AI 中文总结
该研究针对等离子体尾场加速器，通过求解准相对论薛定谔方程获得电子涡旋态的解析解，验证了等离子体泡可稳定约束涡旋电子，为其后续加速研究提供了基础。
AI 中文摘要
等离子体尾场加速器（PWFAs）可提供10-100 GV/m的加速梯度，且相对论性传播的等离子体泡能够约束带电粒子。我们通过求解对应的准相对论薛定谔方程，研究泡中心处涡旋电子的稳定态，获得了拉盖尔-高斯横向模式与厄米-高斯纵向包络的解析解。将所得束流参数与实验可获得的涡旋电子束对比，发现等离子体泡支持的横向束腰与当前电子光学技术达到的相当；纵向约束还为稳定注入提供了有利参数范围。我们的结果表明，在等离子体泡尾场中维持局域化涡旋电子态是可行的，为研究其后续加速与稳定性提供了解析起点。
英文摘要
Plasma wakefield accelerators (PWFAs) offer accelerating gradients of 10-100~GV/m and relativistically propagating plasma bubbles capable of confining charged particles. We study the stationary states of a vortex electron at the bubble center by solving the corresponding quasi-relativistic Schrödinger equation. Analytical solutions are obtained with Laguerre-Gaussian transverse modes and Hermite-Gaussian longitudinal envelopes. Comparing the resulting beam parameters with experimentally accessible vortex-electron bundles, we find that the transverse beam waist supported by the plasma bubble is comparable to that achieved by current electron-optical techniques. The longitudinal confinement further provides a favorable parameter regime for stable injection. Our results indicate the feasibility of maintaining localized vortex-electron states in a plasma-bubble wakefield and provide an analytical starting point for investigating their subsequent acceleration and stability.
