Magnetic Behavior of LHC Correctors: Issues for Machine Operation

W. Venturini Delsolaro AT-MTM;

Inputs from A. Lombardi, M. Giovannozzi, S. Fartoukh, J.P. Koutchouk, V. Remondino, R.Wolf

LHC workshop “Chamonix XIV”

January 18-21, 2005

Outline

Magnetic measurements available today Issues on the magnetic behavior

Transfer functions: required accuracy, hysteresis and reproducibility of machine settings

Field quality panorama Cross talks

Plan for the remaining (cold) measurements Conclusions

Corrector Zoo

SHORT SUMMARY OF CORRECTOR MAGNET PARAMETERS. Magnet

Assembly Nr of

correctors Aperture

(mm) number Main

Component Nominal Strength BN or AN

Current (A)

Magn. Length (mm)

MCDO 2 nested

58 1232 B5 B4

1.2 E6 T/m4 8200 T/m3

550 100

66 66

MCS 1 58 2464 B3 1630 T/m2 550 110 MO 2 56 168 B4 6.3 E4 T/m3 550 320

MQT 2 56 160 B2 123 T/m 550 320 MQS 2 56 32 A2 123 T/m 550 320

MSCB 4 56 376 B3, A3 B1, A1

4430 T/m2 2.9 T

550 55

369 647

MQTL 2 56 60 B2 129 T/m 550 1300 MCBC 2 56 84 B1, A1 3.1 T 100 904 MCBY 2 70 38 B1, A1 2.5 T at 4.5K 72 899 MCBX 2

nested 90 18 A1

B1 3.26 T 3.35 T

550 550

480 450

MCBXA =MCBX + MCSTX

4 nested

70 9 A1 B1

B3

B6

3.26 T 3.35 T

52 T/m2 7.22E6T/m5

550 550 50 80

480 450 576 615

MQSX 1 70 9 A2 80.2 T/m 550 223 MCSOX 3

nested 70 9 A4

B4 A3

9666 T/m3 9229 T/m3 377 T/m2

100 100 100

138 137 132

Where we are: summary of cold measurements and c/w campaigns (FQWG 16/11/04)

Corrector type Pre series Series Cold/warm

MCS 10+10 none good

MCDO 10+10 none poor

MO 3 assemblies none 1 mod., fair

MQT/S 3 assemblies 8 modules poor, improving

MCB 1 assembly 2 ass. + 4 mod. good

MS 1 assembly 1 ass. + 3 mod. 1 mod., fair

MCBC 1 assembly 1 module 1 mod., fair

MCBY none none -

MQTL 2 modules - -

MCBX+MCBXA 2 17/25 fair

MQSX+MCSOX 1 8/9 to check

Tolerable uncertainties on the settings of main components (1)

Orbit Correctors in the Arcs (MCB, individually powered):

Closed orbit perturbation from N randomly distributed kicks:

For any given <x>, the tolerable ΔBlrms is found, as a function of

Bρ, and of correction scenario taking <x>rms=2 mm, N=200, the tolerable ΔBlrms at 7 TeV

is

about 4 10-2 Tm, that is 2% of the maximum value (same at injection to get a circulating pilot beam?)

Becomes 1‰, if we take <x>= 0.1 mm (for efficiency of collimation) 1.28 10-4 Tm absolute rms error at injection

0.3% of rms excitation of arc correctors

)(22

)()( 1

QSin

Ns

B

lBsx

Tolerable uncertainties on the settings of main components (2): Tuning Quadrupoles (MQT)

From the operational tolerance on tune shifts (±3 10-3)

At injection, it corresponds to a total integrated MQT field (in Tm at 17 mm) of 5.3 10-3 Tm 6.7 10-4 Tm accuracy

for one single magnet

Figures 10 times lower if we take 10% of the operational tolerance

4

lkQ

)(4 2

ml

Qk

)(4

2 TmQBR

lB ref

From which one gets Q/B2l=0.56/Tm at 17 mm at injection

Tolerable uncertainties (3)… MCS: 1.5 10-4 Tm absolute accuracy at

injection to assure reproducibility of Q’ within 10 units

MS: 7 10-4 Tm absolute accuracy at injection 10 unit of Q’

MO to be determined, not critical: 5% should be OK

IR correctors to be determined, potentially critical

Sample sizes for cold tests

From σ of cold measurements (when available), and required uncertainty u, for a 100(1- α)% confidence interval

Deduce n(u, α) from the usual formula for the estimated standard error of a sample of n units

u= σ t(α, n-1)√(1/n-1/N)

Where t is the Student distr. and N the population number

Different u, σ and N for each corrector type

The problem of hysteresis

Magnetic hysteresis from the superconducting filaments and from the iron affects all the sc correctors

“Likely” settings at injection for some correctors (orbit, tuning, b3 spool pieces) are at very low current

Trims might be numerous and require reversing of current ramps (for example orbit corrections)

As a consequence, hysteresis on the corrector transfer functions results in a “randomization” of the corrector magnetic state (position on the hysteresis loops: upper or lower branch)

Consequences on reproducibility of settings, notably between runs

compare the resulting “uncertainty” to operational optics tolerances

Table of Hysteresis at 0A for some corrector types (Mainly from pre series measurements)

Orbit

Lattice

Multipole

Tm @ 17 mm

Tm @ 17 mm

Tm @ 17 mm

MCB

10-3

MQT

2 10-4

MCS

6 10-5

MCBC

1.3 10-3

MQTL

1.6 10-4

MCD

10-5

MCBY

?

MS

10-3

MCO

10-4

MCBX

6 10-3

MO

4.6 10-4

Hysteresis of orbit corrections Compare kick at injection due to hysteresis

to some tolerance on CO displacement….

10-3 Tm at injection randomly distributed amongst 200 MCB 782 μm rms on CO

1) Reproducibility at 100 μm level not to be obtained if hysteresis is ignored

2) May have an influence on the convergence of correction algorithms

Hysteresis of tune corrections

Taking ΔQ/ΔB2l=0.56/Tm at injection,

the hysteresis width of a single MQT corresponds to ΔQ=1.1 10-4

For one circuit of 8 MQT 9 10-4 ,

Remember the tolerance on ΔQ=±3 10-3

Considering 8 circuits 7 ·10-3 (!)

Consequence on tune corrections at injection From cold measurement of MQT-MA-003

2.0E-02

3.0E-02

4.0E-02

5.0E-02

6.0E-02

7.0E-02

8.0E-02

9.0E-02

1.0E-01

1 1.2 1.4 1.6 1.8 2

Current in 8 MQT circuits [A]

Q

ΔI to cross the loop is related to re-penetration of filaments plus iron hysteresis: Hp =30 mT (1 A for the MQT)

7 10-3

MA-E-0001, Coil 0607, 1.8K

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

-600 -400 -200 0 200 400 600

Current [A]

B3 @

r=

17m

m [T

m]

-6.E-05

-5.E-05

-4.E-05

-3.E-05

-2.E-05

-1.E-05

0.E+00

1.E-05

2.E-05

3.E-05

4.E-05

5.E-05

B3 d

evi

atio

n @

r=17m

m [T

m]

Corresponds to a jump in Q’ of 3.8 units

Excitation curve of a pre series MCS

Hysteresis of Lattice Sextupoles

0.E+00

2.E-04

4.E-04

6.E-04

8.E-04

1.E-03

1.E-03

1.E-03

0 50 100 150 200 250 300 350

Current [A]

Wid

th o

f B

3 h

yste

resi

s lo

op

(T

m @

17

mm

)

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

-30 -10 10 30Current (A)

B3

(Tm

@ 1

7 m

m)

Corresponds to

more than 10 units of Q’

Field quality panorama

Warm measurements: the emerging spikes

-45-40-35-30-25-20-15-10

-505

1015202530354045

0 2 4 6 8 10 12 14

FQWG target

mec. target

measured

MQT modules: systematic vs

b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12 b13 b14

0

2

4

6

8

10

12

-50 -40 -30 -20 -10 0 10 20

Mean= -40.281Standard deviation=2.003Target value= 0

freq

ue

[units]

b3

b3=-40 units in MCBC

b6=-10 units and b10=-15 units in MQT, and… MQTL!

Field quality at warm and at 1.9 K of the first 2 MQTL modules (pre series)

-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

14

16

18

20

b3 a3 b4 a4 b5 a5 b6 a6 b7 a7 b8 a8 b9 a9 b10 a10

Harmonic No.

Un

its

@ r

=1

7 m

m

MQTL1_COLD_avg100A

MQTL1_WARM_bench2

MQTL2_COLD_avg100A

MQTL2_WARM_bench2

Likely field quality of Q6 in IR3 and IR7, done with 6 MQTL

Series MCBC module measured

at warm and at 1.9 K

MCBC 35 (August 2004)

-60.00

-50.00

-40.00

-30.00

-20.00

-10.00

0.00

10.00

warm

cold at 100 A

Cross talks

Between apertures at high field (MSCB, MQTL) Checked for 2 MSCB variants and found to be

negligible (order of 10-4 Tm between the MCB) Effects foreseen for the MQTL assemblies

In nested magnets (MCDO, Inner Triplet correctors) Very few measurements, to be completed with

extended programs on the spare units

Cross talk effects in nested magnets (MCBX)

-0.0015

-0.001

-0.0005

0

0.0005

0.001

0.0015

-0.3 -0.2 -0.1 0 0.1 0.2 0.3B1 (T )

T @

17

mm

B 3

A 3

B1

A1

Proposal for minimal cold measurements plan

Corrector type TF Hysteresis measurement

setting up cycle

MCS 10+10 (1%) yes

MCDO 10+10 (1%) ?

MO 9 no

MQT/S 9 yes

MSCB 12 yes

MCBC 9 yes

MCBY 9 yes

MQTL 4 yes

MCBX+MCBXA - yes

MQSX+MCSOX - yes

Conclusions The knowledge of the transfer functions with 10-3

accuracy would be needed to set some corrections. Transfer functions are not linear.

Very few measurements so far. Sample sizes not defined The hysteresis of main components is an issue. Set up

cycles will have to be defined, in particular for nested magnets. Refined measurements and models may be needed for operation

Field quality of MQTL and MCBC is at the limit of tolerance Plan for the cold series measurements must provide

sufficient experimental data for modeling work

Thanks to

L. Bottura,

A. Lombardi,

S. Fartoukh,

M. Giovannozzi,

J. P. Koutchouk,

V. Remondino,

L. Walckiers

R. Wolf