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For present projects, such as X-FEL and ILC, the SC technology is chosen for the main linacs. However, in some special parts, NC cavities are applied, operating with high electric and magnetic fields. RF gun cavities with an electric field up to 60 MV/m at the photo cathode are now under development. Capture cavities in the ILC positron source should operate with an accelerating gradient of up to 15 MV/m, practically the same value (14 MV/m), as for the CDS booster cavity in the Photo Injector Test Facility at DESY in Zeuthen (PITZ). High field strength leads to high specific RF heat loading. In combination with long RF pulses (~ 1ms) it results in substantial surface temperature rise, small cavity shape deformations and measurable frequency shifts. In this report we discuss both particularities and some general regularities related to long pulse operation of L-band cavities. Results of 3D numerical simulations for cavity surface temperature, displacements distributions and corresponding frequency shifts for different cavities are presented and compared with existing experimental data. The presented results will give the input for cavities optimization and sub-systems improvements.
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