In this paper, the nonlinear transport of intense bunched beams in electrostatic quadrupoles is analyzed using the Lie algebraic method, and the results are briefly presented of the linear matrix approximation and the second order correction of particle trajectory in the state space. Beam having K-V distribution and Gaussian distribution approximation are respectively considered. A brief discussion is also given of the total effects of the quadrupole and the space charge forces on the evolution of the beam envelope.
Recent calculations of the transport of a high-current beam in a solenoidal lens have made progress to the second order with the Lie algebraic method. A review of the theory and our simulation to realize it will be described. Then we will present the results of simulation. A brief discussion on the space charge effect＇s contribution to the transportation will also be made.
This paper uses the Lie algebraic method to analyse the charged particle trajectories in the spherical electrostatic analyser, and obtains the nonlinear solutions. The results show that the focusing abilities both in the x and y directions of the analyser are almost the same. Moreover, there exist dispersion effects in the x direction, and no dispersion effects in the y direction.
A code LEADS based on the Lie algebraic analysis for the continuous beam dynamics with space charge effect in beam transport has been developed. The program is used for the simulations of axial-symmetric and unsymmetrical intense continuous beam in the channels including drift spaces, electrostatic lenses and DC electrostatic accelerating tubes. In order to get the accuracy required, all elements are divided into many small segments, and the electric field in the segments is regarded as uniform field, and the dividing points are treated as thin lenses. Iteration procedures are adopted in the program to obtain self-consistent solutions. The code can be used in the designs of low energy beam transport systems, electrostatic accelerators and ion implantation machines.
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.
