1

Hints for a systematic b3 in the TI8 main bends

K. Fuchsberger

2009-06-29

2

Kick response measurements

Dispersion measurement

2009-06-29

Contents

Kick - Response measurement

Vertical error increasing (phase)

H response (MCIAH.80204)V response (MCIAV.80104)

42009-06-29

Off-momentum KR-measurmentsnominal model

H:Dp/p dep.Only partly reproduced by model

V:Phase error for Dp/p=0, but almost no Dp/p dep. of measured data.

002.0pp 002.0

pp

(Data: 2008-09-05)

52009-06-29

Off-momentum KR-measurmentsfitted model

H:

V:

002.0pp 002.0

pp

06.585.0

1061.5

1051.7

3

2

3

40

bbKKpp

(Data: 2008-09-05)

6

b3: flat-top-length dependent?

FT-length (s) b2 b3 deltak/k deltap/p deltarms0.25 2.64 -4.79 0.0029 -0.0021 1.94 +- 0.33

0.5 2.55 -4.61 0.0029 -0.0020 2.00 +- 0.302 2.57 -4.65 0.0030 -0.0021 1.99 +- 0.34

average 2.59 -4.68 0.0029 -0.0021stddev 0.04 0.09 0.0001 0.0000

0 0.5 1 1.5 2 2.5

-6.00-5.00-4.00-3.00-2.00-1.000.001.002.003.004.00

b2, b3

b2b3

length of FT (s)

units

0 0.5 1 1.5 2 2.5

-0.0030-0.0020-0.00100.00000.00100.00200.00300.0040

deltak/k, deltap/p

deltak/kdeltap/p

length of FT (s)

1

b3 is independent on FT length (average = -4.68)

• b2, deltak/k, deltap/p unrealistic, but related by transformation.

(Data: 2009-06-07)

Fits to Kick-response data:

2009-06-29

7

Dispersion, nominal model

(Data: 2009-06-07) 2009-06-29

8

Dispersion nominal model

• BPM scaling polynomials applied• additional factor of 1/1.12 applied (after polynomials)

2nd order Dispersion higher than predicted by model!

(Data: 2009-06-07) 2009-06-29

9

Dispersion, model b3=-4.68

2009-06-29(Data: 2009-06-07)

10

Dispersion, model b3=-4.68

• BPM scaling polynomials applied• additional factor of 1/1.12 applied (after polynomials)

!?

(Data: 2009-06-07) 2009-06-29

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Results from fit:1. Calc parameters from Kick-

Response2. With resulting values fit xi

and Dp/p to Dispersion.3. Fit Kick-Response with fixed

Dp/p4. Go to 2.

2009-06-29

b3 – best estimate for the moment

67.477.0

1022.6

101.9

3

2

3

40

bbKKpp

(Data: 2009-06-07)

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Preliminary Conclusions: A model including b3 (between about -4 and -5

units) reproduces very well both the measured dispersion- and kick-response- data.

The effect is independent on the flat-top length.

Questions: What is a realistic (measured) average value for a

b3 the MBIs used in TI8? What else could be the source of the observed

effects?

Conclusions and Questions

2009-06-29

132009-06-29

Thank You!

14

Fit to extract deltap/p and xi

2009-06-29(Data: 2009-06-07)

15

Dispersion using this model (without xi)

2009-06-29(Data: 2009-06-07)

!?

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Model of Dp-dependence

ppbCbB

pp

KKAR ijijijij

32

pp

pp

pp 0

with

Relation to madx strengths:

!110 41

ref1

nlR

bk nn

n