1. FFAG Acceleration David Neuffer Fermilab FFAG Workshop ‘03

2. 2 JNF Scenario  Use 50 GeV p-bunch to produce pions  Capture beam in 20-T  5-T transport channel  Short decay line; inject beam directly into low-energy FFAG  Capture beam in low-frequency rf bucket  Accelerate up chain of FFAGs to 20GeV  Inject into 20GeV storage ring

3. 3 JNF- FFAGs lattice design  Lattices are “scaling” radial- sector FFAGs  Triplet focusing with reverse- bend D-quads  Low to high energy orbit width is ~0.5m  0.3  1.0 GeV,  1  3.0 GeV  3.0  10 GeV  10  20 GeV FFAGs  Lattices have been generated using SAD, DIMAD

4. 4 Parameters for JNF FFAG lattices

5. 5 Acceleration and Decay  Acceleration must avoid muon decay  Need ~1MV/m to avoid decay (2 MV/m gradient in cavities)

6. 6 JNF Acceleration Parameters  For acceleration, use superconducting (smaller-radius) FFAGs  At 1MV/m, ~ 10 turns acceleration / FFAG  Assume harmonic h = 1 on lowest-energy FFAG; keep frequency constant  h = 1  4.75 MHz rf (???)  Initial beam from decay  300  150MeV/c;  10ns 

7. 7 Longitudinal Motion in FFAG  Equations of motion:  Motion is fairly isochronous (at low frequencies)  h = 1 and h = 2 accelerations are OK  (~4.75 and 9.5 MHz)

8. 8 Scenario requires ~2MV/m rf  Harmonic=1 (for lowest energy FFAG) implies 4.75 MHz;  Harmonic=2 implies 9.5 MHz; works OK in 1-D simulation  Experience indicates 26MHz cavity is more realistic (Iwashita)  Use 26 MHz + 3 rd harmonic ?

9. 9 ~25MHz OK (from 1 to 20 GeV)  Third harmonic useful; particularly for 1  3 GeV FFAG  1  3  10  20 GeV  Could not get a good fit for 0.3 to 1.0 GeV FFAG 1 GeV 3 GeV 10 GeV 20 GeV

10. 10 Bunch sizes for various rf scenarios CaseRf frequency  E (MeV) (±)  z (m) (±)(eV-s) JNF (~300MeV) 5 MHz ??1503.004.7 ~Study 2 (~125MeV) 200MHz250.250.065 250 MeV200MHz500.250.13 125 MeV100MHz250.50.13 250 MeV100MHz500.50.26 125 MeV50MHz251.00.26 250 MeV50MHz501.00.52

11. 11 “Scaling” FFAG longitudinal dynamics  Longitudinal motion changes:  Position change has quadratic dependence on energy  Example I: A=-0.15, B=0.45, E 0 =12.5 GeV,  E 0 = 6.5 GeV, 6  20 GeV acceleration  Example II: A=-0.05, B=0.15, E 0 =15 GeV,  E 0 = 5 GeV, 10  20 GeV acceleration Example I

12. 12 “Acceptable” Solutions  Example I (6  20;45 cm)  200 MHz, 6 turns, 2.75GV/turn  20% 3 rd harmonic reduces distortion  200 MHz, with 3 rd harmonic, 8turns, 2GV/turn +1 GV/turn 3 rd  100MHz, 11 turns, 1.4 GV/turn  Example II (10  20; 15cm)  200 MHz, 16 turns, 0.7 GV/turn  20% third harmonic reduces distortion (0.75 GV +0.15 3 rd ) Example II –16 turns

13. 13 With third harmonic Example II –16 turns With 20% third harmonic

14. 14 Summary  Baseline acceleration scenario for JNF is ~25MHz  Set by 1 initial bunch scenario (0.3  1.0 Gev at ~10MHz or less)  Multiple-bunch scenario should allow higher frequency  “Guttertron” acceleration works OK at 200MHz if  z(E) < ~15cm + third harmonic