1. Adiabatic eRHIC Extraction June 3, 2015Stephen Brooks, eRHIC meeting1 With emittance growth analysis

2. 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 3, 2015Stephen Brooks, eRHIC meeting2 I’m going to use this one to increase the orbit separation in eRHIC FFAG2

3. Adiabatic Cell Expansion Length factor goes as a = exp(3p 2 -2p 3 ) – p = cell#/N cells, 0  1 in expansion section – Then reverse (N cells =30 so 60 in total, 56.4° angle) Cells increase in length by factor e ~= 2.718 – Orbits separate by factor e 2 ~= 7.389 June 3, 2015Stephen Brooks, eRHIC meeting3 Transverse orbit exaggeration x256

4. The Expanded Cell ElementLength (m)Gradient (T/m)Expanded Length (m) Expanded Gradient (T/m) BD1.27195629.2563.4469893.983632 Short drift0.060.162599 QF1.809009-254.902398-3.404115 Long drift0.451.219496 June 3, 2015Stephen Brooks, eRHIC meeting4 Separation of highest energy turns is 2.18cm – Total orbit range ~14cm – Enough room for septum for upper half of orbits Original cell had 3mm separation, ~2cm range

5. Fine Correction Orbits look good macroscopically but need to return to closed orbits to with ~micron level – Or oscillations+energy spread will grow emittance First just the 11 central energies were run – Then dp/p = ±0.5e-3, ±1e-3 were added (55 in all) Dipole correctors in 60 cells either side of the extraction point were allowed up to 0.005T June 3, 2015Stephen Brooks, eRHIC meeting5

6. Lattice Includes Matching Sections Straight-to-arc [17 cells], Expand orbits [30], Contract orbits [30], Arc-to-straight [17] – So I can launch and collect particles at x=x’=0! Only the central 30+30 corrected to begin June 3, 2015Stephen Brooks, eRHIC meeting6 Transverse orbit exaggeration x512

7. Correction of 11 Central Energies June 3, 2015Stephen Brooks, eRHIC meeting7 Uncorrected adiabatic formula gives up to 0.9mm offsets

8. Correction of 11 Central Energies June 3, 2015Stephen Brooks, eRHIC meeting8 Log scale “Perfect” at 42 cells, 84 correctors

9. Correction with dp/p ±1e-3 June 3, 2015Stephen Brooks, eRHIC meeting9

10. Correction with dp/p ±1e-3 June 3, 2015Stephen Brooks, eRHIC meeting10 Log scale Still some residual offsets up to 5.3um

11. dp/p ±1e-3 Correcting in Matchers June 3, 2015Stephen Brooks, eRHIC meeting11 Gives a total of 94 cells (188 correctors) instead of 60 cells (120 correctors)

12. dp/p ±1e-3 Correcting in Matchers June 3, 2015Stephen Brooks, eRHIC meeting12 Log scale Residual offsets no more than 67nm

13. Corrector Strengths (T) June 3, 2015Stephen Brooks, eRHIC meeting13

14. Emittance Growth The 11 beams are tracked through an extraction sextant to test for nonlinear- dispersion-related emittance growth dp/p of ±1e-3, uniform distribution 20 mm.mrad initial normalised emittance – Transverse Gaussian distribution – Beams initially have matched  x,y,  x,y functions 5000 particles per beam June 3, 2015Stephen Brooks, eRHIC meeting14

15. Check: 100 Straight Cells June 3, 2015Stephen Brooks, eRHIC meeting15

16. Check: 100 Arc Cells June 3, 2015Stephen Brooks, eRHIC meeting16 Mistake: initial beams had D=0!

17. Uncorrected Extraction Sextant June 3, 2015Stephen Brooks, eRHIC meeting17 x growth ranges from 0.13% to 15.75% Not sure where y growth on 21.2GeV comes from

18. Uncorrected Beam Centroids June 3, 2015Stephen Brooks, eRHIC meeting18

19. Corrected Extraction Sextant June 3, 2015Stephen Brooks, eRHIC meeting19 y growth on 21.2GeV again

20. Corrected Extraction Sextant (x) June 3, 2015Stephen Brooks, eRHIC meeting20 x growth ranges from 0.002% to 0.030%

21. Corrected Beam Centroids June 3, 2015Stephen Brooks, eRHIC meeting21 NB: from tracking rather than linear model of tracking; also contains statistical noise

22. Septum Design Example June 3, 2015Stephen Brooks, eRHIC meeting22 Holger Witte’s permanent magnet septum design 0.7T vertical bending field Field-free region for other beams 5mm septum thickness! 11mrad kick in 1.12m length for 21.2GeV beam

23. eRHIC Septum Issues Probably easier to kick beams horizontally in several cells to build up oscillation within pipe Synchrotron radiation would hit the septum barrier so prefer “massless septum” POP FFAG massless septum was only 0.1T Design from Y. Iwashita, A. Noda of Kyoto U. achieves 0.8T although fit of field falloff within 2cm distance is marginal (some leakage) June 3, 2015Stephen Brooks, eRHIC meeting23

24. Iwashita/Noda Septum Design June 3, 2015Stephen Brooks, eRHIC meeting24 Mitigations could include smaller aperture (±15mm is used here) and/or putting the penultimate beam on a field zero-crossing with zero integral rather than totally field-free

25. Dynamics with Three “Septums” June 3, 2015Stephen Brooks, eRHIC meeting25 Transverse orbit exaggeration x64 Purple = 21.2GeV (ignore others) Septum positions: 10cm