Analytical treatment of the emittance growth in the main Linacs of future linear colliders

In this paper the single and multibunch emittance growths in the main linac of a linear collider are 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 is derived also by solving directly Fokker-Planck equation. Comparisons with numerical simulation results are made and the agreement is quite well.