ELENA

PS magnetic & optical model: Preliminary results, status & plans

A. Huschauer, M. Juchno, D. Schoerling, R. WasefOctober 3, 2012

Thanks to all people involved in the continuous improvement of the PS machine for many discussions

2OverviewStudy of the field distribution in the PS main magnetsIntroduction2D structural analysis (ANSYS)2D magnetic including Gaussian distribution of the position of the coils and the shape of the iron with up to 22 DOFs per magnet (OPERA)3D magnetic study (OPERA)Permeability of welds in vacuum chambersBH curve optimization in OperaImplementation in the optical model of PS Including errors in MAD latticeVerification and calibration of the magnetic modelOptical model enhancementsAB TE-MSC-MNC

3PART AStudy of the field distribution in the PS main magnetsIntroduction2D structural analysis (ANSYS)2D magnetic including Gaussian distribution of the position of the coils and the shape of the iron with up to 22 DOFs per magnet (OPERA)3D magnetic study (OPERA)Permeability of welds in vacuum chambersBH curve optimization in OperaImplementation in the optical model of PS Including errors in MAD latticeVerification and calibration of the magnetic modelOptical model enhancementsAB TE-MSC-MNC

4A. I. PS main magnets

B11.2 TB25.2 T/mB32.8 T/m2B436.4 T/m3Taylor decomposition of field (26 GeV/c)

+++ =Normal field components (B1, B2, B3, ) are normal on xz-planeSkew components (A1, A2, A3, ) are normal on yz-plane5+1 independent currents allow for many different settings of multipolesDue to symmetry constraints no skew components allowed in perfect PS main magnets3x2y - y3 = r3 2xy= r2 y= r Dipole: B1Quadrupole: B2Sextupole: B3yxzMain coilsFigure-of-eightW + N PFW TE-MSC-MNC

TE-MSC-MNC5A. I. PS main magnets

Open and closed block of the main magnet units + different current modes (effects PFW + F8)5+1 independent currents available to control the field components and therewith the beam properties (underactuated system):Momentum pTune Qx, QyLinear chromaticity x, yNon-linear chromaticity Qx, Qy

ClosedOpenClosedClosedClosedClosedOpenOpenOpenOpen TE-MSC-MNC

TE-MSC-MNC6A. I. PS main magnets

FocusingDefocusingDipole ContributionB [T/A]Quadrupole ContributionG [Tm-1/A]Fits from simulation exist for multipoles up to octupoleInfluence of currents on field components varies strongly with position and has to be taken therefore into accountIs the pick-up system center aligned with the magnet models center? See also A. Huschauer, 2012xxxx TE-MSC-MNC

TE-MSC-MNC7A. I. Motivation of magnetic studyWorking point controlIdentification of resonancesReasons for resonances: magnet alignment errorsmagnet manufacturing errors

A. Huschauer, Diplomarbeit, Working point and resonance studies at the CERN Proton Synhrotron, 2012A magnetic model with 10-4 precision for the whole machine at all currents including all alignment errors would allow for answering the above questionsCalculated 5-current mode matrix gives good predictions for machine tunes but needs polishing for linear and second order chromaticities.One of the major problems turned out to be the small validity of the matrix, more measurements are either challenging due to beam instability or time consuming, a precise magnetic model is required.Skew sextupole components

LossesNew reference working point with PFWs (constant beam intensity)Skew sextupolar component TE-MSC-MNC

TE-MSC-MNC8A. II. Structural analysis (ANSYS)The simulation and measurement [1] of the deformation of the magnet are similarThe magnetic field is used to derive the normal and skew components of the magnetic fields in Taylor seriesThe effect on the optics of the machine were calculated with MAD-X and PTCThe effect of the deformation is especially visible for 26 GeV/c, because F B2The mechanical deformations cannot explain the measured skew components at low energy[1] M. Buzio, M. Tortrat, Deformation of the PS reference magnet U101 during operation: geometrical survey and impact on B-train magnetic field measurements, April 2010QxQyxy14 GeV/c, normal components (negligible difference between magnetic and structural)6.20586.30320.20230.683714 GeV/c, normal & skew com.6.20586.30320.20220.683926 GeV/c, no deformation, only normal components6.26866.22190.03810.477026 GeV/c, with deformation, only normal components6.26476.21790.11960.396126 GeV/c, with deformation, normal & skew components6.26476.21790.16460.3506

UY TE-MSC-MNC

TE-MSC-MNC9A. III. 2D statistical analysis (Opera)2D calculation including Gaussian distribution of the position of the coils and the shape of the iron with up to 22 DOFs per magnet (OPERA)1000 models per magnet type and current level have to be calculated (