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FFAG Accelerators for High-Intensity Proton Beams

FFAG Accelerators for High-Intensity Proton Beams. 1.5-GeV BNL-AGS Upgrade C = 807 m 1.0-GeV 10-MWatt Proton Driver C = 202 m 250-MeV Medical Facility C = 36 m. Alessandro G. Ruggiero Brookhaven National Laboratory FFAG’04 Workshop at KEK -- October 13-16, 2004.

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FFAG Accelerators for High-Intensity Proton Beams

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  1. FFAG Accelerators for High-Intensity Proton Beams 1.5-GeV BNL-AGS Upgrade C = 807 m 1.0-GeV 10-MWatt Proton Driver C = 202 m 250-MeV Medical Facility C = 36 m Alessandro G. Ruggiero Brookhaven National Laboratory FFAG’04 Workshop at KEK -- October 13-16, 2004 All these Projects are feasible, but there are 2 main Issues

  2. H– Stripping Foil Target 200-MeV DTL 1.0-GeV FFAG Acceleration Filling 1.0-GeV 10-MWatt Proton Driver Injection Energy, Ui200 MeV Extraction Energy, Uf1.0 GeV Beam Ave. Power, P = IUf10.0 MWatt Repetition Rate, F1.0 kHz Repet. Period,    1.0 ms Beam Ave. Current, I = Ne F 10.0 mA Total No. Protons, N 6.25 x 1013 DTL Peak Current IL Revol. Freq. f = c inj / C Chopping Ratio Revol. Period T = 1 / f FFAG Circumference C No. Protons / Turn NP= ILT / e Injection injNo. Injected Turns n = N / NP = Ne /  IL T Acceleration Period Tacc Rep. Period  = Tinj + Tacc Injection Period Tinj= nT = Ne /  IL --> not dependent on C and inj  = 0.5 IL = 60 mA--> Tinj = 0.333 ms & Tacc = 0.667 ms Alessandro G. Ruggiero FFAG'04 Workshop

  3. General Beam- RF Considerations Average Energy Gain / Turn W No. Revol. Acceleration Period m = (Uf – Ui) / W Average Revol. Period Tave = C /ave c Acceleration Period Tacc = m Tave = Tave (1 – Ui / Uf) (1 + ) Uf / W  extra acceleration time dilation factor (1 – Ui / Uf) (1 + ) ~ 1 Uf = P  / Ne Acceleration Period Tacc = Tave P  / Ne W Cycle Period  = Tinj + Tacc = Tinj / (1 – P / PB) Average Beam Accel. Power PB = W N e / Tave PB = (3 / 2) P = 15 MWatt Average RF Power PRF = PB + Pcavity = 2 PB = 30 Mwatt FFAG Cycle Efficiency P / PRF = 33% or P / PAC = 25% Energy Gain / Unit Length W / C = (5.0 / ave) keV /m Alessandro G. Ruggiero FFAG'04 Workshop

  4. More on RF Acceleration System • FFAG Circumference C = 201.8 m •  ave = 0.75 • Energy Gain W = 1.35 MeV / Turn • RF Peak Voltage VRF = 1.8 Mvolt • Harmonic Number h = 36 • No. Empty Buckets 9 out of 36 • Protons / Bunch 2.4 x 1012 • No. of RF Cavities 40 • No. of Gaps / Cavity 1 • Cavity Length 1 m • Peak RF Voltage / Gap 45 kVolt • Power Amplifier / Cavity 0.8 MWatt • Cavity Inter. Diameter 10 cm Issue # 1 Can the RF ferrite be swept in 2/3 ms ? Energy Range, MeV 2001,000  0.566 0.875 Rev. Frequency, MHz 0.841 1.300 Revolution Period, µs 1.189 0.769 RF Frequency, MHz 30.28 46.80 Peak Current, Amp 12.65 19.55 Peak Beam Power, MW 15.2 23.5 Alessandro G. Ruggiero FFAG'04 Workshop

  5. 180 90 60 90 45 30  Rule #1 for the FFAG Design • The Momentum Range between 200 and 1,000 MeV is ± 45% around the Central Momentum • It has been so far customary to tune (90o / period) the Lattice at the Central Momentum • Tune the Lattice at the lower (Injection) Momentum x + h2 (1 + n) x / (1 + ) = h  / (1 + ) y – h2 n y / (1 + ) = 0 h2 n / (1 + ) p = p0 (1 + ) p0 = Injection Momentum  = 0  = 1.632 Alessandro G. Ruggiero FFAG'04 Workshop

  6. D F F S S g g Rule #2 for the FFAG Design EmployFDF triplet arrangement, since this, as it was well known from the lattice studies of electron storage rings for the production of synchrotron radiation, yields a considerable lower dispersion when compared to the DFD arrangement, and thus a more compact momentum spread and smaller magnet width. Non-Scaling Lattice Reference Trajectory (Injection) Circumference 201.773 m Number of Periods 68 Period Length 2.96725 m Short Drift, g 0.15 m Long Drift, S (total) 1.26725 m H max ( in S) 2.27 m V max (in D) 5.854 m  max (in S) 0.0603 m Phase Adv. / Period, H/V 105.10o / 99.802o Betatron Tunes, H/V 19.8515 / 18.8514 Natural Chromaticity, H/V –0.915 / –1.787 Transition Energy, T 53.755 i Packing Factor 0.472 Magnet Type F D Arc Length, m 0.35 0.70 Bending Field B, kG – 2.118 4.956 Gradient G, kG/m 71.12 –23.30 Bending Radius , m –40.60 62.65 Bending Angle, mrad –34.49 80.69 Bending Ratio (D/F)2.34 Alessandro G. Ruggiero FFAG'04 Workshop

  7. Rule #3 for the FFAG Design •Linearized Equations of Motion • Introduce the field index n(x) = G(x) / h B0 x + h2 (1 + n) x / (1 + ) = h  / (1 + ) y – h2 n y / (1 + ) = 0 • Consider the general case where the field index is a nonlinear function of both x and s, namely n = n(x, s). At any location s, for each momentum value  there is one unique solution x = x(, s) and by inversion is a function of x and s, namely =(x, s). • We pose the following problem: Determine the field distribution, namely n = n(x, s), that compensates the momentum dependence of (1 + ) at the denominator: n(x, s) = n0 [1 + (x, s)] --> G(x, s) = G0 [1 + (x, s)] <--- where n0 is related to the gradient G0 = n0 h B0 on the reference trajectory. • Then the equations of motion reduce to x + h2 x / (1 + ) + h2 n0 x = h  / (1 + ) --> x = x(, s) --> = (x, s) y – h2 n0 y = 0 Alessandro G. Ruggiero FFAG'04 Workshop

  8. x, cm Half Period 1 GeV 200 MeV s, m Adjusted Field Profile (AFP) kG F - Magnet kG D - Magnet x, m x, m Fractional Betatron Tunes  V  Alessandro G. Ruggiero FFAG'04 Workshop

  9. 2.0 feet F-Magnet 2.0 feet D-Magnet Magnet Design (1) Alessandro G. Ruggiero FFAG'04 Workshop

  10. 1.0 GeV 1.0 GeV 200 MeV 1.0 GeV 200 MeV 200 MeV Variable Width Variable Gap > 10 cm Magnet Design (2) F-Sector D-Sector RF Long Straight 10 cm x 20 cm Elliptical Vacuum Chamber 10 cm Diameter Circular Vacuum Chamber Issue # 2 Are these Magnets feasible ? Manufacturing Errors? How close we need to reproduce the AFP? Alessandro G. Ruggiero FFAG'04 Workshop

  11. Diagnostic & Steering Boxes Flanges & Bellows D-Sector Magnet 20 cm Top View Vacuum Pump F-Sector Magnets Diagnostic & Steering Boxes Flanges & Bellows D-Sector Magnet 10 cm Side View Diagnostic & Steering Boxes Vacuum Pump F-Sector Magnets D-Sector Magnet RF Cavity Vacuum Pump F-Sector Magnets Period Layout (68 Cells) 0 m 1.0 m 2.0 m 3.0 m 100 k$ 600 k$ Alessandro G. Ruggiero FFAG'04 Workshop

  12. Circulating Beam 20 x 20 mm Foil Injected Beam 1.0 GeV 200 MeV 10 cm x 20 cm Vacuum Chamber B1 Injection Orbit B2 Bump Orbit C1 Foil C2 From DTL Multi-Turn Injection (H–) Linac Peak Current 60 mA Revolution Period 1.89 µs No. of Protons / FFAG pulse 6.25 x 1013 Chopping Ratio 0.50 Chopping Frequency 30.283 MHz Single Pulse Length 0.333 ms No. of Turns Injected / pulse 165 Linac/FFAG Rep. Rate 1.0 kHz Linac Duty Cycle 0.33 % Linac Beam Emittance, rms norm. 1 π mm-mrad Final Beam Emittance, full norm. 150 π mm-mrad Bunching Factor 3 Space-Charge Tune-Shift 0.35 Alessandro G. Ruggiero FFAG'04 Workshop

  13. Kicker Septum F D F F D F F D F Single-Turn Extraction Revolution Period 1.89 µs Beam Gap 330 ns Kicker Magnet, Length 1.0 m Field 1 kG Rise-Time < 300 ns Septum Magnet, Length 1.0 m Field 10 kG Repetition Rate 1.0 kHz The Kicker field remains constant for the duration of the beam pulse (about 1.6 µs), and it is finally reset to zero-value in about 1.0 ms, to be fired again the next cycle. Alessandro G. Ruggiero FFAG'04 Workshop

  14. hi Bi(xco) (tan xco') y Bi (1 + ) y' = – x, cm Half Period 1 GeV D F xco xco' 200 MeV s, m Rule #4 for the FFAG Design Make FFAG Circumference as large as possible Chose a number as large as possible of Periods Avoid the Curvature effect at Low Energy small Rings x + h2 x / (1 + ) + h2 n y / (1 + ) = h  / (1 + ) y – h2 n y / (1 + ) = 0 To keep small Tune Variation with the AFP minimize the Edge Effects Vertical == Focusing Horizontal == Defocusing Alessandro G. Ruggiero FFAG'04 Workshop

  15. H– Stripping Foil Target 200-MeV DTL 1.0-GeV FFAG AC Power Sub-critical Fissionable material Experimental Areas: Spallation Neutrons Waste Transmutation Tritium Production Radio-Isothops Production Exotic Elements Production, ….. Conclusions FFAG Proton Accelerators are a very promising alternative to other Accelerator Architectures (Super-Conducting Linacs, Cyclotrons, Rapid Cycling Synchrotrons), especially in view of the recent progress in beam dynamics and of new proposed design approaches. FFAG’s rely on conventional Magnet Technology, thus appealing to many centers of research. They are supposed to be less expensive: a crude estimate of the Proton Driver described here shows a cost of about 50M$ (excluding DTL and Tunnels). In the case of Protons, the Path Length variation with Momentum is not a concern if there is at any time only a single beam pulse circulating. A 10 MWatt beam power requires a AC source of about 40-50 MWatt. It is then imperative to demonstrate methods to create energy with the use of sub-critical nuclear material. The next step is to resolve the 2 main Issues Alessandro G. Ruggiero FFAG'04 Workshop

  16. DTL cycle for Protons with 1.5-GeV FFAG 0.4 sec 1 x 960 µs @ 35 mA (H–) 1.5-GeV Booster 28-GeV AGS 400-MeV DTL HI Tandem AGS Upgrade with 1.5-GeV FFAG Performance Rep. Rate 2.5 Hz Top Energy 28 GeV Intensity 1.0 x 1014 ppp Ave. Power 1.0 MW Protons, and HI (??) 1.5-GeV FFAG AGS Cycle with 1.5-GeV FFAG 0.4 sec Alessandro G. Ruggiero FFAG'04 Workshop

  17. S F g D g F S 1.5-GeV FFAG Lattice Design Energy Range 400 MeV - 1.5 GeV p = p0 ( 1 + ) Reference Momentum, p0 954.263 MeV/c Momentum Range,  0 - 1.36 Circumference 807.091 m No. of Periods 136 Period Length 5.9345 m Drifts: Long (S) 2.5345 m Short (g) 0.3 m F-sector: Length 0.70 m Field – 0.7841 kG Gradient 26.58 kG/m D-sector: Length 1.40 m Field 1.8345 kG Gradient – 23.30 kG/m Phase Advance / Period 105.23o / 99.93o Betatron Tunes, H / V 39.755 / 37.755 Transition Energy, T 105.482 i Non-Scaling FFAG Lattice Alessandro G. Ruggiero FFAG'04 Workshop

  18. H V  xco, cm F 1.5 GeV D 400 MeV s, m AGS FFAG -- Magnet Field Profiles kG, F-sector x, m n = 1,376 n = 220 kG, D-sector x, m Alessandro G. Ruggiero FFAG'04 Workshop

  19. kG 2.0 GeV 2.5 GeV 3.0 GeV kG F - Magnet D - Magnet x, m x, m kG kG F - Magnet D - Magnet x, m x, m kG kG F - Magnet D - Magnet x, m x, m Energy Tuneability -- Field Alessandro G. Ruggiero FFAG'04 Workshop

  20. x, cm 2.0 GeV 2.5 GeV 3.0 GeV H 2.0 GeV V 400 MeV  s, m x, cm H 2.5 GeV V 400 MeV  s, m x, cm 3.0 GeV H V 400 MeV  s, m Energy Tuneability -- Tunes Alessandro G. Ruggiero FFAG'04 Workshop

  21. Medical Facility -- 25-250 MeV Circumference 35.7626 m Number of Periods 24 Period Length 1.49011 m Drifts: S 0.320055 m g 0.075 m Sector Magnet FD Length, m 0.175 0.350 Field, kG –4.06078 9.50083 Gradient, kG/m 94.9977 –87.2587 Bend Radius, m –1.79099 0.76549 Bend Angle, rad –97.7112 2 x 228.611 Bending Ratio (D/F) 2.34 Packing Factor 0.472 Phase Advance (H/V) 111.6o/110.8o Betatron Tunes (H/V) 7.44/7.39 Transition Energy, T 18.12 i Alessandro G. Ruggiero FFAG'04 Workshop

  22. Medical Facility -- AFP Alessandro G. Ruggiero FFAG'04 Workshop

  23. Medical Facility -- Acceleration Harmonic Number 8 Energy Gain 100 keV/turn RF Peak Voltage 200 kVolt Number of Revolution 2,250 Acceleration Period 0.610 ms Repetition Rate 1 kHz Number of Protons per Cycle 1 x 1010 Emittance, rms normalized 1 π mm mrad Alessandro G. Ruggiero FFAG'04 Workshop

  24. Path Length versus Momentum AGS Upgrade = ( / f) df / d  = P –– P = T– P P P Medical Proton Driver Alessandro G. Ruggiero FFAG'04 Workshop

  25. CW Mode of Operation of FFAG In Preparation Alessandro G. Ruggiero FFAG'04 Workshop

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