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Touschek Lifetime of an Elliptical Electron Beam with Horizontal and Vertical Betatron Oscillations

The Touschek lifetime of an elliptical electron beam is discussed considering the horizontal and vertical betatron oscillations using the cross section for nonrelativistic Möller scattering. Complex integration of the lifetime is numerically calculated and formulated in an analytical expression for the convenience of practical application. The present lifetime is reduced to the conventional ribbon beam formula in the extreme case of a flat beam. The results agree with the lifetime experimentally determined in a small storage ring, SOR-RING, in the whole range of small and large coupling of horizontal and vertical oscillations.