Cb Magnet and Lattice Status January 20, 2016 Stephen Brooks, Cbeta Meeting

From last time: Iron quads Currently a fall-back rather than main option Holger produced quad designs with pole tip radii 16mm, 23mm Very good apart from mechanical conflict with vacuum chamber, mostly in strong QF quadrupole Georg also wanted 12mm not 6mm beam centroid-to-pipe clearance Iron poles 16mm 6mm Extremal beams in QF Pipe shape(s) January 20, 2016 Stephen Brooks, Cbeta Meeting

Current magnets: Halbach-derived QF BD 37.2mm 30.7mm 12mm Outer radii = 62.4mm (QF), 59.4mm (BD) January 20, 2016 Stephen Brooks, Cbeta Meeting

Differences Halbach vs. Iron Iron Poles Halbach Field quality + tuning Determined by iron pole shape. Adjustment would be via conventional pole shimming. Determined by block magnetisation vectors. Adjustment via floating shims/iron wires just inside aperture. Field strength + tuning Iron shunts to partially short-circuit flux applied to outside. Determined by block magnetisation vectors. Tune with EM normal quad and dipole online correctors. Temperature sensitivity + compensation 0.1%/K for NdFeB but can (at ~25% strength penalty) incorporate NiFe material to passively compensate. 0.1%/K for NdFeB, cancelled by using EM normal quad and dipole online correctors. Cross-talk in doublet + compensation Few percent cross-talk, can be corrected with shunts. Negligible cross talk, mu~1 linear field superposition. Correctors (online/EM) Can be coils would around each pole. (Putting coils within the bore turned out too crowded). Window-frame outside Halbach magnet using field superposition, because Halbach is magnetically transparent. January 20, 2016 Stephen Brooks, Cbeta Meeting

Magnet Prototyping Status Pieces ordered from AllStar Magnetics NB: ±5° magnetisation angle tolerance (bad?) Ordered 3 cells (3xBD, 3xQF) for $10`863.99 Delivery 70 days (end of March) Shin-Etsu quoted for similar pieces, 3 cells ±1° magnetisation angle tolerance (much better) $52k including $23.7k one-off tooling Also ordered Holger’s iron quad (lowers risk) January 20, 2016 Stephen Brooks, Cbeta Meeting

Rotating Coil at BNL Magnet Dept. Prototype Halbach quadrupole bought in 2014 for an eRHIC magnet lab-directed R&D (LDRD) January 20, 2016 Stephen Brooks, Cbeta Meeting

Halbach Quad + Iron Wire Shims January 20, 2016 Stephen Brooks, Cbeta Meeting

“eRHIC” Quad Prototype vs. Cb Parameter eRHIC prototype quad “5A” Cb requirement QF BD Gradient 27.5 T/m (measured) -23.6 T/m 19.1 T/m Central dipole 0 (by realignment) -0.377 T Material SmCo R26HS (Shin-Etsu) NdFeB N35SH (AllStar Magnetics) Min R of physical magnet pieces 22.5mm (design) 23.5mm (measured) 37.2mm 30.7mm Max R of beam centroid 10mm (rotating coil) 15mm (extrapolated) 20.2mm 13.7mm Rmax,beam/Rmin,magnet 43% (coil) 64% (extrapolated) 54% 45% January 20, 2016 Stephen Brooks, Cbeta Meeting

Stephen Brooks, Cbeta Meeting Shimming Results Unshimmed Shimmed sextupole only Shimmed all poles Error fields across horizontal aperture, extrapolated from measured harmonics Max relative error: 4.7e-3 (unshimmed) 1.2e-3 (shimmed) BD 45% QF 54% January 20, 2016 Stephen Brooks, Cbeta Meeting

Computer-generated Model of BD Magnet  3D Printer Software January 20, 2016 Stephen Brooks, Cbeta Meeting

Dummy Blocks as Spacers during Construction January 20, 2016 Stephen Brooks, Cbeta Meeting

Co-Optimisation of Lattice with Magnets Developed an automated tool to output the outer radius (and cross-sectional area) of combined-function Halbach magnets given their dipole, quad and bore requirements Optimised the lattice to minimise largest outer radius of either magnet NB: Halbach quad radii tend quickly to infinity if the bore*gradient goes too high Then we have to wrap an EM quad corrector outside it January 20, 2016 Stephen Brooks, Cbeta Meeting

Stephen Brooks, Cbeta Meeting Cb Brooks_2015-12-11 Cell QF magnet By(local x) = B0 + Gx B0 = -0.018693 T G = -23.6236 T/m Length = 0.114882 m BD magnet By (local x) = B0 + Gx B0 = -0.395517 T G = 19.1191 T/m Length = 0.123719 m ORIGIN Cell x Beams local x range: (fieldmap) -0.02031 to 0.018074 m Cell z Local x Cell entry point (z,x) = (0,0) q = 0 Local x=0 line Beams local x range: (fieldmap) -0.01285 to 0.014581m QF start (z,x) = (0.059998731,-0.000759972) m q = -0.001636043 rad Local x QF end (z,x) = (0.174880931,-0.000947925) m q = -0.001636043 rad Local x=0 line BD start (z,x) = (0.22493844,0.001395855) m q = -0.040550502 rad BD end (z,x) = (0.348556194,-0.003619656) m q = -0.040550502 rad NB: this spec shows the original “lattice” combined-function magnets; the physical BD was later realigned to span the orbits symmetrically and QF to be a B0=0 pure quad. Next cell entry point (origin) (z,x) = (0.408289377,-0.010030928) m q = -0.077828917 rad January 20, 2016 Stephen Brooks, Cbeta Meeting

Stephen Brooks, Cbeta Meeting Orbits to Scale January 20, 2016 Stephen Brooks, Cbeta Meeting

Tracking Racetrack with Fieldmaps Fieldmaps imported directly from Nick Tsoupas’ OPERA-3D models, no strength scaling January 20, 2016 Stephen Brooks, Cbeta Meeting

Stephen Brooks, Cbeta Meeting Dynamic Aperture Chris Mayes has more detailed views of the apertures but… In the resonance simulations I launched uniform beams of r=1cm size (huge!) ~10% gets through, so area p/10 cm2 This is for lowest (67MeV) energy, which has worst DA due to the high tune Beams of 500 mm.mrad normalised emittance get through with minimal distortion January 20, 2016 Stephen Brooks, Cbeta Meeting

Old Lattice Resonance-Space Plot 20 T/m F gradient 30 T/m Each coloured square represents the transmission of a simulation of a large beam with varied magnet strengths. Trenches of losses are resonance features. This forms part of the canonical “necktie” example below. 15 T/m Qx = 0.321 Qy = 0.252 D gradient Lattice shown with ★ 25 T/m January 20, 2016 Stephen Brooks, Cbeta Meeting

New Lattice Resonance-Space Plot 90% F strength 110% 90% Qx = 0.380 Qy = 0.283 ±5% beam momentum errors OK with reasonable apertures D strength Tracked using fieldmaps, transmissions are lower because I forgot the pipe apertures in the last one 110% January 20, 2016 Stephen Brooks, Cbeta Meeting

Vacuum Pipe Shape Issues A variable-sized pipe is required for this lattice Consequences of using a fixed radius is shown by Chris Mayes’ lattice Magnet outer radii below Magnet Variable radius pipe Fixed-size pipe (Chris) QF 62.4mm 55.8mm BD 59.4mm 87.4mm BD becomes quad-like, requires far larger magnet Potentially serious problem for quad EM correctors January 20, 2016 Stephen Brooks, Cbeta Meeting

Provisional List of Magnet Types Area Subarea Name Type Notes FFAG Arc QF PM+EM corrector Halbach quad BD Combined-function Halbach Transition BDT Combined-function Halbach with extended good field range to B=0 Straight QFS Small Halbach quad BDS Splitter Common Common dipole EM Wide-aperture splitting dipole Fan-out Septum dipole 1 Bends 3,4 but avoids 2 Septum dipole 2 Bends 4 but avoids 3 Lines Splitter dipole PM Halbach dipole ~0.9T Splitter dipole adjust Electromagnetic dipole Splitter quad All quads are the same January 20, 2016 Stephen Brooks, Cbeta Meeting

Stephen Brooks, Cbeta Meeting Conclusion Should make lattice choice ASAP so work on design and CDR can continue Choice hinges on practicality of vaccum pipe vs. practicality of EM correctors if they get large Exploit commonality to reduce magnet types Get fieldmaps for all types allowing end-to-end simulation with fieldmaps This also means we will have 3D physics designs for all of them in hand January 20, 2016 Stephen Brooks, Cbeta Meeting