The possibilities to accelerate vortex electrons with orbital angular momentum (OAM) to relativistic energies and to produce vortex ions, protons, and other charged particles crucially depend on whether the OAM is conserved during the acceleration and on how phase space of the wave packet evolves. We show that both the OAM and a mean emittance of the packet, the latter obeying the Schrdinger uncertainty relation, are conserved in axially symmetric fields of electric and magnetic lenses, typical for accelerators and electron microscopes, as well as in Penning traps. Moreover, a linear approximation of weakly inhomogeneous fields works much better for single packets than for classical beams. We analyze quantum dynamics of the packet’s rms radius ⟨ρ ²⟩, relate this dynamics to a generalized form of the van Cittert–Zernike theorem, applicable at arbitrary distances from a source and for non-Gaussian packets, and adapt the Courant–Snyder formalism to describe the evolution of the packet’s phase space. The vortex beams can therefore be accelerated, focused, steered, trapped, and even stored in azimuthally symmetric fields and traps, somewhat analogously to the classical angular-momentum-dominated beams. We also give a quantum version of the Busch theorem, which states how one can produce vortex electrons with a magnetized cathode during either field- or photoemission, as well as vortex ions and protons by using a magnetized stripping foil employed to change a charge state of ions. Spatial coherence of the packets plays a crucial role in these applications and we provide the necessary estimates for particles of different masses.

将具有轨道角动量 (OAM) 的涡旋电子加速到相对论能量并产生涡旋离子、质子和其他带电粒子的可能性，关键取决于 OAM 在加速过程中是否守恒以及波包的相空间如何演变。我们表明，OAM 和数据包的平均发射率（后者服从薛定谔不确定性关系）在电和磁透镜的轴对称场中是守恒的，典型的用于加速器和电子显微镜，以及在 Penning 陷阱中。此外，弱非均匀场的线性近似对于单个数据包比经典波束更有效。我们分析数据包的均方根半径 ⟨ ρ ^{2 的}量子动力学⟩，将此动力学与范西特-泽尼克定理的广义形式联系起来，适用于距源的任意距离和非高斯数据包，并采用 Courant-Snyder 形式主义来描述数据包相空间的演变。因此，涡旋光束可以被加速、聚焦、转向、捕获，甚至存储在方位对称的场和陷阱中，有点类似于经典的角动量主导光束。我们还给出了布施定理的量子版本，该定理说明了在场发射或光发射过程中如何通过磁化阴极产生涡流电子，以及通过使用磁化剥离箔来改变电荷状态的涡流离子和质子离子。