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

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.