1. EMMA injection & extraction Takeichiro Yokoi(Oxford University)

2. Injection and extraction with linear model

3. Presumed conditions…. Kicker field :≤0.6kgauss(bipolar) Kicker length : 0.1m Beam emittance: 3πmm (normalized) Energy: 10~20MeV(1MeV step) 4 operation mode (latest lattice:parallel elements) 070221b,c,d,e Tracking code (ZGOUBI: sharp edge field) Septum boundary: +5mm from the outer-most beam envelope

4. Lattices … ∆x QF ∆x QD B1 QD (T/m) B1 QF (T/m) ∆x QD (mm) ∆x QF (mm) 070221b-4.7046.69534.0487.514 070221c-4.1266.10839.1958.171 070221d-3.5975.23046.5329.535 070221e-3.7646.55340.7977.684 Horizontal tune

5. Setup of tracking study QF0 QF1 QF2 Beam QD0 QD1 QD2 Kicker Septum QF0 QF1 QF2QD0 QD1 QD2 Kicker Septum injection extraction * Backtracking from CO * Beam position was monitored at the center of each magnet and drift space

6. Beam distribution at septum (injection) ∆x’:270mrad ∆x:4mm 70221b

7. Beam envelope at magnet center QD1 QD2 QF1 QF2 70221b 70221c 70221d 70221e xmax xmin Magnet center QF requires large good field region (max 80mm) Large orbit swing comes form 10MeV QD1 requires a little larger good field region than that inscribed. (max 60mm) ±32mm ±56m m *Beam position at the center of magnet is plotted for the orbit inside of target box

8. Beam envelope at magnet center (2) QD1 QD2 QF1 QF2 70221b 70221c 70221d 70221e xmax xmin Magnet center ±32mm ±56m m 10MeV of 70221b enlarges the target box…. Excluding it, orbit swing decreases.

9. Injection energy and GFR of QF GFR70221b70221c70221d70221e ±32mm15MeV~ 14MeV~13MeV~ ±35mm15MeV~14MeV~13MeV~12MeV~ ±40mm13MeV~12MeV~11MeV~ ±45mm12MeV~11MeV~10MeV~11MeV~ ±50mm11MeV~10MeV~

10. Beam distribution at septum (extraction) ∆x’:40mrad ∆x:2.5mm 70221b

11. Beam envelope at magnet center QD1 QD2 QF1 QF2 70221b 70221c 70221d 70221e xmax xmin Magnet center QF1 requires large good field region (max 49mm) Large orbit swing comes form 10MeV QD1 requires a little larger good field region than that inscribed. (max 60mm) If larger target box size is accepted, except 10MeV of 70221c and d, extraction is possible with present good field region ±32mm ±56m m Beam position at the center of magnet is plotted for the orbit inside of target box

12. Injection and extraction with TOSCA 3D field Injection and extraction orbits are one-pass orbits. For such orbits, what is important is bending component, and requirement to quadrupole component might be released.

13. Magnet & cell modeling QD Pole width:100mm Xt: 15mm QF Pole width:73mm Xt: 11mm Aperture of clamp is 45° rotated square( side: 14cm:D, 10cm:F) Vertical symmetry is introduced Optimized mesh size obtained through individual magnet modeling is used As typical lattices, 4 lattices are modeled (070221b,c,d,e) GFR:±36mm GFR:±26mm

14. Parameterization of current 2.0cm QF QD     ++ As a nominal focusing power, focusing power of region   2 was taken

15. Comparison with baseline design Baseline (By. S. Berg) Tracking 070221b: D 4680 AT, F 2960AT 070221c: D 4000AT, F 2640AT 070221d: D3400AT, F 2080AT Except the vertical tune of low energy, the results show so so good agreement with the design

16. Map geometry for injection study QD QF clamp Insertion insertion Putting the map boundary at 5.5cm from the magnet end, field error caused by the map geometry is less than 0.2% map

17. 8.5714˚ ±65mm X Y 55mm55.76mm 8.5714˚ 288mm Map geometry(2) Field map Mesh size X: 1mm,Y: 1mm, Z: 1mm (rough optimization was carried out) Drift space for adjustment 51.891mm 54.589mm Center of long drift 83mm 57mm 61mm 87mm

18. Beam distribution at septum (injection) 70221b septum 5mm 140mrad septum For 10, 11MeV of 70221b, 10MeV of 70221c, there is no injection orbit

19. Beam envelope in magnet (injection) QF1 Required GFR(±32mm) 70221b 70221c QD2 70221b 70221c 70221d QD1 Required GFR(±56mm) X max X min 70221b 70221c 70221d QF2 70221b 70221c 70221d Center of magnet Injection orbit outside GFR anyhow exists (matching problem remains)

20. Beam distribution at septum (extraction) 70221b Septum septum 50mrad. 3mm

21. Beam envelope in magnet (extraction) QF1 Required GFR(±32mm) 70221b 70221c 70221d QD1 Required GFR(±56mm) X max X min 70221b 70221c 70221d QF2 70221b 70221c 70221d QD2 70221b 70221c 70221d Center of magnet Extraction orbit outside GFR anyhow works

22. Remaining work …. Optimize current setting Include septum into tracking (matching) Check the remaining 5 operation modes (70221e,f,g,h,l) Confirm the result with final magnet design

23. Summary Tracking study with the hard edge model indicates that orbit swing of injection and extraction orbit goes beyond the present required good field region of QF. Tracking with 3d model shows extraction and extraction orbits outside of good field region anyhow work, but threre are missing injection conditions ( 10,11MeV of 70221b, 10MeV of 70221c), and beam distribution at septum is broader than that of extraction.  Any possibilities to reverse the magnet sequence ??