In this paper the single bunch emittance growth in the main linac of a linear collider is analytically treated in analogy to the Brownian motion of a molecule, and the analytical formulae for the emittance growth due to accelerating structure misalignment errors are obtained by solving Langevin equation. The same set of formulae are derived also by solving directly Fokker-Planck equation. Comparison with numerical simulation result is made and the agreement is quite well. The problem of the single bunch emittance growth in an electron storage ring is also discussed.

In this paper, we investigate the dynamical behaviours of a continuous intense charged particle beam in a transport system. It is assumed that fermion particles, such as electron and proton, in the beam follow Fermi-Dirac statistics in the equilibrium state. The halo particles executing stochastic motions due to the envelope oscillation induced nonlinear resonances are investigated. Analytical formulae for the halo current and halo current loss rate on the beam pipe wall are established.

After giving an analytical expression for the single bunch short range wake potential of a storage ring, we have discussed separately the roles of linear and nonlinear terms of the Taylor expansion of the wake potential on the bunch longitudinal motion. The equations describing bunch lengthening and increase in energy spread are established. Applications to different operatingmachines are made.