Calculation of electrostatic fields using quasi-Green's functions: application to the hybrid Penning trap
Calculation of electrostatic fields using quasi-Green's functions: application to the hybrid Penning trap
复制标题
使用准格林函数计算静电场：在混合潘宁陷阱中的应用
DOI：
10.1088/1367-2630/10/10/103009
复制
发表时间：
2008
影响因子：
3.3
通讯作者：
J. Walz
中科院分区：
文献类型：
--
作者：
J. Verdú;S. Kreim;K. Blaum;H. Kracke;W. Quint;S. Ulmer;J. Walz
潘宁阱为储存、操纵和研究带电粒子提供了独特的可能性，具有很高的灵敏度和准确性。彭宁陷阱在物理和化学领域的广泛应用包括质谱、激光光谱、电子和核磁矩的测量、化学样品分析和反应研究。我们开发了一种基于格林函数方法的方法，该方法允许对具有任意电极的Penning陷阱的静电特性进行分析计算。该分析将狄利克雷问题扩展到非平凡几何，并得到拉普拉斯方程的解析解。作为一个例子，我们讨论了为我们计划测量（反）质子的磁矩而设计的环形混合彭宁阱。与圆柱形Penning陷阱的情况一样，可以优化电陷阱场的性质，这对于单带电粒子的高精度实验是必不可少的。特别令人感兴趣的是量子跃迁光谱仪中连续斯特恩-格拉赫效应的非调和补偿、正交性和频移的最佳调节。所发展的数学形式主义不仅仅是设计新颖的潘宁陷阱，而且在物理和工程的其他领域有潜在的应用。
Penning traps offer unique possibilities for storing, manipulating and investigating charged particles with high sensitivity and accuracy. The widespread applications of Penning traps in physics and chemistry comprise e.g. mass spectrometry, laser spectroscopy, measurements of electronic and nuclear magnetic moments, chemical sample analysis and reaction studies. We have developed a method, based on the Green's function approach, which allows for the analytical calculation of the electrostatic properties of a Penning trap with arbitrary electrodes. The ansatz features an extension of Dirichlet's problem to nontrivial geometries and leads to an analytical solution of the Laplace equation. As an example we discuss the toroidal hybrid Penning trap designed for our planned measurements of the magnetic moment of the (anti)proton. As in the case of cylindrical Penning traps, it is possible to optimize the properties of the electric trapping fields, which is mandatory for high-precision experiments with single charged particles. Of particular interest are the anharmonicity compensation, orthogonality and optimum adjustment of frequency shifts by the continuous Stern–Gerlach effect in a quantum jump spectrometer. The mathematical formalism developed goes beyond the mere design of novel Penning traps and has potential applications in other fields of physics and engineering.