标题： 静电和磁四极子中的固有三阶像差 显示英文标题

标题： Intrinsic Third Order Aberrations in Electrostatic and Magnetic Quadrupoles

摘要： 固有像差是由于期望场配置的有限长度而产生的像差。 它们通常被松散地归因于边缘场。 这是具有误导性的，因为它暗示可以通过塑造场来减小这些影响。 事实上，存在一个与对称性破缺相关的不可消除分量。 即使在硬边缘极限情况下也存在，并且此外，其他（软边缘）效应可以简单地归因于在有限长度上分布的固有像差。 我们使用哈密顿形式重新推导了四极子的像差公式。 这使得静电和磁四极子之间的比较变得容易。 对于两个横向平面中大和小发射度的不同组合，发现某些情况下静电四极子的像差较低，而在其他情况下，磁四极子更好。 此外，我们讨论了现有传输代码如何处理四极子边缘场。 指出了潜在的问题并提出了改进建议。 显示英文摘要

摘要： Intrinsic aberrations are those which occur due to the finite length of the desired field configuration. They are often loosely ascribed to the fringing field. This is misleading as it implies that the effects can be minimized by shaping the fields. In fact, there is an irreducible component related to the broken symmetry. It is present even in the hard-edge limit, and moreover, the other (soft-edge) effects can be simply ascribed to the intrinsic aberration spread over a finite length. We rederive the aberration formulas for quadrupoles using a Hamiltonian formalism. This allows for an easy comparison of electrostatic and magnetic quadrupoles. For different combinations of large and small emittances in the two transverse planes, it is found that in some situations electrostatic quadrupoles have lower aberrations, while in others, magnetic quadrupoles are better. As well, we discuss the ways in which existing transport codes handle quadrupole fringe fields. Pitfalls are pointed out and improvements proposed.