Analysis of Thermally Induced Frequency Shift for the Spallation Neutron   Source RFQ
  The Spallation Neutron Source (SNS) Front-End Systems Group at Lawrence Berkeley National Lab (LBNL) is developing a Radio Frequency Quadrupole (RFQ) to accelerate an H- beam from 65 keV to 2.5 MeV at the operating frequency of 402.5 MHz. The 4 section, 3.7 meter long RFQ is a 4 vane structure operating at 6% duty factor. The cavity walls are made from OFE Copper with a GlidCop outer layer to add mechanical strength. A set of 12 cooling channels in the RFQ cavity walls are fed and controlled separately from 4 channels embedded in the vanes. An ANSYS finite-element model has been developed to calculate the deformed shape of the cavity for given RF heat loads and cooling water temperatures. By combining the FEA results with a SUPERFISH RF cavity simulation, the relative shift in frequency for a given change in coolant temperature or heat load can be predicted. The calculated cavity frequency sensitivity is -33 kHz per 1 degC change in vane water temperature with constant-temperature wall water. The system start-up transient was also studied using the previously mentioned FEA model. By controlling the RF power ramp rate and the independent wall and vane cooling circuit temperatures, the system turn-on time can be minimized while limiting the frequency shift. 
S. Virostek, J. Staples