Bent combined function bending magnets and optics: the case of SESAME Attilio Milanese 3 Dec. 2014

Attilio Milanese2 SESAME storage ring: the optics and the magnets

SESAME: a light source in the Middle East 3 Dec. 2014Attilio Milanese3 courtesy of Amor Nadji Synchrotron-light for Experimental Science and Applications in the Middle East

SESAME storage ring: basic optical functions 3 Dec. 2014Attilio Milanese4 courtesy of Maher Attal Double-Bend Achromat with dispersive straight sections

SESAME storage ring: the magnets inventory 3 Dec. 2014Attilio Milanese5 16 BM: combined function bending (here in Nov the pre-series at ALBA, Spain, undergoing magnetic measurements) 32 QF: focusing quadrupoles 32 QD: defocusing quadrupoles 64 SF/SD: sextupoles correctors embedded in the sextupoles (here in summer 2014 all pre-series multipole magnets at CERN for magnetic measurements and acceptance tests)

The dipole: basic requirements and features 1 Feb. 2013Attilio Milanese6 laminations stacked parallel along a circular arc end pole shims: 3 stacks tuneable from 0 to 14 mm each in 50 mm thick solid end plate (magnetic) bending angle22.5 deg magnetic length2.250 m bending radius m 2D 2.5 GeV T field index11 2D 2.5 GeV-2.79 T/m combined function (dipole + quad.): circular arc (no hyperbola) in the poles

3 Dec. 2014Attilio Milanese7 How does the field look like? OPERA 3D simulations and measurements at ALBA of last week

The usual jargon… 3 Dec. 2014Attilio Milanese8 Ex. from MAD-X : a set of parameters magnetic length rectangular / sector magnet fringe fields, hard-edge, field drop-off pole face rotation (entrance / exit), edge focusing / defocusing RBEND L=real ANGLE=real TILT=real K0=real K0S=real K1=real E1=real E2=real FINT=real FINTX=real HGAP=real K2=real H1=real H2=real

The “raw” data: B x, B y and B z 3 Dec. 2014Attilio Milanese9 Field maps on the midplane from 3D simulations (B x = B z = 0) from 3D Hall probe measuring bench [at coordinates, 4 hours] X Y Z B x [T]B y [T]B z [T] [ex. from 2014_11_28 field map]

B y along reference path, 2.5 GeV 3 Dec. 2014Attilio Milanese10 drop-off due to saturation (flatter at injection energy) fringe field [ simulated ∫By 1.1% above the measured value ]

Gradient along reference path, 2.5 GeV 3 Dec. 2014Attilio Milanese11 [ simulated ∫G 1.3% above the measured value ] [ simulated ∫G/∫B y 0.2% above the measured value ] in(famous) edge effect (less commented upon) 1/cos(  ) “central” effect Gradient taken in the “radial” direction, orthogonal to the beam

Non-linear field components 3 Dec. 2014Attilio Milanese12 No change needed to the end pole shims. [We keep the nonlinearities small so we don’t deal with them…] integrated field homogeneity 1∙ ∙10 -4

Non-linear field components 3 Dec. 2014Attilio Milanese13 “Sextupole” / “octupole” along the magnet, from polynomial fits of field vs. radial coordinate. A little mathematical blasphemy, but for the beam… “Nonlinear edge effects” can be well simulated with symmetric 3D models. Lead end / return end coil asymmetry does not play a considerable role.

3 Dec. 2014Attilio Milanese14 Dipole meets optics: let’s stay tuned…

as a common language the 2×2 transfer matrices – radial position x and divergence x’ – vertical position y and divergence y’ 3 methods are applied to simulated field maps (different end pole shimming configuration than on final magnet) in all cases an “equivalent” transfer matrix can be fit – composition of sector bending magnet × thin quadrupole × drift results are shown next for the betatron tunes Q x / Q y – several digits reported for sake of numerical comparison Dipole meets optics (first talks) 3 Dec. 2014Attilio Milanese15

Method 1: integrating B, G overall in fine steps 3 Dec. 2014Attilio Milanese16 break the integration path in small  z multiply the many  M matrices to get a single M zz B, G energypath zz QxQx 2.5 GeVtrajectory1 mm GeVtrajectory5 mm GeVcircular arc + line1 mm GeVtrajectory1 mm ref. path ℓ ref

Method 2: integrating B and G in blocks 3 Dec. 2014Attilio Milanese17 slices according to variations of B and G along the way keep intermediate M i matrices, fewer than before energypath# of M i QxQx 2.5 GeVcircular arc + line GeVcircular arc + line GeVcircular arc + line GeVcircular arc + line G z

Method 3: tracking offset particles 3 Dec. 2014Attilio Milanese18 no computation of G as intermediate quantity compute single M from transfer, ex. M 11 = x out /x in symplecticity can be enforced normalizing M energy  z of RK4 ∫ offsetQxQx 2.5 GeV1 mm1 mm / 1 mrad GeV0.1 mm1 mm / 1 mrad GeV1 mm0.5 mm / 0.5 mrad GeV1 mm0.5 mm / 0.5 mrad x=0 x=x in x=0 x=x out

Comparison Q x at 2.5 GeV 3 Dec. 2014Attilio Milanese19 Method 1 path zz QxQx trajectory1 mm trajectory5 mm circular arc + line1 mm Method 3 path# of M i QxQx circular arc + line circular arc + line circular arc + line Method 2  z of RK4 ∫ offsetQxQx 1 mm1 mm / 1 mrad mm1 mm / 1 mrad mm0.5 mm / 0.5 mrad /

good agreement on Q x among methods based on integrating B, G and tracking, at 2.5 GeV and 0.8 GeV Q x variation of 0.02 between 0.8 and 2.5 GeV – computation of trajectories also show an overall length decrease of 2.0 mm for whole ring from 0.8 to 2.5 GeV, due to different iron saturation in the ends similar results for Q y (not shown), using Further comparisons 3 Dec. 2014Attilio Milanese20 methodQxQx 1 – integrating B and G in fine steps – integrating B and G in 32 blocks – tracking offset particles / GeV

Possible future work / extensions 3 Dec. 2014Attilio Milanese21 apply the methods to the measured field maps, including also skew (not-allowed) terms and misalignments interface the data directly to beam dynamics software (so far the tunes were computed via elementary matrix operations), as to include dispersion, beta functions, coupling, non-linear terms, and so on characterize the series of 16 magnets, to form a basis for possible sorting (although high reproducibility is a target)

3 Dec. 2014Attilio Milanese22 Special thanks to the EC for the CESSAMag (CERN-EC Support for SESAME Magnets) funds, FP7 contract the colleagues at CERN, ALBA and SESAME TESLA, the industry partner for the manufacturing of the dipoles thank you شكرا (shukran) eυχαριστώ (efharistó) ممنون (mamnoon) شكريه (shukriya) teşekkür ederim תודה (toda)

A few references 3 Dec. 2014Attilio Milanese23 H. Winick, “Synchrotron radiation sources, a primer,” World Scientific, 1994 (ch. 7, Magnetic Measurements, by R. P. Walker) G. Vignola, M. Attal, “SESAME lattice,” SESAME Technical Note O-1, Dec D. Einfeld et al., “Modelling of gradient bending magnets for the beam dynamics studies at ALBA”, PAC07 A. Milanese et al., “Design of the main magnets of the SESAME storage ring,” IPAC 2014 A. Milanese, “Coupling field maps of the combined function bending magnets to linear optics for the SESAME storage ring,” CERN-ACC-NOTE