1. Rough Power Estimates for Fully Electromagnetic Quadrupoles June 30, 2014Stephen Brooks, eRHIC FFAG meeting1

2. Amp-Turns Required in Quad Coil June 30, 2014Stephen Brooks, eRHIC FFAG meeting2

3. Amp-Turns Required in Quad Coil Ringg = Gradient (T/m)R = Pole radius (m)I (Amp.Turns) FFAG249.5150.0175693.702 FFAG19.5 (averaged)0.044088 (scaled)7347.216 June 30, 2014Stephen Brooks, eRHIC FFAG meeting3 Pole radius calculated by – FFAG2: measuring from Wuzheng’s diagram – FFAG1: scaling by orbit r max from magnetic centre FFAG1 gradients actually differ by ~10% between F and D magnets but not significant

4. Power/Resistivity Calculation P =  Vj 2 P/L =  Aj 2 j = I/A P/L =  I 2 /A Let A = s 2 /2 P/L = 2  I 2 /s 2 As there are 8 coils, P ring = 16L magnets  I 2 /s 2 – L magnets = 2985.821m for full eRHIC hexagon June 30, 2014Stephen Brooks, eRHIC FFAG meeting4 s

5. Power/Resistivity Calculation Rings = Coil side (m) Coil material Resistivity ( .m) P/L (W/m)Ring Power (MW) FFAG20.10Copper1.68 × 10 −8 108.92532.602 FFAG10.15Copper1.68 × 10 −8 80.61251.926 Total 189.53784.527 FFAG20.10Aluminium2.82 × 10 −8 182.83894.367 FFAG10.15Aluminium2.82 × 10 −8 135.31383.232 Total 318.15287.600 FFAG20.15Aluminium2.82 × 10 −8 81.261741.941 FFAG10.20Aluminium2.82 × 10 −8 76.114031.818 Total 157.37583.759 June 30, 2014Stephen Brooks, eRHIC FFAG meeting5 Comparison: at least 12MW is going into the RF for synchrotron radiation loss compensation

6. Conductor Cost Calculation RingMaterialVolume (m 3 )Mass (kg)Price ($/kg)Cost (M$) FFAG2Copper 119.43281070118 6.981 7.470 FFAG1Copper 268.72392407766 6.981 16.809 Total(s=10,15cm) 388.15673477884 24.279 FFAG2Aluminium 119.4328322468.6 1.866 0.602 FFAG1Aluminium 268.7239725554.5 1.866 1.354 Total(s=10,15cm) 388.15671048023 1.956 FFAG2Aluminium 268.7239725554.5 1.866 1.354 FFAG1Aluminium 477.73131289875 1.866 2.407 Total(s=15,20cm) 746.45522015429 3.761 June 30, 2014Stephen Brooks, eRHIC FFAG meeting6 Aluminium benefits doubly since  Al = 2700 kg/m 3 but  Cu = 8960 kg/m 3

7. Conclusions Our current design uses 1.812MW just for the correctors (due to small area) – And almost as many channels since we would replace 3 correctors by 4 coil trims Could have series bus and low-power trims separately The larger Al design doubles this to 3.759MW and materials cost is very small – Only possible issue: magnets are now ~50cm across for each ring June 30, 2014Stephen Brooks, eRHIC FFAG meeting7