FFAG Accelerators for Proton Driver Alessandro G. Ruggiero Brookhaven National Laboratory FFAG 2007, Grenoble, France April 12-17, 2007

4/16/2007FFAG Alessandro G. Ruggiero2/10 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 Energy1 GeV Average Power10 MWatt Average Current10 mA I.S. Inj. Linac RFQ 50 MeV 250 MeV 1000 MeV FFAG-1FFAG-2 10 mA ±40.3% ±39.9% Positive Ions

4/16/2007FFAG Alessandro G. Ruggiero3/10 FFAG Size and Layout, Parameters Long Drift1.089 m Short Drift0.130 m F-Length0.301 m D-Length0.602 m No. of Periods80 Circumference = 204 m FFAG-1FFAG-2 Inj. Ej.

4/16/2007FFAG Alessandro G. Ruggiero4/10 CW Mode of Operation (  < 1) UraniumMass Number, A = 1 Charge State, Q = +1 Rest Energy, E 0 = MeV Kinetic Energy, E = 1000 MeV Average Power, P = 10 MWatt Average Current, I = P/AE = 10 mA 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 IS Linac Cyclotron, MuonsProtons,  < 1

4/16/2007FFAG Alessandro G. Ruggiero5/10 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. Ruggiero6/10 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. Ruggiero7/10 Beam-Bunch Time Structure FFAG-1FFAG-2 Cavity Groups42 Cavities per Group816  Cavity Gap, cm RF Phase30 o 60 o RF Voltage / Cavity6 MVolt25 MVolt Orbit Separation, mm Beam rms Width, mm Beam rms Height, mm Ion Source 10 mA T final T initial Bunching Freq. = 57 MHz (1 bunch / 14 rf buckets) 45 Bunches

4/16/2007FFAG Alessandro G. Ruggiero8/10 CW Mode of Acceleration by HNJ FFAG-1FFAG-2 InjectionExtractionInjectionExtraction Circumferencem204 Kinetic EnergyMeV  Revol. Freq.MHz Revol.Periodµs h436 x 4223 x 4446 x 2313 x 2 hh RF FrequencyMHz RF Peak VoltageMVolt6x (4 x 8) cavities1 x (2 x 16) cavities RF Phasedegrees3060 Bunch AreaeV/u-µs10 Emittance, norm.π mm- mrad 10 N ions / turnx Accel. Periodµs No. of Revol.53 +1/ /2 Rep. RateCW

4/16/2007FFAG Alessandro G. Ruggiero9/10 Energy Gain Profile FFAG-1FFAG-2

4/16/2007FFAG Alessandro G. Ruggiero10/10 RF Voltage Cavity Profile for HNJ cm TM 11 TM 01 TM MHz Gap = cm 8 MV/m ± 3 MV/m 20 cm 1 m