Introduction Modal Analysis: Elliptical Cavity

Technical Division *under Contract No. DE-AC02-07CH11359

Project X

Project X is a proposed proton accelerator complex at Fermilab The CW low current operation of the Project X requires superconducting cavities to operate at a high loaded Q Therefore it requires mechanical design optimization of cavities to minimize the sensitivity to microphonics We present our experience in using COMSOL Multiphysics for evaluation of sensitivity of operatingfrequency shift due to both fluctuations in the helium pressure (df/dP) and mechanical resonances

Conclusion and References

M. Awida, I. Gonin, T. Khabiboulline, Y. Pischalnikov, W. Schappert, and V. Yakovlev Fermi National Accelerator Laboratory, P.O. Box 500, Batavia, IL, 60510, USA

Optimization of Mechanical Properties of Superconducting Cavities for Project X LINAC

Fermilab

Microphonics: Spoke Cavity

EM

• Eigen frequency simulation to findthe resonant frequency (f0)

Solid

Mech

• Find the deformation under givenpressure load (PL)

Moving Mesh

• Update the mesh after deformation

EM

• Eigen frequency simulation to findthe resonant frequency afterdeformation (fp)

Study1

• Eigen-frequency (tofind f0)

Study2

• Stationary (solvingonly for solidmechanics andmoving mesh)

• Eigen-frequency (tofind fp)

Electromagnetic Waves

• Solving only for the RFdomain

• Applying the proberboundary conditions

Solid Mechanics

• Solving only for the CavityVessel

• Applying the proper fixedconstraints, symmetries,displacements, andboundary load

Moving Mesh

• Solving for all domains

• Applying the properprescribed and free meshdeformation/displacement

Two Simulation Studies

Three Multiphysic

Modules

Niobium Shell

RF Domain

Stainless Steel Vessel

PMC

PEC

Fixed Constraint

Symmetry Boundaries

Pressure Boundary

Load

EM

• Eigen frequency simulation to find theresonant frequency (f0)

Solid

Mech

• Solid Model analysis in “mechanical”domain

Moving Mesh

• Update the mesh after deformation

EM

• Eigen frequency simulation to find theresonant frequency after deformation (fp)

Frequency shifts due helium pressure fluctuations is a major issue in superconducting RF cavities Here is an example for how df/dP is calulcated using COMSOL for a spoke cavity

Prescribed Displacement

u,v,w

Multiphysics analysis is essentially needed to model components for particle accelerators Frequency shifts due to pressure fluctuation needs to be carefully modeled in SRF cavities COMSOL as a multiphysics tool helped us a lot inthat perspective

References: 1. S. D. Holmes,”Project X functional requirementsspecification”, IPAC’12, New Orleans, THPPP090

𝒅𝒇

𝒅𝒑=𝒇𝒑−𝒇

𝟎

𝑷𝑳

Mechanical resonances are another concern for SRF cavities Here is an example for how we used COMSOLto resolve this issue for an elliptical cavity

df/dP [Hz/Torr]