To simulate the intense bunched beam transport, a computer program LEADS-3D has been developed. The particle trajectories are analysed with the Lie algebraic method. The third order approximation of the trajectory solutions is made with space charge forces off, and the second order approximation is made with space charge forces on. The particle distribution in the 3D ellipsoid is uniform or Gaussian. Most of the conventional beam optical elements are incorporated in the code. The optimization procedures are provided to fit the beam lines to satisfy the given optical conditions.
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.
The intense dc beam transport in the solenoid lenses is analyzed with the Lie algebraic method,and the transfer matrix with space charge effects is obtained.Two cases are considered:one of them is that the external focusing force is greater than the space charge force;another is that the external force is less than the space charge force.The theoretical results are coded and used in the calculations of a low energy beam transport after the ECR ion source.
