1. Multi-bunch acceleration in NS-FFAG Takeichiro Yokoi (Oxford University)

2. Requirement for PAMELA rf system (1)Energy : 30MeV  230MeV(∆E :200MeV) (2) Typical ring size ~ 10m (C~30m)  revolution frequency : 2~6 MHz (3) Medical requirements Treatment scheme : spot scanning scanning speed :>100 voxel/ sec Final beam emittance <10  mm mrad (norm)  1kHz repetition (4) Dynamics Half integer resonance crossing (* emittance blow up margin~5)  50kV/turn

3. Acceleration Scheme time Energy 1ms Option 1 time Energy 1ms Option 2 Option 1: P  N rep 2 Option 2: P  N rep Multi-bunch acceleration is preferable from the viewpoint of efficiency and upgradeability (* Number of bunch is restricted by the extraction scheme) Repetition rate: 1kHz  min. acceleration rate : 50kV/turn (=250Hz)  How to bridge two requirements ?? Low Q cavity (ex MA) can mix wide range of frequencies

4. Multi-bunch acceleration 2-bunch acceleration using POP-FFAG (PAC 01 proceedings p.588, K. Koba et. al) ∆f  4 f sy Multi-bunch acceleration has already been demonstrated In the lattice considered, typical synchrotron tune <0.01 (20kHz)  more than 20 bunches can be accelerated simultaneously (6D Tracking study is required) “Hardware-wise, how many frequencies can be superposed ??”

5. Test of multi-bunch acceleration Extraction (5.5MHz) 50kV Injection (2.3MHz) 50kV PRISM RF PRISM rf can provide 200kV/cavity It covers similar frequency region B rf -wise, MA can superpose more than 20 bunches

6. Test items using PRISM RF Frequency response Whether two frequencies can be surely superposed : up to 100kHz (∆f) Amplitude response Whether two rf waves can be surely superposed in amplitude-wise  Response function of cavity is determined  Used for dynamics study  Used for specifying the rf requirement

7. PRISM RF and rf amplifier

8. Typical wave form of PRISM RF cavity (1)Input (2)Output of tetrode 1 (3)Output of tetrode 2 (4) RF output [(2)-(3)] * push-pull 30  sec.

9. Frequency response of PRISM rf system *V pp : 4V PAMELA For the application to PAMELA, it is desirable to shift the peak (amplifier should be optimized) * PRISM rf system is optimized for 2MHz operation

10. Amplitude dependence (single frequency) Frequency spectrum (FFT) 2.34MHz 4.28MHz 5.31MHz Applying FFT to rf output (∆f~30KHz), amplitude dependence of main frequency component was examined

11. Frequency gap dependence  f: 160kHz  f: 120kHz  f: 80kHz  f: 40kHz Varying frequency gap from 200kHz to 20kHz, two frequencies were mixed in one cavity and examined the linearity of response

12. Frequency gap dependence 2.34MHz 4.28MHz 5.31MHz Up to 60kHz, separation and linearity was sufficiently good. Below 60kHz,they are unclear due to the precision limit of FFT.  Frequency linearity-wise, 100kHz frequency separation is sufficiently large. (30 bunch acceleration is capable)

13. Amplitude dependence (double frequencies) 4.28MHz V pp : 1V V pp : 2V V pp : 3V V pp : 4V 5.31MHz V pp : 1V V pp : 2V V pp : 3V V pp : 4V Fixing frequency gap in 100kHz, two frequencies were mixed in one cavity with various amplitude and examined the amplitude linearity of response Saturation

14. Amplitude dependence (double frequencies) 5.31MHz 4.28MHz 2.34MHz Though the saturation is clearly observed, the amplitude linearity is sufficiently good within the narrow amplitude region. (**Amplitude linearity between large frequency difference should be examined)  In estimating the specifications for rf system, the scheme is similar to the single bunch rf scheme  V max (rf system)=∑V max, i

15. N f :1 N f :2 N f :3 N f :4 N f :10 N f :15 N f :20 N f :25 N f :1 N f :2 N f :3 N f :4 N f :10 N f :15 N f :20 N f :25 Amplitude Distribution in Multi-Frequency Superposition N f :2 N f :4 N f :1 N f :3 Frequencies of constant frequency separation are superposed

16. Amplitude Distribution in Multi-Frequency Superposition N f :1 N f :2 N f :3 N f :4 N f :10 N f :15 N f :20 N f :25 N f :1 N f :2 N f :3 N f :4 N f :10 N f :15 N f :20 N f :25 projected As the number of frequency increases, the potion of high amplitude is rapidly reduced.

17. Amplitude Distribution in Multi-Frequency Superposition Ex. In the case of 20 bunch case, ~97% of the time portion is <0.5V max.  Is the higher part crucially important from the viewpoint of beam acceleration? If not, requirement of maximum power of RF driver can be considerably reduced.  It can be experimentally examined using real FFAG beam (ex KURRI’s 3-FFAG) N f :1 N f :2 N f :3 N f :10 N f :20 N f :30

18. Remaining studies and future plan Investigation of amplitude linearity for the large frequency gap Generating the real rf pattern and carrying out tracking simulation using the rf pattern Beam experiment using real FFAG (KURRI’s FFAG?) Estimating cooling power for 1kHz operation( cavity and system) Fixing actual required field gradient ( *related to lattice design and extraction scheme)