In this paper, we derive the longitudinal and transverse resistive wall impedance for a beam traveling in a round pipe with $v<c$. We argue that from the general formulas for the impedance obtained from the solution of the Maxwell equations one has to subtract the space charge component. After such subtraction, we find that the classical expressions for the impedance derived in the ultrarelativistic limit are also applicable for long bunches even when they are nonrelativistic—in contrast to the conclusion of Zimmermann and Oide [Phys. Rev. Accel. Beams 7, 044201 (2004)]. We also calculate the resistive wall Green-function wake for $v<c$ at small distances and show that the jump at the origin in the longitudinal wake and in the derivative of the transverse wake are smeared out and the wake propagates in front of the source charge.

• Received 26 June 2020
• Accepted 21 August 2020

DOI:https://doi.org/10.1103/PhysRevAccelBeams.23.094401

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Published by the American Physical Society