Matrix method and program design of intense beam transport in quadrupole magnet

It is very difficult to calculate the nonlinear transport of a intense beam,because the particle trajectories depend on the electric potentials excited by the particle beams, and the electric potentials of the beams depend on the particle trajectories and the particle distributions in the phase spaces. So, it is necessary to solve the problem by iterations to get self-consistent solutions. We use transport matrix method to analyze the transportation in quadrupole magnet of non-intense pulsed beam and intense pulsed beam respectively, and write a computer code for the pulsed beam transporting in quadrupole magnet. The self-consistent solution can obtained by using iteration calculation method. During the calculation, the result can be shown by the prompt graph. (authors)