1. FFAG 4-Bend Injection Line into EMMA C. Johnstone, Fermilab EMMA phone conference July 24, 2007

2. FFAG Design Considerations For a bend/reverse bend pair, to ~cancel dispersion (as is required in the EMMA lattice) –360  of phase advance is required between bends –180  is the maximum phase advance across a minimum in the  function (where  * the value at the minimum) Such minima are very achromatic and are generally only found in IRs (EMMA survives with low betas because the cell length is extremely short and therefore the phase advance never approaches 180  - above 130  /cell EMMA demonstrates stability problems) The momentum acceptance of such IRs, which scale with 1/  *, are only a fraction of a percent and even this small acceptance requires sextupole correction –A short drift between a 2-bend achromat requires very deep minima – and at least two. –A 1% deviation in momentum will exhibit very different optical functions from the central momentum and cannot be controlled or matched into EMMA.

3. FFAG Design Considerations cont… Matching or ~canceling D’ further requires either –Reflection symmetry about the center point between bends –Adjustment, then fixing the bend from the ERLP – given the fixed bend in the septum Matching a different injection energy into EMMA requires a different D and D’ and therefore the value of this bend must change with energy. A 3- bend design is also very constrained and difficult to vary.

4. FFAG 2-bend solution 360  of phase advance + fixed bends

5. FFAG Proposed Solution : 4-bend design With a 4 bend design one can lengthen the injection line considerably and allow for the critical, dispersion-free, transverse emittance measurement from the ERLP. The 4-bend solution permits tuning and matching if designed as follows: –Two –same sign center bends effectively compensate for each other with 180  of phase advance between the two. –The “reverse-bend” septum is paired with an ~ equal bend from the ERLP. Now only 180  of bend is required outside of the insert between the two center bends. This remaining phase advance between the septum and this insert and the insert and the bend to the ERLP can be adjusted to match and cancel D’ and track matching conditions at different injection energies. –The two center bends can be changed together to align the line into EMMA.

6. FFAG Center - Insert Center bends Septum – set to 0  1 st bend from ERLP – set to 0 

7. FFAG 4-bends – canceling dispersion @10MeV Septum – set to 75  1 st bend from ERLP – set to 75 

8. FFAG Adding injection kickers

9. FFAG Emittance measurement section @10MeV

10. FFAG 20-MeV tune

11. FFAG 50 deg septum example

12. FFAG Possible injection lines 180  phase 360  phase advance impossible Line 1 Line 2

13. FFAG Inside Injection 60  phase advance

14. FFAG Outside vs. Inside Outside injection –Line 1 is too short to support matching, diagnostics, and vertical phase space painting, and dispersion suppression –Line 2 horizontal bends are too close, required phase advance for dispersion suppression is impossible Inside injection –Long line, easily match to required phase advance for dispersion suppression and accommodate other functions

15. FFAG Injection kicker locations : same kickers 10-20 MeV kick @20 MeV ~50mr/ kicker Injection septum Injection kicker #1 Injection kicker #2

16. FFAG Extraction kickers: 10 – 20 MeV Extraction kicker #1 Extraction kicker #2 Extraction septum

17. FFAG Proposal When studying the higher energies, 15-20, use all kickers for injection –Resonance study – no acceleration –For long-term resonance studies, there is time to re-fire the kickers for extraction –Or beam simply slowly dissipates –For quick resonances, it is likely we won’t have time to trigger and extract anyway. –New strength requirements would be half – or ~25 mr/kicker @20 MeV