdev 0.64 0.44 0.15 0.81 0.20 0.20 0.23 0.04 0.02 0.03 0.01 0.02 0.01 0.01 0.01

Min -1.26 -0.85 -0.33 -1.85 -0.47 -0.34 0.45 -0.04 -0.02 -0.06 -0.02 -0.04 -0.02 -0.01 -0.05

Max 1.52 0.75 0.30 1.18 0.29 0.47 1.27 0.07 0.06 0.05 0.02 0.03 0.01 0.01 -0.02

Aft

er 2

0 m

inut

esA

fter

200

m

inut

es

E. Todesco 30th March 2009 – Decay and harmonics in MQXA- 8

CONTENTS

Decay

Field harmonicsAllowedNot allowed

E. Todesco 30th March 2009 – Decay and harmonics in MQXA- 9

Field harmonics: ALLOWED

The MQXA are critical after the squeezeWe propose to set the model at high field exactly on the measured valuesGeometric set at value at 7 TeVA persistent component can recover the 1.1 unit difference at injection

For the allowed b6, b10

Small changes from 3.3 to 6.8 TeVNo need of different settings at 4-7 TeVb10 always negligible

b6 b10Ave -0.81 0.04Std 0.22 0.01Ave 0.38 -0.01Std 0.08 0.00Ave 0.33 -0.01Std 0.08 0.01Ave 0.33 -0.01Std 0.09 0.01Ave 1.13 -0.06

Std 0.24 0.01

392 A

3207 A (3.3 TeV)

6177 A (6.3 TeV)

6677 A (6.8 TeV)

6677 A - 392 A

E. Todesco 30th March 2009 – Decay and harmonics in MQXA- 10

Field harmonics: ALLOWED

Geometric:One per magnetSet at the value at 7 TeV

Persistent componentOne per family, to take into account of about -1 units at injection

pinjError of ~0.2 units at 2000-4000 A

b6 b102 0.520 -0.0043 0.462 -0.0024 0.457 -0.0035 0.486 -0.0036 0.441 -0.0057 0.378 -0.0058 0.396 -0.0159 0.347 -0.013

10 0.214 -0.01111 0.424 -0.01112 0.348 -0.01213 0.334 -0.01614 0.359 -0.01115 0.302 -0.00816 0.360 -0.00617 0.311 -0.00818 0.338 -0.01019 0.348 -0.007

-1.5

-1.0

-0.5

0.0

0.5

0 2000 4000 6000 8000

b6

(uni

ts)

Current (A)

Integral

Dcloop

Fit

E. Todesco 30th March 2009 – Decay and harmonics in MQXA- 11

Field harmonics: NOT ALLOWED

The MQXA are critical after the squeezeWe propose to set the geometric on the measured value at 7 TeV

For the not allowedSystematic b4 of about 1.3 units - relevant

Systematic a3 of 0.2 units – all the other systematic to zero

Offset at injection: all close to zero except a4, which has a systematic at injection of -1.3 unitsSpread at injection much larger than at high field – to be added in the MAD model as a random component

b3 b4 b5 b7 b8 b9 a3 a4 a5 a6 a7 a8 a9Ave -0.12 1.28 0.04 0.00 0.03 -0.01 0.35 -1.32 0.09 -0.01 -0.01 0.00 0.00Std 1.05 0.15 0.31 0.03 0.02 0.02 1.01 1.27 0.27 0.04 0.03 0.02 0.01Ave 0.01 1.24 0.00 0.00 0.02 0.00 0.21 -0.06 0.02 -0.03 0.00 0.00 0.00Std 0.28 0.11 0.04 0.01 0.00 0.00 0.35 0.26 0.04 0.02 0.01 0.01 0.00Ave 0.03 1.28 -0.01 0.00 0.02 0.00 0.21 -0.02 0.01 -0.03 0.00 0.00 0.00Std 0.30 0.11 0.04 0.01 0.00 0.01 0.36 0.27 0.04 0.02 0.01 0.01 0.00Ave 0.04 1.30 0.00 0.00 0.02 0.00 0.21 -0.02 0.01 -0.03 0.00 0.00 0.00Std 0.31 0.11 0.04 0.01 0.00 0.01 0.37 0.28 0.04 0.02 0.01 0.01 0.00Ave 0.17 0.02 -0.05 0.00 0.00 0.00 -0.14 1.30 -0.08 -0.02 0.01 0.00 0.00

Std 1.08 0.14 0.29 0.03 0.02 0.02 1.08 1.26 0.29 0.04 0.03 0.02 0.01

392 A

3207 A (3.3 TeV)

6177 A (6.3 TeV)

6677 A (6.8 TeV)

6677 A - 392 A

E. Todesco 30th March 2009 – Decay and harmonics in MQXA- 12

CONCLUSIONS

Geometric: set on values at collision (about 7 TeV), one component per magnet

Negligible difference from 5 to 7 TeV

Persistent: about -1 unit on b6, taken into account by a persistent component, the same for every magnetPersistent: about 0.06 units in b10, neglected

For MAD: additional spreads from collision to injection given

Decay: negligible effect on TF, b6, b10Fit for b6 has been computed as an excercise