In this paper we present the theoretical analysis and the computer code design for the intense pulsed beam transport. Intense beam dynamics is a very important issue in low-energy high-current accelerators and beam transport systems. This problem affects beam transmission and beam qualities. Therefore, it attracts the attention of the accelerator physicists worldwide. The analysis and calculation for the intense beam dynamics are very complicated, because the state of particle motion is dominated not only by the applied electromagnetic fields, but also by the beam-induced electromagnetic fields （self-fields）. Moreover, the self fields are related to the beam dimensions and particle distributions. So, it is very difficult to get the self-consistent solutions of particle motion analytically. For this reason, we combine the Lie algebraic method and the particle in cell （PIC） scheme together to simulate intense 3D beam transport. With the Lie algebraic method we analyze the particle nonlinear trajectories in the applied electromagnetic fields up to third order approximation, and with the PIC algorithm we calculate the space charge effects to the particle motion. Based on the theoretical analysis, we have developed a computer code, which calculates beam transport systems consisting of electrostatic lenses, electrostatic accelerating columns, solenoid lenses, magnetic and electric quadruples, magnetic sextupoles, octopuses and different kinds of electromagnetic analyzers. The optimization calculations and the graphic display for the calculated results are provided by the code.
An intense dc beam nonlinear transport code has been developed. The code is written in Visual FORTRAN 6.6 and has ~13000 lines. The particle distribution in the transverse cross section is uniform or Gaussian. The space charge forces are calculated by the PIC (particle in cell) scheme, and the effects of the applied fields on the particle motion are calculated with the Lie algebraic method through the third order approximation. Obviously,the solutions to the equations of particle motion are self-consistent. The results obtained from the theoretical analysis have been put in the computer code. Many optical beam elements are contained in the code. So, the code can simulate the intense dc particle motions in the beam transport lines, high voltage dc accelerators and ion implanters.
The intense dc beam nonlinear transport was analyzed with the Lie algebraic method, and the particle trajectories of the second order approximation were obtained. Based on the theoretical analysis a computer code was designed. To get self-consistent solutions, iteration procedures were used in the code. As an example, we calculated a beam line (drift-electrostatic quadrupole doublet-drift). The results agree to the results calculated by using the PIC method.
Both the PIC (Particle-In-Cell) model and the Lie algebraic method can be used to simulate the transport of intense continuous beams. The PIC model is to calculate the space charge field, which is blended into the external field, and then simulate the trajectories of particles in the total field; the Lie algebraic method is to simulate the intense continuous beam transport with transport matrixes. Two simulation codes based on the two methods are developed respectively, and the simulated results of transport in a set of electrostatic lenses are compared. It is found that the results from the two codes are in agreement with each other, and both approaches have their own merits.
