The expression of the exact transverse resistive-wall impedance of a round pipe with finite thickness was analytically derived and then the transverse resistive-wall wake functions of three pipes were numerically calculated from the impedance expression. Each of the calculated wake functions rapidly decreases around a time corresponding to the peak frequency of the impedance real part as compared with the conventional wake function so far used. As a result, the multi-bunch beam position displacement due to the resistive-wall wake in an ERL vacuum pipe is saturated around the time and does not increase unlimitedly with time. The saturated position displacement can be easily corrected with some correction scheme.
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