Analysis of the longitudinal space charge impedance of a round uniform   beam inside parallel plates and rectangular chamber
  This paper analyzes the longitudinal space charge (LSC) impedances of a round uniform beam inside a rectangular and parallel plate chambers using the image charge method. This analysis is valid for arbitrary wavelengths and the calculation converges fast. The research shows that only a few of the image beams are needed to obtain a relative error less than 0.1%. The beam offset effect is also discussed in the analysis. 
Lanfa Wang (SLAC National Accelerator Laboratory), Yingjie Li   (Michigan State University)
physics.acc-ph