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Comparison of the PIC model and the lie algebraic method in the simulation of intense continuous beam transport

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Chinese Physics C 2009年第S2期33卷 125-127页

作者：赵小松吕建钦 State Key Laboratory of Nuclear Physics and Technology Peking University

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.

关键词： PIC model lie algebraic method intense continuous beam

Studies of Rigid Rotor-Rigid Surface Scattering in Dynamical lie algebraic method

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Communications in Theoretical Physics 2004年第3期41卷 357-361页

作者： WANGXiao-Yan DINGShi-Liang SchoolofPhysicalandMicroelectronics ShandongUniversityJinan250100China

The dynamical lie algebraic method is used for the description of statistical mechanics of rotationally inelastic molecule-surface scattering. It can give the time-evolution operators about the low power of and by solving a set of coupled nonlinear differential equations. For considering the contribution of the high power of and , we use the Magnus formula. Thus, with the time-evolution operators we can get the statistical average values of the measurable quantities in terms of the density operator formalism in statistical mechanics. The method is applied to the scattering of (rigid rotor) by a flat, rigid surface to illustrate its general procedure. The results demonstrate that the method is useful for describing the statistical dynamics of gas-surface scattering.

关键词： lie algebraic method scattering rigid rotor

lie algebraic analysis for the beam transport in the spherical electrostatic analyser

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Chinese Physics B 2007年第5期16卷 1280-1284页

作者：吕建钦张卓 Institute of Heavy Ion Physics Peking University Beijing 100871 China

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.

关键词： lie algebraic method spherical electrostatic analyser optical properties nonlinearity

Intense DC beam nonlinear transport-analysis & simulation

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Chinese Physics C 2009年第S2期33卷 121-124页

作者：吕建钦赵小松 State Key Laboratory of Nuclear Physics and Technology Peking University

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.

关键词： intense dc beam nonlinear trajectory lie algebraic method

Transport of 3D space charge dominated beams

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Chinese Physics C 2013年第10期37卷 75-77页

作者：吕建钦 State Key Laboratory of Nuclear Physics and Technology Peking University

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.

关键词： intense 3D beam nonlinear trajectory lie algebraic method PIC scheme

LEADS-DC:A computer code for intense dc beam nonlinear transport simulation

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LEADS-DC:A computer code for intense dc beam nonlinear trans...