REGULAR AND CHAOTIC MOTIONS IN ION TRAPS - A NONLINEAR-ANALYSIS OF TRAP EQUATIONS

被引:33
作者
BAUMANN, G
NONNENMACHER, TF
机构
[1] Abteilung f̈r Mathematische Physik, Universität Ulm, D-7900 Ulm
来源
PHYSICAL REVIEW A | 1992年 / 46卷 / 05期
关键词
D O I
10.1103/PhysRevA.46.2682
中图分类号
O43 [光学];
学科分类号
070207 ; 0803 ;
摘要
Using Lie group methods and prolongation techniques for vector fields, we present heretofore undiscovered symmetries of nonlinear-dynamical equations that describe ion motion in the Paul and in the Penning trap, respectively. The two-ion motion in the trap is investigated in detail. Checking integrability of the nonlinear equations, both Painleve and modified Painleve tests failed. However, using symmetry properties discovered by prolongation techniques, we are able to construct integrals of motion and to discover conditions for those parameter combinations that lead to regular motion in the trap. These parameters, which can be related to experimentally adjustable physical quantities, axe listed. In the case of rotational invariance, the corresponding analytical solutions are derived from the integrals of motion. Parameter choices different from these values lead to chaotic motion, as demonstrated numerically by the calculation of Poincare sections as well as by the determination of the Lyapunov spectrum.
引用
收藏
页码:2682 / 2692
页数:11
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