FFAG Accelerators for Radio-Isotopes Production Alessandro G. Ruggiero Brookhaven National Laboratory FFAG 2007, Grenoble, France April 12-17, 2007

4/16/2007FFAG Alessandro G. Ruggiero2/18 FFAG for Hadron (proton and HI) Applications Non-Relativistic Velocity  < 1(forget µ and e !) High Power Mode Mwatt Medium Energy range GeV/u High Repetition Rate50 Hz kHz CW Narrow Width10-30 cm Long Drifts> 1 m Strong Focusing(d) FDF (d) Non Isochronous  <<  T RI and EN production Energy Production Pulsed and Continuous Neutron Production Nuclear Waste Transmutation Tritium Production Nuclear Physics (K, π, … mesons) Proton Drivers for Neutrino Factory, -SuperBeams, µ-Colliders No Medical or Lower Energy or Lower Intensity Applications RCS SCL expensive Cyclotron FFAG

4/16/2007FFAG Alessandro G. Ruggiero3/18 Previous Studies AGS-based Facility for RIP following FAIR (T. Roser, Februray 2006) too complicateRCS needed accumulator ring(s)ande-cooling A.G. Ruggiero “AGS-less RIA with FFAG Accelerators”, BNL Internal Report, C-A/AP 238, May 2006 Abstract We have studied the use of Non-Scaling Fixed-Field Alternating-Gradient (FFAG) accelerators for the acceleration of heavy ions to produce radioisotopes and exotic nuclear fragments. We have taken as reference a beam of nuclei of Uranium 238 partially stripped to +28 charge state. A.G. Ruggiero, T. Roser, D. Trbjevic, “A Non-Scaling FFAG for Rare Isotopes Production”, Proceedings of EPAC, Edinburgh, Scotland TUPLS027 Abstract This is a report to demonstrate the use of Non-Scaling Fixed-Field Alternating-Gradient (FFAG) accelerators [1] in acceleration of partially stripped ions of Uranium-238 for Rare Isotopes Production. The following example assumes a beam final energy of 500 MeV/u with an average beam output current of 1 µA-particle and a beam average power of 120 kWatt. P.N. Ostroumov, Phys. Rev. Spec. Topics Acc. and Beams, 5(2002)

4/16/2007FFAG Alessandro G. Ruggiero4/18 Goals of RIA (SCL)Uranium 238 ECR12 keV/uCharge State 30 RFQ168 keV/u Low-  SCL9.3 MeV/u57.5 and 115 MHz Stripper 1 (Lithium Film)Charge State Medium-  SCL80.3 MeV/u172.5 and 345 MHz Stripper 2 (Carbon Wheel)Charge State High-  SCL400 MeV/u805 MHz CW Mode of Operation 4.2µA-particle 400 kWatt Reliable but Expensive Project360 SC Cavities ECR RFQ Low-  Medium-  High-  Section  G = 0.81  G = 0.61  G = 0.49 Stripper 2Stripper 1

4/16/2007FFAG Alessandro G. Ruggiero5/18 FFAG-Scenarios Three possible modes of operation; A. Acceleration with Broadband RF Cavity f rep = 1 kHz B. Pulsed Mode with Harmonic Number Jumpf rep = 10 kHz C. CW Mode with Harmonic Number Jumpf rep = CW Final Energy400 MeV/u Average Power400 kWatt Average Current4.2 µA-particle I.S. Inj. Linac RFQ 15 MeV/u 80 MeV/u 400 MeV/u FFAG-1FFAG µA- particle Charge State 30+ Charge State 90+ Charge State 70+ ±40.3% ±41.4%

4/16/2007FFAG Alessandro G. Ruggiero6/18 A. Acceleration with Broadband RF Cavity FFAG-1 (+70)FFAG-2 (+90) InjectionExtractionInjectionExtraction Circumferencem204 Kinetic EnergyMeV/u  Revol. Freq.MHz Revol.Periodµs h66 RF FrequencyMHz RF Peak VoltageMVolt RF Phasedegrees60 Bunch AreaeV/u-s0.02 Emittance, norm.π mm- mrad 110  sp. ch N ions / pulsex Accel. Periodms No. of Revol Rep. RatekHz11 Ave. CurrentµA-particle RF Beam PowerkWatt turns 18 µA-p IonSource

4/16/2007FFAG Alessandro G. Ruggiero7/18 A. Acceleration with Broadband RF Cavity Revol. Freq µs I.S.4 µA-particle Stored Current1093 µA-particle Injected Turns275 Filling Period1 ms Long Drift1.089 m Short Drift0.130 m F-Length0.301 m D-Length0.602 m No. of Periods80 I.S. Inj. Linac RFQ 15 MeV/u 80 MeV/u 400 MeV/u FFAG-1FFAG-2 Accumulator

4/16/2007FFAG Alessandro G. Ruggiero8/18 Lattice Function along one period Injection Ejection

4/16/2007FFAG Alessandro G. Ruggiero9/18 FFAG heavy ion driver 400 MeV/u, 400 kW, 1 kHz  6.3 x nucleon/pulse = 2.6 x U/pulse = 4.2 p  A (OK for ECR) Use EBIS as space charge neutralized accumulator. Extract pulses for single turn injection. Accelerate multiple charge states. Energy choices:Kinetic EMomentumBetaRev. Frequency (C=153m) Injection Ring 1 10 MeV/u137 MeV/c/u MHz Injection Ring 2 67 MeV/u381 MeV/c/u MHz Extraction400 MeV/u954 MeV/c/u MHz Ring 1: U 28+ ; B  max = 9.2 Tm  B ~ 0.8 T for 50% filling factor; 1ms acc. time  500 turn acceleration  2 MeV/turn  40 keV/m for 50 m rf  broadband Finemet cavities? Ring 2: U 56+ ; B  max = 12.2 Tm  B ~ 1.0 T for 50% filling factor; 1ms acc. time  1000 turn acceleration  3 MeV/turn  60 keV/m for 50 m rf  broadband Finemet cavities? 10 MeV/n To target station and fast fragment spectrometer 67 MeV/n400 MeV/nECREBISRFQLinacStripperU 28+ U 56+ Ring 1Ring 2 Thomas Roser

4/16/2007FFAG Alessandro G. Ruggiero10/18 B. Acceleration with Harmonic Number Jump FFAG-1 (+70)FFAG-2 (+90) InjectionExtractionInjectionExtraction Circumferencem204 Kinetic EnergyMeV/u  Revol. Freq.MHz Revol.Periodµs h388 x 8176 x 8352 x 4192 x 4 RF FrequencyMHz RF Peak VoltageMVolt2 x (8 x 4) cavities1 x (4 x 8) cavities RF Phasedegrees3060 Bunch AreaeV/u-µs10 Emittance, norm.π mm- mrad 100  sp. ch N ions / pulsex Accel. Periodµs No. of Revol.26 +4/840 Rep. RatekHz10 Ave. CurrentµA-particle RF Beam PowerkWatt turns 75 µA-p Ion Src

4/16/2007FFAG Alessandro G. Ruggiero11/18 Constant-RF Voltage Profile (805 MHz) Using these RF Voltage Profiles it is possible to operate in CW mode provided that the Ion Source delivers continuously 4.2 µA-particles. Ratio of Initial to Final Harmonic Number =  f /  i = 4.04 FFAG-2FFAG-1

4/16/2007FFAG Alessandro G. Ruggiero12/18 CW Mode of Operation (  < 1) UraniumMass Number, A = 238 Charge State, Q = +90 Rest Energy, E 0 = 931.?? MeV/u Kinetic Energy, E = 400 keV/u Average Power, P = 400 kWatt Average Current, I = P/AE = 4.2 µA-ion M equally-spaced cavities around ring at constant frequency f RF and phase  RF Energy Gain  E n = (Q/A) eV n sin  RF f RF = constant =  n h n f ∞ -->  n+1 h n+1 =  n h n f ∞ = C / c  T / T =  C / C –  /   C / C <<  /  = 0, Isochronous TnTn T n + 1 T n - 1 VnVn V n + 1 V n - 1 ECR Cyclotron, MuonsProtons,  < 1

4/16/2007FFAG Alessandro G. Ruggiero13/18 Harmonic Number Jump (HNJ) The variation of h with  can be calculated precisely on a computer, but here we use a linear approximation ( a very good one indeed!)  E n+1 = E 0  n 2  n 3  h / (1 –  p  n 2 ) h n  h = h n+1 – h n = (Q/A) eV n sin  RF  h n is local value between cavity crossings  h is harmonic number jump between cavity crossings = –1  p  n 2 << 1 By integration Max. energy gain per crossing  E max = E f  f  f 2  h M c / f RF C tot Number of Crossingsn f = f RF C tot (1 –  i /  f ) / M  i c  h Acceleration Periodt f = f RF C tot 2 (1 –  i 2 /  f 2 ) / 2 M 2  i 2 c 2  h V n = g  n TTF (  0 /  n ) Cavity gap g = RF  0 / 2 Physical Review ST A&B 9, (2006)

4/16/2007FFAG Alessandro G. Ruggiero14/18 Consequences of Harmonic-Number Jump To avoid beam losses, the number of bunches ought to be less than the harmonic number at all time. On the other end, because of the change of the revolution period, the number of RF buckets will vary. There is a difference between the case of acceleration below and above transition energy. Below transition energy the beam extension at injection ought to be shorter than the revolution period. That is, the number of injected bunches cannot be larger than the RF harmonic number at extraction. The situation is different when the beam is injected above the transition energy. In this case the revolution period decreases and the harmonic number increases during acceleration. Below TransitionAbove Transition h f / h i =  f /  i

4/16/2007FFAG Alessandro G. Ruggiero15/18 Beam-Bunch Time Structure FFAG-1FFAG-2 Cavity Groups84 Cavities per Group48  Cavity Gap, cm RF Phase30 o 60 o RF Voltage / Cavity2 MVolt1 MVolt Orbit Separation, mm Beam rms Width, mm Beam rms Height, mm ECR Ion Source 4.2 µA-ion T final T initial Bunching Freq. = 57 MHz (1 bunch / 14 rf buckets)

4/16/2007FFAG Alessandro G. Ruggiero16/18 C. CW Mode of Acceleration by HNJ FFAG-1 (+70)FFAG-2 (+90) InjectionExtractionInjectionExtraction Circumferencem204 Kinetic EnergyMeV/u  Revol. Freq.MHz Revol.Periodµs h388 x 8176 x 8352 x 4192 x 4 hh RF FrequencyMHz RF Peak VoltageMVolt2 x (8 x 4) cavities1 x (4 x 8) cavities RF Phasedegrees3060 Bunch AreaeV/u-µs10 Emittance, norm.π mm- mrad 10 N ions / turnx Accel. Periodµs No. of Revol.26 +4/840 Rep. RateCW

4/16/2007FFAG Alessandro G. Ruggiero17/18 Energy Gain Profile FFAG-1FFAG-2

4/16/2007FFAG Alessandro G. Ruggiero18/18 RF Voltage Cavity Profile for HNJ cm TM 11 TM 01 TM MHz Gap =4-9 cm 8 MV/m ± 3 MV/m 20 cm 1 m