We investigate the dynamics of electrons counter-propagating along a radially polarized optical Bessel beam (OBB). (i) It is shown that a significant fraction of the electrons can be transversally trapped by the OBB even in the case of "un-matched’’ injection. Moreover, (ii) these transversally trapped particles (TTP) can be transported without loss along many thousands of wavelengths. As long as there is full longitudinal overlap between the electrons and laser pulse, this transport distance is only limited by the length of the OBB region. (iii) The unique profile of the transverse field components facilitates guiding either azimuthally symmetric pencil beams or annular beams. Space-charge tends to totally suppress the annular beams and it reduces the amount of charge trapped on axis for pencil beams. (iv) Assessment of the emittance of the TTP alone, reveals typical values of 10-50 pm. In fact, our simulations indicate if we trace the emittance of those particles that are trapped from the input to the output of the OBB, we find within the error associated with a relatively small number of micro-particles used in the simulation that this emittance is conserved. (v) We developed an analytic model whereby we average over the fast oscillation associated with the counter-propagating electrons and OBB The resulting Hamiltonian has a Bessel potential $J_1^2(u)$, which when operated in the linear regime near equilibrium, causes rotation of the phase-space. This permits determining the analytic conditions for the transverse emittance to be conserved. A Kapchinskij – Vladimirskij beam-envelope equation is derived including space-charge and emittance effects. In the OBB the beam radius at equilibrium is reconfigured according to the intensity of the OBB, electron energy and space-charge. Relying on conservation of the longitudinal canonical momentum, the energyspread in the interaction region is determined in terms of the OBB intensity and the electron energy. We show there is an inherent advantage on using a counter-propagating electron beam.

中文翻译：

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激光贝塞尔光束引导电子束

我们研究了沿径向偏振贝塞尔光束（OBB）反向传播的电子动力学。（i）已表明，即使在“不匹配”注入的情况下，OBB仍可将很大一部分电子横向俘获；此外，（ii）这些横向俘获粒子（TTP）可以无损失地被传输只要电子和激光脉冲之间存在完全的纵向重叠，该传输距离就仅受OBB区域长度的限制（iii）横向场分量的独特轮廓有利于任一方位角的引导对称的笔形光束或环形光束，空间电荷趋于完全抑制环形光束，并减少了笔形光束在轴上捕获的电荷量。（iv）仅对TTP的发射率进行评估，发现典型值为10-50 pm。实际上，我们的仿真表明，如果我们跟踪从OBB的输入到输出被捕获的那些粒子的发射率，则在与该仿真中使用的相对少量的微粒相关的误差范围内，我们发现该发射率是保守的。（v）我们开发了一个解析模型，可以对与反向传播的电子和OBB相关的快速振荡求平均。我们发现，在与模拟中使用的微粒数量相对较少相关的误差范围内，这种发射率是守恒的。（v）我们建立了一个解析模型，可以对与反向传播的电子和OBB相关的快速振荡求平均。我们发现，在与模拟中使用的相对较少数量的微粒相关的误差范围内，该发射率是守恒的。（v）我们建立了一个解析模型，可以对与反向传播的电子和OBB相关的快速振荡求平均。${Ĵ}_{\mathrm{1个}}^2（ü）$当在接近平衡的线性状态下运行时，会引起相空间旋转。这允许确定要保存的横向发射的分析条件。推导了一个Kapchinskij – Vladimirskij束包络方程，其中包括空间电荷和发射效应。在OBB中，根据OBB的强度，电子能量和空间电荷重新配置处于平衡状态的束半径。依赖于纵向规范动量的守恒，相互作用区域中散布的能量取决于OBB强度和电子能。我们证明了使用反向传播的电子束具有固有的优势。