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.

中文翻译：

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再谈非相对论梁的电阻墙尾流

在本文中，我们推导了在圆形管道中传播的梁的纵向和横向电阻壁阻抗， $v<C$。我们认为，从麦克斯韦方程组求解中获得的阻抗的一般公式中，必须减去空间电荷成分。经过这样的减法运算后，我们发现，即使相对于非相对论，在超相对论极限中得出的阻抗的经典表达式也适用于长束，这与Zimmermann和Oide的结论相反。牧师 梁 7，044201（2004）]。我们还计算了电阻墙的绿色功能唤醒$v<C$ 在较小的距离处，这表明在纵向尾波的原点和横向尾波的导数处的跳变被抹平了，并且尾波在源电荷的前面传播。