Eddy current loss calculation in thin rectangular plates at cryogenic temperatures and its experimental verification

Eddy current losses in conducting plates placed in a non-uniform alternating magnetic held at cryogenic temperatures have been calculated taking into account temperature dependencies of resistivity, heat capacity and heat-transfer coefficient. The calculation method is based on a coupled solution of a quasi-stationary electromagnetic problem and a non-stationary heat-conduction equation. A simplification of the task is achieved by neglecting eddy current reaction and free space charge. In this case the problem is solved in two stages: (1) the calculation of electromagnetic field; (2) the determination of a temperature distribution in the plate. As the first boundary condition for heat-conduction equation it is assumed that the heat transfer from edges of the plate equals zero. The second boundary condition is determined as a solution of the integral equation describing the law of conservation of energy relevant to the plate. The nonlinear two-dimensional heat conduction equation has been solved using partition of coordinates, implicit difference approximation and modified Thomas algorithm for obtained finite-difference equations. The numerical results remain in good agreement with data obtained by means of an experimental model of the cryogenic device, while neglecting thermal processes results in substantial errors amounting up to several hundreds percent