标题： 形式因子$g$在纵向空间电荷阻抗中 显示英文标题

标题： Form Factor $g$ In Longitudinal Space Charge Impedance

摘要： 在进行纵向空间电荷对纵向运动影响的计算时，横向束流尺寸出现在一个形式因子中，通常写为$g=1+2\ln (b/a)$。 事实上，这个表达式适用于束流中横向分布均匀且贝特龙振幅为零的粒子。 认为应该使用横向分布的平均值，而不是轴上的值。 显示对于现实的“二项式”分布族，如果将$a$解释为束流均方根宽度的两倍，则上述$g$表达式中的 1 应替换为接近 0.5 的值。 显示英文摘要

摘要： In carrying out calculations of the effect of longitudinal space charge on longitudinal motion, the transverse beam size appears in a form factor which is usually written as $g=1+2\ln (b/a)$. In fact, this expression applies to particles with vanishing betatron amplitude in a beam with uniform transverse distribution. It is argued that an average over the transverse distribution should be used instead of the value on axis. It is shown that for the realistic `binomial' family of distributions the 1 in the above expression for $g$ should be replaced by a value near 0.5 if $a$ is interpreted as twice the rms width of the beam.