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The incoherent space-charge self-force tune shift of a bi-Gaussian coasting beam is revisited. The distribution density of the incoherent horizontal or vertical space-charge tune shift is computed numerically using a statistical method. Analytic approach has also been made with approximation. The results show a broad peak centered about 0.633 with a rms spread 0.168 of the linear space-charge tune shift.

Distribution of incoherent space-charge tune shift of bi-Gaussian beam