Form Factor $g$ In Longitudinal Space Charge Impedance
Abstract
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.
 Publication:

arXiv eprints
 Pub Date:
 August 2015
 arXiv:
 arXiv:1508.00153
 Bibcode:
 2015arXiv150800153B
 Keywords:

 Physics  Accelerator Physics