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Performance Limitations of the Booster Cavity Mohamed Hassan, Vyacheslav Yakovlev, John Reid

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Booster Parameters The Fermilab Booster is a synchrotron that accelerates protons from 400 MeV to 8 GeV The Booster circumference is 474.2 meters, the magnetic cycle is a biased 15 Hz sinusoid, and the RF operates at harmonic 84 of the revolution frequency

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Ferrite Tuners Stack Pole Toshiba Inner Conductor Taper Tetrode Conn? Tuner Conn Gap Details? Some Drawing Details is Still Missing Tuner Inner Taper? Ceramic? Geometry of Booster Cavity

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Material Properties Stack PoleToshiba µ max 12.520 Magnetic Loss Tangent @ 50 MHz 0.0050.007 Dielectric Const10.512 Dielectric Loss Tangent @ 50 MHz 0.005 Ferrite Tuners Stack Pole Toshiba Stack Pole Differential PermeabilityToshiba Differential Permeability Some Material Properties are Still Missing Not enough range

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Simplified EM Model µ=1.5 56.2 MHz µ=3 42.9 MHz µ=5 34.3 MHz

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More Realistic Tuner Added the 5 Toshiba ferrites, and the 9 Stack Pole pieces separated by the copper washers Tuner Connection is not correct yet here

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Mu=20, 12.5 Mu=1.5, 1.5 More Realistic Tuner—Permability Bounds The upper bound of permeability gives very close resonance frequency (26.99 MHz) from the measured value 26.17 MHz

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Latest Model

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Voltage Breakdown In Air ~ 3 MV/m (30 KV/cm) In Vacuum (according to Kilpatrick) is ~ 10 MV/m (theoretical) 18 MV/m (measured) Theoretical Kilpatrick Theoretical Peter et. Al. Measured W. Peter, R. J. Fael, A. Kadish, and L. E. Thode, “Criteria for Vacuum Breakdown in RF Cavities,” IEEE Transactions on Nuclear Science, Vol. Ns-30, No. 4, Aug 1983

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µ tp =8.4 µ sp =12.5/20.µ tp fres=37.5e6+j88.8e3 Vacc=55 KV (2 Gaps) R/Q=60 Q=212 Without Blending Edges

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µ tp =8.4 µ sp =12.5/20.µ tp fres=37.7e6+j88.8e3 Vacc=55 KV (2 Gaps) R/Q=59.8 Q=212 Emax-Vac=3.70 MV/m Ez-max=920 KV/m Emax-Air=2.1 MV/m Blend Radius=0.125” 2.1 MV/m1.65 MV/m 1.69 MV/m 1.71 MV/m With Blending Edges

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µ tp =3 µ sp =12.5/20.µ tp fres=53.9e6+j86.3e3 Vacc=55 KV (2 Gaps) R/Q=130 Q=312 Emax-Vacuum=2.85 MV/m Ez-max=720 KV/m Emax-Air=1.1 MV/m Blend Radius=0.125” 1 MV/m0.83 MV/m 0.85 MV/m 0.82 MV/m With Blending Edges

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Tuner Fields at 37 MHz Difficulties in getting accurate field representation of the triple points singularities due to limited computational resources

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Tuner Fields at 37 MHz 2D 2D simulation suggests that the max field exists at the 10 th, 11 th ferrite piece Abs(Ez)

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Simulation vs. Measurements

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Specifications for Design of New Accelerating Cavities for the Fermilab Booster CurrentModified Frequency Range37.80-52.82 MHzSame V acc 55 KV86 KV R/Q>50 Duty CycleEffectively 25%50% Repetition RateEffectively 7 Hz15 Hz Cavity TuningHorizontal BiasSame Beam Pipe Diameter 2.25”>3” Higher Order Mode Impedance <1000 Ohm CoolingLCW at 95 F, Water flow up to 21 gpm Same

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Challenges of the Cavity Modifications Weak points of max fields in Vacuum and Air will be more susceptible to break down Higher Gap Voltage Current cooling design may not tolerate the additional heating in tuners Higher Repetition Rate To resolve the activation problem Larger Beam Pipe

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Conclusion Full 3D model with most of the fine details has been created 3D EM simulation has been carried out at different frequencies Identified weak points of max electric field in air and vacuum at the different frequencies Need more data (material, geometry, and measured performance) to get the model closer to the physical structure

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What is next? More data collection – Material (Stack-Pole permeability vs. Bias Field N/A … So may be we measure it) – Geometrical features (Blended Edges, Tetrode Conn, Tuner Conn, Bias Geometry) – Measured Cavity Performance (Gap voltage vs. time, R/Q vs. freq) -- John promised to provide these data Improve the current model to get it closer to the physical cavity Thermal simulation to get a temperature profile along the cavity and specially in the tuner Double the repetition rate to 15 Hz and repeat the thermal simulation Change the pipe diameter to 3” and repeat the EM analysis Increase the gap voltage to 86 KV and find the max fields in vacuum and air

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