According to the B-H curve and structural dimensions of the snubber by the Fink- Baker Method, the inductive voltage and the eddy current of any core tape with the thickness of the saturated regions are derived when the accelerator breakdown occurs. Using the Ampere's law, in each core tape, the eddy current of the core lamination is equal to the arc current, and the relation of the thickness of the saturated regions for different laminations can be deduced. The total equivalent resistance of the snubber can be obtained. The transient eddy current model based on the stray capacitance and the equivalent resistance is analyzed, and the solving process is given in detail. The exponential time constant and the arc current are obtained. Then, the maximum width of the lamination and the minimum thickness of the core tape are determined. The experimental time constant of the eddy current obtained, with or without the bias current, is approximately the same as that by the analytical method, which proves the accuracy of the adopted assumptions and the analysis method.