Lorentz detuning of superconducting cavities with unbalanced field profiles

Tests on the prototype SNS medium beta cryomodule showed a strong correlation between the flatness of the field profile and the Lorentz detuning coefficient (both static and dynamic). We present an analytical model for the enhancement of the Lorentz detuning as a function of the flatness of the field profile resulting from a spread of the frequencies of the individual cells of the cavity.