Lie Algebraic Analysis for the Nonlinear Transport of Intense Pulsed Beams in Electrostatic Lenses

Abstract：

The nonlinear transport of intense pulsed beams is analyzed with the Lie algebraic method in the case of K-V distribution , and the particle trajectories of second order approximation in the 6-D phase space (x,x′,y, y′, τ, pτ) are obtained. The beams could be axial-symmetrical or non-axial-symmetrical in the transverse direction. In the analysis, the effective fields of lens are divided into several small intervals. Each interval is treated as a uniform accelerating field and each dividing point is considered as a thin lens. Let the Lie map act on each uniform accelerating field and thin lens, the nonlinear particle trajectories can be obtained.