The process of emission of electromagnetic radiation does not occur instantaneously, but is “formed” over a finite time known as the radiation formation time. In the ultrarelativistic regime, the corresponding (longitudinal) formation length is given by the formation time times the speed of light and controls several features of radiation. Here, we elucidate the importance of the transverse formation length (TFL) by investigating nonlinear Compton scattering by an electron initially counterpropagating with respect to a flying focus laser beam. The TFL is related to the transverse size of the radiation formation “volume” and, unlike the longitudinal formation length, has a quantum origin. Since the TFL is typically of the order of the Compton wavelength, where any laser field can be assumed to be approximately uniform, related quantum interference effects have been ignored. However, we show analytically that if the focus in a flying focus beam with $n_L\gg 1$ cycles moves at the speed of light and backwards with respect to the beam propagation direction, the effects of the TFL undergo a large enhancement proportional to $n_L$ and may substantially alter the differential emission probability for feasible flying focus pulses.

中文翻译：

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揭示非线性康普顿散射的横向形成长度

电磁辐射的发射过程不是立即发生的，而是在称为辐射形成时间的有限时间内“形成”的。在超相对论体系中，相应的（纵向）形成长度由形成时间乘以光速得出，并控制辐射的几个特征。在这里，我们通过研究电子最初相对于飞行焦点反向传播的非线性康普顿散射来阐明横向形成长度（TFL）的重要性激光束。TFL与辐射地层“体积”的横向尺寸有关，与纵向地层长度不同，它具有量子起源。由于TFL通常约为康普顿波长的量级，在此可以假定任何激光场都近似均匀，因此已忽略了相关的量子干涉效应。但是，我们通过分析表明，如果焦点在飞行聚焦光束中${ñ}_{\mathrm{大号}}\gg \mathrm{1个}$ 周期以光速移动并相对于光束传播方向向后移动，TFL的影响与 ${ñ}_{\mathrm{大号}}$ 并且可能会实质上改变可行的飞行聚焦脉冲的差分发射概率。