Steady state inverse thermal analysis in supercooled accelerator cavities.

摘要

A heat conduction problem in Super Conducting Radio Frequency (SRF) cavities has been studied. The wall thickness is 1–4mm niobium and a ‘point heating’ source on the inner surface of the evacuated niobium cavity is assumed. Liquid helium acts as a coolant on the outer surface of the cavity to make the niobium electrically super conducting below its critical temperature. Using finite difference techniques, a computer program has been developed to solve the direct steady-state heat conduction equation. To simulate the actual thermal diagnostic setup at the Cyclotron Laboratory as closely as possible, the geometry for this computer program is 3-dimensional with insulated thermal sensors installed on the outer surface of the cavity. The insulated enclosures have different thermal properties from those of the niobium.; The results obtained through the program are useful for understanding the maximum sensor spacing, which allows detection of a 1 degree temperature rise at the heated surface (inner side) of the cavity.; Code verification is done with results obtained through the exact solutions generated by COND3D, developed for Sandia National Laboratory, and through the Kokopelli Finite Element Method program developed for Los Alamos National Laboratory. The results are discussed in detail with suggestions for future research.