SNS SRF time dependent cavity RF resonance shift due to Lorentz force induced mechanical excitation

The Spallation Neutron Source (SNS) accelerator incorporates a Superconducting RF (SRF) accelerator for the final section of the three-section pulsed mode linac. The SRF linac cavities are of conventional thin-walled niobium construction. Dynamic detuning of the SRF cavities due to Lorentz force induced mechanical excitation is a critical concern in the design of such cavities. The pulsed RF induces cyclic Lorentz forces on the cavity surface that are proportional to the rising and falling surface magnetic and electric fields. The induced Lorentz force levels are small but will mechanically excite a thin-walled structurally compliant cavity. A FORTRAN code has been developed that calculates the time varying cavity frequency shift due to the cyclic Lorentz force excitation. The code generates an ABAQUS finite element mesh representing the cavity geometry and applies calculated Lorentz forces to the mesh utilizing cavity SUPERFISH results as input. ABAQUS is then utilized to calculate the deformed cavity shape due to the dynamic excitation, using very small time steps. The ABAQUS solver accounts for the time dependency of the Lorentz forces, inertial effects, material damping, and structural boundary conditions. An algorithm incorporating the Slater-perturbation theory is subsequently utilized to calculate the resonant frequency shift for the deformed cavity shape at every time increment