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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

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performance limitations of the booster cavity

Performance Limitations of the Booster Cavity

Mohamed Hassan, VyacheslavYakovlev, John Reid

booster parameters
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
geometry of booster cavity
Geometry of Booster Cavity

Tetrode Conn?

Gap Details?


Inner Conductor Taper

Stack Pole


Tuner Conn

Ferrite Tuners

Some Drawing Details is Still Missing

Tuner Inner Taper?

material properties
Material Properties

Stack Pole


Ferrite Tuners

Toshiba Differential Permeability

Stack Pole Differential Permeability

Not enough range

Some Material Properties are Still Missing

simplified em model
Simplified EM Model


56.2 MHz


42.9 MHz


34.3 MHz

more realistic tuner
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
more realistic tuner permability bounds
More Realistic Tuner—Permability Bounds

Mu=20, 12.5

Mu=1.5, 1.5

The upper bound of permeability gives very close resonance frequency (26.99 MHz) from the measured value 26.17 MHz

voltage breakdown
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.

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


Without Blending Edges




Vacc=55 KV (2 Gaps)




With Blending Edges




Vacc=55 KV (2 Gaps)



Emax-Vac=3.70 MV/m

Ez-max=920 KV/m

Emax-Air=2.1 MV/m

Blend Radius=0.125”

1.65 MV/m

2.1 MV/m

1.69 MV/m

1.71 MV/m


With Blending Edges




Vacc=55 KV (2 Gaps)



Emax-Vacuum=2.85 MV/m

Ez-max=720 KV/m

Emax-Air=1.1 MV/m

Blend Radius=0.125”

0.83 MV/m

1 MV/m

0.85 MV/m

0.82 MV/m

tuner fields at 37 mhz
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
Tuner Fields at 37 MHz 2D


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

  • 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
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