Performance Limitations of the Booster Cavity

Mohamed Hassan, Vyacheslav Yakovlev, John Reid

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

Ferrite Tuners

Stack Pole Toshiba

Inner Conductor Taper

Tetrode Conn?

Tuner Conn

Gap Details?

Some Drawing Details is Still MissingTuner Inner Taper?

Ceramic?

Geometry of Booster Cavity

Material PropertiesStack Pole Toshiba

µmax 12.5 20

Magnetic Loss Tangent @ 50 MHz

0.005 0.007

Dielectric Const 10.5 12

Dielectric Loss Tangent @ 50 MHz

0.005 0.005 Ferrite Tuners

Stack Pole Toshiba

Stack Pole Differential PermeabilityToshiba Differential Permeability

Some Material Properties are Still Missing

Not enough range

Simplified EM Model

µ=1.556.2 MHz

µ=342.9 MHz

µ=534.3 MHz

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

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

Latest Model

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 KilpatrickTheoretical 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

µtp=8.4µsp=12.5/20.µtp

fres=37.5e6+j88.8e3Vacc=55 KV (2 Gaps)R/Q=60Q=212

Without Blending Edges

µtp=8.4µsp=12.5/20.µtp

fres=37.7e6+j88.8e3Vacc=55 KV (2 Gaps)R/Q=59.8Q=212Emax-Vac=3.70 MV/mEz-max=920 KV/mEmax-Air=2.1 MV/mBlend Radius=0.125”

2.1 MV/m1.65 MV/m

1.69 MV/m1.71 MV/m

With Blending Edges

µtp=3µsp=12.5/20.µtp

fres=53.9e6+j86.3e3Vacc=55 KV (2 Gaps)R/Q=130Q=312Emax-Vacuum=2.85 MV/mEz-max=720 KV/mEmax-Air=1.1 MV/mBlend Radius=0.125”

1 MV/m0.83 MV/m

0.85 MV/m0.82 MV/m

With Blending Edges

Tuner Fields at 37 MHz

Difficulties in getting accurate field representation of the triple points singularities due to limited computational resources

Tuner Fields at 37 MHz 2D

2D simulation suggests that the max field exists at the 10th , 11th ferrite piece

Abs(Ez)

Simulation vs. Measurements

Specifications for Design of New Accelerating Cavities for the Fermilab Booster

Current Modified

Frequency Range 37.80-52.82 MHz Same

Vacc 55 KV 86 KV

R/Q >50

Duty Cycle Effectively 25% 50%

Repetition Rate Effectively 7 Hz 15 Hz

Cavity Tuning Horizontal Bias Same

Beam Pipe Diameter

2.25” >3”

Higher Order Mode Impedance

<1000 Ohm

Cooling LCW at 95 F, Water flow up to 21 gpm

Same

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

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

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