banana dispersion& kick-response

Data taken during Ti8 Test on 7th June 2009

J. Wenninger, K. Fuchsberger

Higher order dispersion

Kick-response measurement and b3

Contents

Third order fits, nominal model

Dispersion derived by third order fits I

• nominal model• trimmed deltap-values

Quite large errors in Dx

Offset in Dx’, Large error at the end

Huge unpredicted valuesFor Dx’’

BPM nonlinear scalingPolynomials provided by BI to apply to data from the frontends (x1, y1):

x, y, x1 and y1 in mm

Dispersion derived by third order fits II

• nominal model• trimmed deltap-values• BPM scaling polynomials applied

Dx’ better centered, but too high

Dx’’ much lower

Response measurement

Vertical error increasing (phase)

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

BPM gains?

BPM gains• Corrector gains fixed• Dataset taken with 25 Correctors• Fit with monitor gains, kqf, kqd

Average gain ~ 1.12

• This was also visible in 2004 (But for some reason not last year?)

Monitor Gains in LHC?LHC S78,August 2008 (we stated ‘perfect’ ;-):

But: reanalyzed and looking a little bit closer:Average gain ~ 1.10

Dispersion derived by third order fits III

• nominal model• trimmed deltap-values• BPM scaling polynomials applied• additional factor of 1/1.12 applied (after polynomials)

Nice Dx!

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.

Third order fits, model b3=-4.68

Dispersion derived by third order fits IV

• model with b3=-4.68• trimmed deltap-values• BPM scaling polynomials applied• additional factor of 1/1.12 applied (after polynomials)

!?

b3 generates Dx’’ (although not the measured one ;-)

Preliminary Conclusions: We can reconstruct second order dispersion

which is in agreement with estimated b3 b3 is not dependent on flat-top length

Open issues: Source for monitor gain factor (~1.1)

unclear How to fix deltap/p ?

Conclusions and open issues