The question of electromagnetic field intensification towards the values typical for strong field quantum electrodynamics is of fundamental importance. One of the most promising intensification schemes is based on the relativistic-flying mirror concept, which shows that the electromagnetic radiation reflected by the mirror will be frequency upshifted by a factor of $4{\gamma }^2$ ($\gamma$ is the Lorentz factor of the mirror). In laser-plasma interactions, such a mirror travels with relativistic velocities through plasma and typically has a parabolic form, which is advantageous for light intensification. Thus, a relativistic-flying parabolic mirror reflects the counterpropagating radiation in the form of a focused and flying electromagnetic wave with a high frequency. The relativistic-flying motion of the laser focus makes the electric and magnetic field distributions of the focus complicated, and the mathematical expressions describing the field distributions of the focus become of fundamental interest. We present analytical expressions describing the field distribution formed by an ideal flying mirror which has a perfect reflectance over the entire surface and wavelength range. The peak field strength of an incident laser pulse with a center wavelength of ${\lambda }_0$ and an effective beam radius of $w_e$ is enhanced by a factor proportional to ${\gamma }^3(w_e/{\lambda }_0)$ in the relativistic limit. Electron-positron pair production is investigated in the context of invariant fields based on the enhanced electromagnetic field. The pair production rate under the relativistic-flying laser focus is modified by the Lorentz $\gamma$-factor and the beam radius-wavelength ratio ($w_e/{\lambda }_0$). We show that the electron-positron pairs can be created by colliding two counterpropagating relativistic-flying laser focuses in vacuum, each of which is formed when a 180 TW laser pulse is reflected by a relativistic-flying parabolic mirror with $\gamma =12.2$.

中文翻译：

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通过激光产生的抛物面等离子体反射镜进行相对论飞行激光聚焦

将电磁场增强到强场量子电动力学的典型值的问题具有根本重要性。最有前途的增强方案之一是基于相对论飞镜的概念，这表明反射镜反射的电磁辐射将频率上移一个因子$4{\gamma }^2$ ($\gamma$是镜子的洛伦兹因子）。在激光-等离子体相互作用中，这样的镜子以相对论速度穿过等离子体，并且通常具有抛物线形式，这有利于光的增强。因此，相对论飞行抛物面镜以聚焦和飞行的高频电磁波的形式反射反向传播的辐射。激光焦点的相对论飞行运动使得焦点的电场和磁场分布变得复杂，描述焦点场分布的数学表达式成为人们最关心的问题。我们提出了描述由理想飞行镜形成的场分布的解析表达式，该飞行镜在整个表面和波长范围内具有完美的反射率。${\lambda }_0$ 和有效光束半径 ${瓦}_{\mathrm{电子}}$ 由一个成正比的因子增强 ${\gamma }^3({瓦}_{\mathrm{电子}}/{\lambda }_0)$在相对论极限。在基于增强电磁场的不变场的背景下研究电子-正电子对的产生。相对论飞行激光聚焦下的对产生率由洛伦兹修正$\gamma$-factor 和光束半径-波长比（${瓦}_{\mathrm{电子}}/{\lambda }_0$）。我们表明，可以通过在真空中碰撞两个反向传播的相对论飞行激光焦点来产生电子 - 正电子对，每个焦点都是在 180 TW 激光脉冲被相对论飞行抛物面镜反射时形成的$\gamma =12.2$.