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arXiv 1111.1260physics.atom-phphysics.class-ph
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非线性可积离子阱

Nonlinear Integrable Ion Traps

S. Nagaitsev, V. Danilov

摘要:

通过引入特殊的静电势,四极离子阱可以转化为运动可积的非线性离子阱。这可以用固定电势(静电加均匀磁场)和时间相关的电势来完成。这些势被选择为使得单粒子Hamilton-Jacobi运动方程在某些坐标系中是可分离的。静电势具有几个可自由调节的参数,允许四极阱被变换成例如双阱或环形阱系统。粒子的运动保持规则,非混沌,可积的积分,并在很宽的参数范围内稳定。我们提出了两个例子,如何实现这样一个系统的情况下的时间无关(潘宁陷阱),以及一个时间相关的(保罗陷阱)配置。

英文摘要:

Quadrupole ion traps can be transformed into nonlinear traps with integrable motion by adding special electrostatic potentials. This can be done with both stationary potentials (electrostatic plus a uniform magnetic field) and with time-dependent electric potentials. These potentials are chosen such that the single particle Hamilton-Jacobi equations of motion are separable in some coordinate systems. The electrostatic potentials have several free adjustable parameters allowing for a quadrupole trap to be transformed into, for example, a double-well or a toroidal-well system. The particle motion remains regular, non-chaotic, integrable in quadratures, and stable for a wide range of parameters. We present two examples of how to realize such a system in case of a time-independent (the Penning trap) as well as a time-dependent (the Paul trap) configuration.

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