Nonlinear Analysis for the Electrostatic Analyzers With Lie Algebraic Methods

Abstract：

With the Lie algebraic methods, the charged particle trajectories in electrostatic analyzers are analyzed,and the third order solutions obtained. In this paper, we briefly describe the Lie algebraic methods and the procedures of calculating the nonlinear orbits. The procedures are: first, set up the Hamiltonian; then expand the Hamiltonian into a sum of homogeneous polynomials of different degrees; next, calculate the Lie map associating to the Hamiltonian; finally, apply the Lie map on the particle initial coordinates in the phase space, and obtain the particle nonlinear trajectories of the first order,the second order, and the third order approximations respectively. Higher orders solutions could be obtained if needed.