Lie map for the nonlinear transport of continuous intense beams in the axial-symmetric electrostatic fields

Nonlinear transport of intense continuous beam in the axial-symmetric electrostatic fields is analyzed with the Lie algebraic method. The K-V particle distribution is adopted in the analysis. The results obtained can be used in the calculations of the intense continuous beam dynamics in the beam optical systems consisting of drift spaces, electrostatic lenses, and DC electrostatic accelerating tubes. A computer code has been designed for practical simulations. To meet the needs of accurate calculation, all the elements are divided into many small segments, the electric fields in each segment are regarded as uniform fields, and the dividing points are treated as thin lenses. Iteration procedures are adopted in the code to obtain self-consistent solutions. The code can be used to design low energy dc beam transport systems, electrostatic accelerators, and ion implantation machines.