1. Jun'15 eRHIC Baseline Arc Cells June 24, 2015Stephen Brooks, eRHIC meeting1 Design for 4+12 turn FFAGs

2. High-Energy Cell Rationale The 5-turn FFAG1 is perceived to be risky – Tunes are near the limits in both directions – Proximity to half-integer tends to give strong chromatic effects Want a 4+12 turn configuration, as published, to work on, do correction studies etc. Based on previous lattices collected by Dejan Not “the best possible”, just “no major issues” June 24, 2015Stephen Brooks, eRHIC meeting2

3. High-Energy Cell (6.6-21.2GeV) ElementLength (m)Angle (mrad)Gradient (T/m)Offset (mm) QF21.8475.418061-20.607.87 BD21.12933.31296728.87-5.61 Both drifts0.180 June 24, 2015Stephen Brooks, eRHIC meeting3 Both equivalent dipoles equal: G  x = -0.1620T – This means “central energy” with same radius of curvature in both magnets exists (R mag =340.88m) Watch out for signs: Muon1 uses negative electrons going anticlockwise…

4. High-Energy Cell Performance June 24, 2015Stephen Brooks, eRHIC meeting4 Parameter Jan’14 (50T/m FODO)Oct’14 (30T/m doublet) Jun’15 Energy range 7.944 – 21.164 GeV 6.622 – 21.164 GeV Energy ratio 2.66× 3.20× Turns (1.322GeV linac) 11 12 Synchrotron power (* L=2138m arcs) 9.8MW @ 21.1GeV, 18mA 10.2MW @ 15.8GeV, 50mA 3.2MW @ 10.5GeV, 50mA 9.9MW @ 21.1GeV, 20mA 9.5MW @ 15.8GeV, 50mA 3.0MW @ 10.5GeV, 50mA 10.1MW @ 21.1GeV, 16mA 10.0MW @ 15.8GeV, 44mA 4.6MW @ 10.5GeV, 50mA TOF range 22.4ppm (5cm)38.0ppm (9cm) 56.9ppm (12cm) Drift space 28.8cm45.0cm (and 6.0cm) 18.0cm Tune range 0.035 – 0.3690.033 – 0.410 0.024 – 0.346 Orbit range (quads) 12.6mm (r max = 9.1mm)21.6mm (r max = 15.8mm) 30.5mm (r max = 21.7mm) Max |B| on orbit 0.451 T0.416 T 0.467 T Max quad strength 49.515 T/m29.256 T/m 28.870 T/m

5. High-Energy Cell Orbits June 24, 2015Stephen Brooks, eRHIC meeting5

6. Cell in Vladimir’s Coordinates  = 0.012470287 m – NB: this is a total "offset" of 13.48 mm in Muon1! Not the same. h = 0.001176114 m R(1-cos  ) = 0.003641082 m R = 382.1117394 m  = 0.004365514 radians = 0.250125528 degrees – Not ¼° due to length rounding We also tried optimising  for minimal SR at 21.2GeV Won 2% at expense of 6% higher B field and 19% more SR at 15.9GeV, so decided to leave as is June 24, 2015Stephen Brooks, eRHIC meeting6 R(1-cos  )

7. Low-Energy Cell Rationale Make a reasonable 4-turn FFAG1 Yue was using a cell with same length as FFAG2 but this resulted in large orbit offsets This made time-of-flight variation very large – Causes problems in longitudinal dynamics, R56 Scale the cell down to 2/3 the length of FFAG2 – While retaining most of the properties – Approximately based on next slide June 24, 2015Stephen Brooks, eRHIC meeting7

8. Scaling type (by factor a) LengthAngleDipoleGradient Quad offset (=dipole/grad) & orbit excursion Momentum (~energy) 11aa1 Machine radiusa1a -1 a -2 a FFAG beta length (fixed bend radius, fixed cell tune) aa1a -2 a2a2 FFAG arc-to-straight (=row 3/row 2) 1aa1a FFAG radius with fixed orbit excursion and field (row 2*row 1/sqrt(row 3)) a 1/2 a -1/2 111 FFAG scaling* laws * not scaling FFAG laws June 24, 2015Stephen Brooks, eRHIC meeting8 I’m going to use this one to reduce the length of the FFAG1 cell to 2/3 (offsets to 4/9)

9. Low-Energy Cell (1.3-5.3GeV) ElementLength (m)Angle (mrad)Gradient (T/m)Offset (mm) QF10.81212.910342-10.65.6 BD10.81212.91034210.6-5.6 Both drifts0.30 June 24, 2015Stephen Brooks, eRHIC meeting9 Equal-length, equal-gradient FODO lattice Both equivalent dipoles equal: G  x = -0.0594T – This means “central energy” with same radius of curvature in both magnets exists (R mag =279.04m) Gradient increased 3.5  10.6 T/m

10. Low-Energy Cell Performance June 24, 2015Stephen Brooks, eRHIC meeting10 ParameterJan’14Oct’14Jun’15 Energy range 1.334 – 6.622 GeV 1.334 – 5.300 GeV Energy ratio 4.96× 3.97× Turns (1.322GeV linac) 554 Synchrotron power 0.26MW @ 50mA0.34MW @ 50mA0.11MW @ 50mA TOF range 54.7ppm (12cm)31.0ppm (7cm)42.7ppm (9cm) Drift space 28.8cm45.0cm30.0cm Tune range 0.036 – 0.4240.033 – 0.4080.062 – 0.277 Orbit range (quads) 31.3mm (r max = 23.6mm) 16.9mm (r max = 11.1mm) 28.1mm (r max = 23.3mm) Max |B| on orbit 0.227 T0.266 T0.238 T Max quad strength 9.986 T/m25 T/m10.6 T/m

11. Low-Energy Cell Orbits June 24, 2015Stephen Brooks, eRHIC meeting11