绕水平轴旋转的圆环上的珠子：一维有质动力陷阱
A bead on a hoop rotating about a horizontal axis: a 1-D ponderomotive trap
摘要：
我们描述了一个简单的机械系统，作为一个有质动力粒子陷阱，包括一个圆形的箍和一个无摩擦珠，与箍旋转的水平轴位于箍的平面。因此，环的框架中的珠子暴露于有效的正弦变化的引力场。这个场沿环的分量在顶部和底部为零。在同一帧中，珠粒经历在顶部和底部也为零的与时间无关的离心力。在理想的情况下，从最小的小位移的系统进行了分析，并显示满足马蒂厄方程的粒子的运动。在旋转轴与环相切的特定情况下，该系统是rf Paul离子阱的精确模拟。各种复杂的因素，如非谐项，摩擦和噪声被认为是。所提出的系统的一个工作模型已经构建，使用一个球轴承滚动在一个管沿一段自行车轮辋的外部。该装置详细演示了一个射频保罗陷阱的操作，通过再现被困原子离子的动力学和说明的方式，其中电势随时间变化。
英文摘要：
We describe a simple mechanical system that operates as a ponderomotive particle trap, consisting of a circular hoop and a frictionless bead, with the hoop rotating about a horizontal axis lying in the plane of the hoop. The bead in the frame of the hoop is thus exposed to an effective sinusoidally-varying gravitational field. This field's component along the hoop is a zero at the top and bottom. In the same frame, the bead experiences a time-independent centrifugal force that is zero at the top and bottom as well. The system is analyzed in the ideal case of small displacements from the minimum, and the motion of the particle is shown to satisfy the Mathieu equation. In the particular case that the axis of rotation is tangential to the hoop, the system is an exact analog for the rf Paul ion trap. Various complicating factors such as anharmonic terms, friction and noise are considered. A working model of the proposed system has been constructed, using a ball-bearing rolling in a tube along the outside of a section of a bicycle rim. The apparatus demonstrates in detail the operation of an rf Paul trap by reproducing the dynamics of trapped atomic ions and illustrating the manner in which the electric potential varies with time.
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