[PPT] - Efficient methods for tune and chromaticity The NAFF method PowerPoint Presentation

SLIDE 1

Efficient methods for tune and chromaticity measurements in lepton and hadron rings

P. Zisopoulos,
Y. Papaphilippou

The NAFF method Simulations

Set-up Results

Results from Experimental Data

ANKA LHC

A method to measure Chromaticity

Results

Summary

Efficient methods for tune and chromaticity measurements in lepton and hadron rings

P. Zisopoulos1,2
Y. Papaphilippou1

1CERN 2Department of High Energy Physics

University of Uppsala

21/1/2016

SLIDE 2

Efficient methods for tune and chromaticity measurements in lepton and hadron rings

P. Zisopoulos,
Y. Papaphilippou

The NAFF method Simulations

Set-up Results

Results from Experimental Data

ANKA LHC

A method to measure Chromaticity

Results

Summary

Frequency analysis for accelerators

◮ Refined Fourier analysis of turn by turn transverse beam

position data measurements can determine several beam properties.

◮ The procedure is quite straightforward. The beam is kicked and

the beam position monitors measure the centroid of the bunches.

SLIDE 3

Efficient methods for tune and chromaticity measurements in lepton and hadron rings

P. Zisopoulos,
Y. Papaphilippou

The NAFF method Simulations

Set-up Results

Results from Experimental Data

ANKA LHC

A method to measure Chromaticity

Results

Summary

The NAFF Algorithm

◮ Given f(t)=∞ k=−∞ αkeiωkt,

an approximation can be constructed f′(t)=N

k=1 α′ keiω′

kt over

[−T, T].

◮ By searching for the maximum of

< f (t), eiσt >=

1 2T

T

−T f (t)eiσtχ(t)dt, where χ(t) is a weight

function, ω1 is found. Obtain α′

1 and repeat on

f1(t) = f (t) − α′

1eiω1t. ◮ For χ(t) a Hanning Window: ω − ωT ∼ 1 T 4

SLIDE 4

Efficient methods for tune and chromaticity measurements in lepton and hadron rings

P. Zisopoulos,
Y. Papaphilippou

The NAFF method Simulations

Set-up Results

Results from Experimental Data

ANKA LHC

A method to measure Chromaticity

Results

Summary

Decoherence effects

◮ Detuning effects on the particles’

distribution leave a limited number of turns for analysis.

◮ Even for refined Fourier Methods, the tune measurements can

be spurious.

◮ In many applications fast tune measurements is needed e.g.

commissioning

SLIDE 5

Efficient methods for tune and chromaticity measurements in lepton and hadron rings

P. Zisopoulos,
Y. Papaphilippou

The NAFF method Simulations

Set-up Results

Results from Experimental Data

ANKA LHC

A method to measure Chromaticity

Results

Summary

Mixing the BPM data together

◮ Suppose the TxT data for N turns and from M BPMs are

stored in a matrix x1[1] x2[1] ... xM[1] x1[2] x2[2] ... xM[2] ... ... ... ... x1[N] x2[N] ... xM[N]

◮ Vectorize the matrix as:

˜ x = [x1[1]x2[1]...xM[1]

First Period

... x1[N]x2[N]...xM[N]

M Period

]

◮ This transformation results in the increase of the sampling rate

from 1 sample/turn to M samples/turn.

◮ The new tune is ˜

Q = Q

M . If M ≥ Q 2 then the integer part of the

tune can be also obtained.

SLIDE 6

Efficient methods for tune and chromaticity measurements in lepton and hadron rings

P. Zisopoulos,
Y. Papaphilippou

The NAFF method Simulations

Set-up Results

Results from Experimental Data

ANKA LHC

A method to measure Chromaticity

Results

Summary

Error in the sampling rate

◮ The BPMs are not symmetrical to the longitudinal position or

to the optics of the lattice. The increase in the sampling rate inherits an error which is 1-periodic.

◮ NAFF convergence with mixed BPMs: ∆Q ∼

1 (MN)4

dominant

+ δ(M)

error ◮ The Fourier spectra are not corrupted by this procedure. The

modulation from the periodic error just adds sidebands in the spectra.

SLIDE 7

Efficient methods for tune and chromaticity measurements in lepton and hadron rings

P. Zisopoulos,
Y. Papaphilippou

The NAFF method Simulations

Set-up Results

Results from Experimental Data

ANKA LHC

A method to measure Chromaticity

Results

Summary

Simulations with MADX-PTC

Table: Main lattice and beam parameters of the ANKA model that was used in simulations. Parameter Value C 110.4 m E 2.5 GeV Lattice 4×2 DBA M 35 BPMS Qx Qy 6.79 2.69 Q′

x Q′ y

2.57 6.89 Qs 1.6×10−2 σδ [10−4] 9.12 σx σy [10−4] 8.9 23

SLIDE 8

Efficient methods for tune and chromaticity measurements in lepton and hadron rings

P. Zisopoulos,
Y. Papaphilippou

The NAFF method Simulations

Set-up Results

Results from Experimental Data

ANKA LHC

A method to measure Chromaticity

Results

Summary

Convergence

◮ Reference tune: The tune of a particle at the center of the

distribution.

SLIDE 9

Efficient methods for tune and chromaticity measurements in lepton and hadron rings

P. Zisopoulos,
Y. Papaphilippou

The NAFF method Simulations

Set-up Results

Results from Experimental Data

ANKA LHC

A method to measure Chromaticity

Results

Summary

Precision

SLIDE 10

Efficient methods for tune and chromaticity measurements in lepton and hadron rings

P. Zisopoulos,
Y. Papaphilippou

The NAFF method Simulations

Set-up Results

Results from Experimental Data

ANKA LHC

A method to measure Chromaticity

Results

Summary

Comparison with Single-BPM analysis

SLIDE 11

Efficient methods for tune and chromaticity measurements in lepton and hadron rings

P. Zisopoulos,
Y. Papaphilippou

The NAFF method Simulations

Set-up Results

Results from Experimental Data

ANKA LHC

A method to measure Chromaticity

Results

Summary

Comparison with Single-BPM analysis

SLIDE 12

Efficient methods for tune and chromaticity measurements in lepton and hadron rings

P. Zisopoulos,
Y. Papaphilippou

The NAFF method Simulations

Set-up Results

Results from Experimental Data

ANKA LHC

A method to measure Chromaticity

Results

Summary

Spectra

SLIDE 13

Efficient methods for tune and chromaticity measurements in lepton and hadron rings

P. Zisopoulos,
Y. Papaphilippou

The NAFF method Simulations

Set-up Results

Results from Experimental Data

ANKA LHC

A method to measure Chromaticity

Results

Summary

Tune measurements by mixing the TxT data

◮ The vertical plane is suffering from strong coupling to the

horizontal motion and the convergence is slower.

SLIDE 14

Efficient methods for tune and chromaticity measurements in lepton and hadron rings

P. Zisopoulos,
Y. Papaphilippou

The NAFF method Simulations

Set-up Results

Results from Experimental Data

ANKA LHC

A method to measure Chromaticity

Results

Summary

Precision

◮ For the experimental data the Singular Value Decomposition

Method was used to lower the noise levels. See. C.X.Wang, Ph.D. thesis (1999)

SLIDE 15

Efficient methods for tune and chromaticity measurements in lepton and hadron rings

P. Zisopoulos,
Y. Papaphilippou

The NAFF method Simulations

Set-up Results

Results from Experimental Data

ANKA LHC

A method to measure Chromaticity

Results

Summary

Tune measurements for the LHC

◮ The TxT from the LHC showed an asynchronous kick between

the BPMs.

◮ Shifting the data accordingly by comparing the phase advances

to the machine’s model, mitigates this effect.

SLIDE 16

Efficient methods for tune and chromaticity measurements in lepton and hadron rings

P. Zisopoulos,
Y. Papaphilippou

The NAFF method Simulations

Set-up Results

Results from Experimental Data

ANKA LHC

A method to measure Chromaticity

Results

Summary

Tune measurements and precision

SLIDE 17

Efficient methods for tune and chromaticity measurements in lepton and hadron rings

P. Zisopoulos,
Y. Papaphilippou

The NAFF method Simulations

Set-up Results

Results from Experimental Data

ANKA LHC

A method to measure Chromaticity

Results

Summary

Chromatic modulation of the centroid’s motion

◮ Due to chromatic decoherence the Fourier amplitudes of the

centroid can be written as Aq = e−s2 ¯ aIq(s2)(1 + ∆β1

2β Qs Q′

x q) with

s = Q′

xσδ

Qs

(see P. Zisopoulos Y. Papaphilippou ’Frequency Maps Analysis of Tracking and Experimental Data’ IPAC 2014)

◮ Q′ is connected to the amplitudes via Q′ = ± Qs σδ

A1+A−1

A0 ◮ Note that strong kicks induce non-linearities and the

relationship does not hold.

SLIDE 18

Efficient methods for tune and chromaticity measurements in lepton and hadron rings

P. Zisopoulos,
Y. Papaphilippou

The NAFF method Simulations

Set-up Results

Results from Experimental Data

ANKA LHC

A method to measure Chromaticity

Results

Summary

Simulations for the ANKA ring

SLIDE 19

Efficient methods for tune and chromaticity measurements in lepton and hadron rings

P. Zisopoulos,
Y. Papaphilippou

The NAFF method Simulations

Set-up Results

Results from Experimental Data

ANKA LHC

A method to measure Chromaticity

Results

Summary

Simulations for the ANKA ring

SLIDE 20

Efficient methods for tune and chromaticity measurements in lepton and hadron rings

P. Zisopoulos,
Y. Papaphilippou

The NAFF method Simulations

Set-up Results

Results from Experimental Data

ANKA LHC

A method to measure Chromaticity

Results

Summary

Simulations for the ANKA ring

SLIDE 21

Efficient methods for tune and chromaticity measurements in lepton and hadron rings

P. Zisopoulos,
Y. Papaphilippou

The NAFF method Simulations

Set-up Results

Results from Experimental Data

ANKA LHC

A method to measure Chromaticity

Results

Summary

Simulations for the ANKA ring

SLIDE 22

Efficient methods for tune and chromaticity measurements in lepton and hadron rings

P. Zisopoulos,
Y. Papaphilippou

The NAFF method Simulations

Set-up Results

Results from Experimental Data

ANKA LHC

A method to measure Chromaticity

Results

Summary

Experimental data from ANKA

SLIDE 23

Efficient methods for tune and chromaticity measurements in lepton and hadron rings

P. Zisopoulos,
Y. Papaphilippou

The NAFF method Simulations

Set-up Results

Results from Experimental Data

ANKA LHC

A method to measure Chromaticity

Results

Summary