Clarke JA

Holder DJ

Marks N

English

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DESIGN OF THE QUADRUPOLE MAGNETS FOR THE DIAMONDSYNCHROTRON SOURCEN.Marks, J.A.Clarke and D.J.Holder, ASTeC, CLRC Daresbury Laboratory,Warrington WA4 4AD, U.K.AbstractThe 3 GeV synchrotron source, DIAMOND, will be alow emittance electron storage ring with a 24 cell lattice,providing beam-lines from insertion devices and bendingmagnets. The lattice requires 240 quadrupole magnetsdivided into ten families, each family having differentaperture and strength requirements. The specificationshave been rationalised into two magnet cross sections andthree lengths to meet the requirements of all quadrupolesin the lattice. The paper provides information of thechoice of these geometries, together with data from twodimensional finite element modelling. Each quadrupolewill have an individual power supply and the parametersof the common current and voltage specification, whichwill meet the requirements of all quadrupoles, arepresented.1 SPECIFICATION OF PARAMETERS1.1 Determination of Inscribed RadiusThe specification of the quadrupole inscribed radius isdetermined by the geometry of the vacuum vesselcontaining the circulating electron beam.  The relevantparameters for determining the inscribed radius are givenin Table 1. These are based on beam stay-cleardimensions defined elsewhere [1]; the vessel dimensionscorrespond to a smooth, uniform profile vacuum vesselaround the complete lattice.Table 1: Parameters determining quadrupole inscribedradius.horizontal beam stay-clear (total) 80 mmvertical beam stay-clear (total) 34 mminternal tolerance clearance (total) 2 mmvessel wall thickness 3 mmexternal tolerance (assembly & location) 3 mmresulting quadrupole inscribed radius 37 mmThe outer dimensions of the octagonal vessel whichwill be used in, including the necessary space forassembly and clearance, together with the 37 mminscribed radius hyperbolic pole are shown in Fig 1.1.2 Quadrupole ParametersThere are a total of 240 quadrupole magnets, split intoten families, required for the DIAMOND lattice. Thelength, number and horizontal  and vertical good gradienthalf aperture for each family are given in Table 2.Figure 1: Cross-section showing outer dimensions of thestorage ring vacuum vessel (including tolerances) and theR = 37 mm quadrupole magnet pole surface.Table 2: Parameters of ten quadrupole familiesFamily Magneticlength (m)No. perfamilyHoriz.goodgradient(mm)Verticalgoodgradient(mm)Q1AB 0.4 36 ±36 ±16Q2AB 0.4 36 ±20 ±16Q1B 0.4 36 ±25 ±12Q2B 0.6 36 ±25 ±12Q3B 0.3 36 ±25 ±12Q1AD 0.4 12 ±36 ±16Q2AD 0.4 12 ±20 ±16Q1D 0.4 12 ±25 ±12Q2D 0.6 12 ±25 ±12Q3D 0.3 12 ±25 ±12It is uneconomic to adopt an individual design for eachof the families identified in Table 2. It can be noted thatthe families fall into two groups: the small number ofmagnets (48) which require 36 mm half aperture, whichwill call for very broad poles, and the remaining muchlarger number of quadrupoles (192) which need either20 mm or 25 mm half aperture and which can be satisfiedwith a single cross-section design with a narrower polewidth. Thus, it is proposed to have two quadrupole crosssections; the broad pole design being described as ‘W’(for wide) types, and the more conventional magnetsdesignated ‘N’ (for narrow) types. The ‘N’ types arerequired in three different magnetic lengths (0.3, 0.4 and0.6 m), and the length specifications are thereforedescribed by the letters ‘S’,‘M’ and ‘L’ (short, medium,0510152025300 10 20 30 40 50 60x (mm)y (mm)Proceedings of EPAC 2002, Paris, France2367and long). The ‘W’ types are all 0.4 m, ‘M’ lengthmagnets.To provide for a wide range of operational tune points,the maximum quadrupole strengths for all families arespecified as:g = 17.5 T/m;with ‘good gradient’ within the apertures defined as :-0.1%  ≤   ∆g/g(0)  ≤   0.1%.The resulting audit for different quadrupole types isgiven in Table 3.Table 3: Parameters of proposed four types of quadrupole.Type No.requiredMagneticlength(m)Horizontalgoodgradient(mm)Verticalgoodgradient(mm)WM 48 0.4 ±36 ±16NL 48 0.6 ± 25 ±12NM 96 0.4 ± 25 ±16NS 48 0.3 ± 25 ±121.3 Steel SpecificationNon-linear finite element investigations of thequadrupole gradient quality and amplitude wereperformed using the steel B/µ curve specified for thedipole steel and described elsewhere [2]. The steel dataused corresponded to the ‘parallel to rolling direction’values.2 LARGE APERTURE (‘W’ TYPE)QUADRUPOLES2.1 Pole GeometryA pole geometry which would generate the requiredquality of field was developed and modelled. The polefollows the equation:xy = R2/2 out to x = 49.2 mm;with a linear tangent extending to the pole corner atx = 60 mm.From the pole corner, the pole receded at an angle of:45° out to x = 70.0 mm.The pole was then broadened, with each side diverging atan angle of:10° to the pole centre line.This broadening had been found to be necessary atgradients of 17.5 T/m to prevent saturation in the poleroot.The magnet was modelled in four-fold symmetry, witha back-leg thickness of 60 mm; the cross section of one-quarter of the ‘W’ quadrupole, as used for the finiteelement modelling, is shown in Fig. 2.Figure.2: One quarter geometry used for modelling the‘W’ type quadrupole; areas 1 & 3 are high permeabilitysteel; areas 2 & 4 are conductor.2.2 Gradient QualityNon-linear exploration of the gradient quality wasperformed on the one-quarter geometry of Fig. 2 using thetwo-dimensional f.e.a. code, OPERA. Results are shownin Fig 3, where the homogeneity in the gradient of thevertical field (dHy/dx) is plotted as a function ofhorizontal position (x) for five vertical positions withinthe good gradient region.Figure 3: Homogeneity of the field gradient in the ‘W’type quadrupole expressed as a percentage of thevariation from dHy/dx at the origin (0,0), as a function ofx, at differing vertical positions (y = 0, to y =16 mm); thedata extends over the whole 'good gradient' ellipse.The quality complies with the ‘good gradient’specification throughout the required transverse region.On the y = 0 axis the predicted gradient has the qualityindicated in Table 4.-0.1-0.0500.050.10 4 8 12 16 20 24 28 32 36x (mm)  dHy/dx (%)y = 0 y = 4 mm y = 8 mm y = 12 mm y = 16 mmProceedings of EPAC 2002, Paris, France2368Table 4: Gradient quality predicted for the ‘W’ typequadrupole on the y = 0 axis. dHy/dx (%) at x value (mm)+ 0.015 260 31-0.09 363  LOW APERTURE (‘N’ TYPE)QUADRUPOLE.3.1 Pole GeometryA narrower pole was developed for the ‘N’ typequadrupole, producing the geometry described below.The pole followed the equation:xy = R2/2 out to x = 37.3,with a linear tangent extending to the pole corner at:x = 48 mm.From the pole corner, the pole followed an angle of:45°out to x = 57.0 mm.The pole was then broadened, each side diverging at anangle of:10° to the pole centre line.As with the ‘W’ type quadrupole, this widening of thepole was necessary to prevent saturation in the pole root.3.2 Gradient QualityThe gradient quality predicted by non-linear modellingusing OPERA is shown in Fig. 4; this again shows thehomogeneity in gradient of the vertical field within thegood gradient region. The gradient quality on the y = 0axis is given numerically in Table 5.Figure 4: Homogeneity of the field gradient in the ‘N’type quadrupole expressed as a percentage of thevariation from dHy/dx at the origin (0,0), as a function ofx, at differing vertical positions (y = 0, to y =16 mm); thedata extends over the whole 'good gradient' ellipse.Table 5: Gradient quality predicted for the ‘N’ typequadrupole on the y = 0 axis. dHy/dx (%) at x value (mm)+ 0.03 200 23-0.06 254 POWER SUPPLY REQUIRMENTS4.1 Coil ParametersWhilst the ‘W’ and ‘N’ type magnets have differingcross-sections, both types have the same amplitudespecification, they will operate at the same current densityand the constraints imposed by power supply economicsindicate that they will have the same maximum operatingcurrent. The coils on the two types of magnet willtherefore have the same cross-section and windinggeometry but with different overall widths and threedifferent lengths. The common parameters of the coils forthe 'W' and 'N' type quadrupoles are given in Table 6.Table 6: Coil data for ‘W’ and ‘N’ type quadrupoles.minimum amplitude linearity 97%total Amp-turns per pole 9818 Atnumber of turns per pole 54operating current at 17.5 T/m 182 Acurrent density in copper 3 A/mm2conductor cross section 60 mm2conductor dimensions 10.1mm x 7.5mmwater cooling tube diameter 4.5 mmmaximum water temperature rise 10°Cmaximum water pressure drop 5 barTo provide full flexibility for the operation of thelattice, all quadrupoles will have a separate power supply.The four types of magnet have the same current ratingsbut differing voltage and power requirements. However, asingle rating power supply design will be specified forgeneral use, simplifying procurement and the provision ofspares [3]. The quadrupole power supplies will have theratings shown in Table 7.Table 7: Ratings of individual quadruple power supplies.Current rating 200 AMaximum power output 6 kWCurrent stability 1:1055 REFERENCES[1] N. Wyles et al, "Defining the DIAMOND StorageRing Apertures", these proceedings.[2] N.Marks et al, "Magnetic Design of the DipoleMagnets for the DIAMOND Synchrotron Source", theseproceedings.[3] S.A.Grifiths et al, " A Power Converter Overview forthe DIAMOND Storage Ring Magnets", theseproceedings.-0.1-0.0500.050.10 5 10 15 20 25x (mm)  dHy/dx (%)y = 0 y = 4 mm; y = 8 mm; y = 12 mm; y = 16 mm;Proceedings of EPAC 2002, Paris, France2369

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