Investigation of the transverse beam dynamics in the thermal wave model   with a functional method
  We investigated the transverse beam dynamics in a thermal wave model by using a functional method. It can describe the beam optical elements separately with a kernel for a component. The method can be applied to general quadrupole magnets beyond a thin lens approximation as well as drift spaces. We found that the model can successfully describe the PARMILA simulation result through an FODO lattice structure for the Gaussian input beam without space charge effects. 
Ji-ho Jang, Yong-sub Cho, Hyeok-jung Kwon