Efficient methods for tune and chromaticity measurements in lepton and hadron rings P. Zisopoulos, Y. Papaphilippou Efficient methods for tune and chromaticity The NAFF method measurements in lepton and hadron rings Simulations Set-up Results Results from P. Zisopoulos 1 , 2 Y. Papaphilippou 1 Experimental Data ANKA LHC A method to 1 CERN measure Chromaticity 2 Department of High Energy Physics Results University of Uppsala Summary 21/1/2016
Efficient methods Frequency analysis for accelerators for tune and chromaticity measurements in ◮ Refined Fourier analysis of turn by turn transverse beam lepton and hadron rings position data measurements can determine several beam P. Zisopoulos, properties. Y. Papaphilippou The NAFF method ◮ The procedure is quite straightforward. The beam is kicked and Simulations Set-up the beam position monitors measure the centroid of the Results bunches. Results from Experimental Data ANKA LHC A method to measure Chromaticity Results Summary
Efficient methods The NAFF Algorithm for tune and chromaticity measurements in lepton and hadron rings P. Zisopoulos, Y. Papaphilippou ◮ Given f(t)= � ∞ k = −∞ α k e i ω k t , The NAFF method an approximation can be Simulations constructed Set-up k t over Results f ′ (t)= � N k e i ω ′ k =1 α ′ Results from Experimental Data [ − T , T ]. ANKA LHC A method to measure Chromaticity Results ◮ By searching for the maximum of Summary � T < f ( t ) , e i σ t > = 1 − T f ( t ) e i σ t χ ( t ) dt , where χ ( t ) is a weight 2 T function, ω 1 is found. Obtain α ′ 1 and repeat on 1 e i ω 1 t . f 1 ( t ) = f ( t ) − α ′ ◮ For χ ( t ) a Hanning Window: ω − ω T ∼ 1 T 4
Efficient methods Decoherence effects for tune and chromaticity measurements in lepton and hadron rings P. Zisopoulos, Y. Papaphilippou ◮ Detuning effects on the particles’ distribution leave a limited The NAFF method number of turns for analysis. Simulations Set-up Results Results from Experimental Data ANKA LHC A method to measure Chromaticity Results ◮ Even for refined Fourier Methods, the tune measurements can Summary be spurious. ◮ In many applications fast tune measurements is needed e.g. commissioning
Efficient methods Mixing the BPM data together for tune and chromaticity measurements in lepton and hadron ◮ Suppose the TxT data for N turns and from M BPMs are rings P. Zisopoulos, stored in a matrix Y. Papaphilippou x 1 [1] x 2 [1] ... x M [1] The NAFF method x 1 [2] x 2 [2] ... x M [2] Simulations ... ... ... ... Set-up Results x 1 [ N ] x 2 [ N ] ... x M [ N ] Results from Experimental Data ANKA LHC A method to ◮ Vectorize the matrix as: measure Chromaticity x = [ x 1 [1] x 2 [1] ... x M [1] ˜ ... x 1 [ N ] x 2 [ N ] ... x M [ N ] ] Results � �� � � �� � Summary First Period 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.
Efficient methods Error in the sampling rate for tune and chromaticity measurements in lepton and hadron rings P. Zisopoulos, Y. Papaphilippou ◮ The BPMs are not symmetrical to the longitudinal position or The NAFF method to the optics of the lattice. The increase in the sampling rate Simulations inherits an error which is 1-periodic. Set-up Results Results from Experimental Data 1 ◮ NAFF convergence with mixed BPMs: ∆ Q ∼ ANKA + δ ( M ) LHC ( MN ) 4 � �� � A method to � �� � error measure dominant Chromaticity Results Summary ◮ The Fourier spectra are not corrupted by this procedure. The modulation from the periodic error just adds sidebands in the spectra.
Efficient methods Simulations with MADX-PTC 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 Table: Main lattice and beam parameters of the ANKA model that was ANKA used in simulations. LHC A method to measure Parameter Value Chromaticity Results C 110.4 m Summary E 2.5 GeV Lattice 4 × 2 DBA M 35 BPMS Q x Q y 6.79 2.69 Q ′ x Q ′ 2.57 6.89 y 1.6 × 10 − 2 Q s σ δ [10 − 4 ] 9.12 σ x σ y [10 − 4 ] 8.9 23
Efficient methods Convergence 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 ◮ Reference tune: The tune of a particle at the center of the distribution.
Efficient methods Precision 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 Comparison with Single-BPM analysis 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 Comparison with Single-BPM analysis 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 Spectra 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 Tune measurements by mixing the TxT data 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 vertical plane is suffering from strong coupling to the horizontal motion and the convergence is slower.
Efficient methods Precision 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 ◮ For the experimental data the Singular Value Decomposition Method was used to lower the noise levels. See. C.X.Wang, Ph.D. thesis (1999)
Efficient methods Tune measurements for the LHC 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 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.
Efficient methods Tune measurements and precision 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 Chromatic modulation of the centroid’s motion for tune and chromaticity measurements in ◮ Due to chromatic decoherence the Fourier amplitudes of the lepton and hadron centroid can be written as A q = e − s 2 ¯ aI q ( s 2 )(1 + ∆ β 1 rings Q s x q ) with 2 β Q ′ P. Zisopoulos, s = Q ′ x σ δ Y. Papaphilippou (see P. Zisopoulos Y. Papaphilippou ’Frequency Maps Q s Analysis of Tracking and Experimental Data’ IPAC 2014) The NAFF method Simulations � Set-up ◮ Q ′ is connected to the amplitudes via Q ′ = ± Q s A 1 + A − 1 Results σ δ A 0 Results from Experimental Data ◮ Note that strong kicks induce non-linearities and the ANKA LHC relationship does not hold. A method to measure Chromaticity Results Summary
Efficient methods Simulations for the ANKA ring 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 Simulations for the ANKA ring 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 Simulations for the ANKA ring 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 Simulations for the ANKA ring 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
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