We examine the effect of laser focusing on the potential of a recently discussed scheme [M.F. Ciappina {\em et al}, Phys. Rev. A 99, 043405 (2019); Las. Phys. Lett. 17, 025301 (2020)] for in situ determination of ultra-high intensities of electromagnetic radiation delivered by multi-petawatt laser facilities. Using two model intensity distributions in the focus of a laser beam, we show how the resulting yields of highly charged ions generated in the process of multiple sequential tunneling of electrons from atoms, depend on the shape of these distributions. Our findings lead to the conclusion that an accurate extraction of the peak laser intensity can be made either in the near-threshold regime when the production of the highest charge state happens only in a small part of the laser focus close to the point where the intensity is maximal, or through the determination of the points where the ion yields of close charges become equal. We show that, for realistic parameters of the gas target, the number of ions generated in the central part of the focus in the threshold regime should be sufficient for a reliable measurement with highly sensitive time-of-flight detectors. Although positions of the intersection points generally depend on the focal shape, they can be used to localize the peak intensity value in a certain interval. Additionally to this analysis, we discuss the method in comparison to other recently proposed approaches for direct measurement of extreme laser intensities.

中文翻译：

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焦点形状对极端激光强度隧道电离探针效率的影响

我们研究了激光聚焦对最近讨论的方案的潜力的影响 [MF Ciappina {\em et al}, Phys. Rev. A 99, 043405 (2019); 拉斯。物理。莱特。17, 025301 (2020)] 用于原位测定多拍瓦激光设施提供的超高强度电磁辐射。使用激光束焦点中的两个模型强度分布，我们展示了在电子从原子的多次连续隧穿过程中产生的高带电离子的最终产量如何取决于这些分布的形状。我们的研究结果得出的结论是，当最高电荷状态的产生仅发生在靠近强度点的激光焦点的一小部分时，可以在接近阈值状态下准确提取峰值激光强度。是最大的，或者通过确定接近电荷的离子产率变得相等的点。我们表明，对于气体目标的实际参数，阈值范围内焦点中心部分生成的离子数量应该足以使用高度灵敏的飞行时间检测器进行可靠测量。虽然交点的位置通常取决于焦点形状，但它们可以用于在一定间隔内定位峰值强度值。除了这种分析之外，我们还讨论了与其他最近提出的直接测量极端激光强度的方法相比的方法。在阈值范围内焦点的中心部分产生的离子数量应该足以使用高度灵敏的飞行时间检测器进行可靠的测量。虽然交点的位置通常取决于焦点形状，但它们可以用于在一定间隔内定位峰值强度值。除了这种分析之外，我们还讨论了与其他最近提出的直接测量极端激光强度的方法相比的方法。在阈值范围内焦点的中心部分产生的离子数量应该足以使用高度灵敏的飞行时间检测器进行可靠的测量。虽然交点的位置通常取决于焦点形状，但它们可以用于在一定间隔内定位峰值强度值。除了这种分析之外，我们还讨论了与其他最近提出的直接测量极端激光强度的方法相比的方法。