3D transient eddy current fields using the u-v integral-eigenvalue formulation

The three-dimensional eddy current transient field problem is formulated using the u-v method. This method breaks the vector Helmholtz equation into two scalar Helmholtz equations. Null field integral equations and the appropriate boundary conditions are used to set up an identification matrix which is independent of null field point locations. Embedded in the identification matrix are the unknown eigenvalues of the problem representing its impulse response in time. These eigenvalues are found by equating the determinant of the identification matrix to zero. When the initial transient forcing function is Fourier decomposed into its spatial harmonics, each Fourier component can be associated with a unique eigenvalue by this technique. The true transient solution comes through a convolution of the impulse response, so obtained with the particular external field decay governing the problem at hand. The technique is applied to the FELIX (fusion electromagnetic induction experiments) medium cylinder experiment; computed results are compared with data. A pseudoanalytic confirmation of the eigenvalues so obtained is formulated to validate the procedure