Particle beam eigenemittances comprise the lowest set of rms-emittances that can be imposed to a beam through symplectic optical elements. For cases of practical relevance this paper introduces an approximation providing a very simple and powerful relation between transverse eigenemittance variation and the beam phase integral. This relation enormously facilitates modeling eigenemittance tailoring scenarios. It reveals that difference of eigenemittances is given by the beam phase integral or vorticity rather than by angular momentum. Within the approximation any beam is equivalent to two objects rotating at angular velocities $\pm \omega$. A description through circular beam modes has been done already in [A. Burov, S. Nagaitsev, and Y. Derbenev, Circular modes, beam adapters, and their applications in beam optics, Phys. Rev. E 66, 016503 (2002)]. The new relation presented here is a complementary and vivid approach to provide a physical picture of the nature of eigenemittances for cases of practical interest.

中文翻译：

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粒子束本征比，相位积分，涡度和旋转

粒子束本征发射率包括可通过辛光学元件施加到光束的最低均方根发射率集合。对于实际相关的情况，本文介绍了一种近似方法，该方法提供了横向本征比变化与光束相位积分之间的非常简单而有效的关系。这种关系极大地促进了模型特征辐射剪裁场景的建模。结果表明，本征导率的差异是由束相位积分或涡度而不是角动量决定的。在近似范围内，任何光束都等效于两个以角速度旋转的物体$\pm \omega$。通过圆光束模式的描述已经在[A. Burov，S。Nagaitsev和Y. Derbenev，“圆形模式”，“光束适配器”及其在光束光学中的应用，《物理学报》。启ê 66，016503（2002）]。此处介绍的新关系是一种补充性的生动方法，可为实际感兴趣的情况提供特征量的性质的物理图景。