The theory of photoionization describing the interaction of x-ray free-electron laser (XFEL) pulses and high-harmonic-generated (HHG) radiation is generalized to ultrashort laser pulses, where the concept of the standard ionization probability per unit time in Fermi’s golden rule and in Einstein’s theory breaks down. Numerical calculations carried out in terms of a generalized photoionization probability for the total duration of pulses in the near-threshold regime demonstrate essentially nonlinear behavior, while absolute values may change by orders of magnitude for typical XFEL and HHG pulses. XFEL self-amplified spontaneous emission pulses are analyzed to reveal general features of photoionization for random and regular spikes: the dependences of the nonlinear photoionization probability on carrier frequency and spike duration are very similar, allowing an analytical expectation value approach that is valid even when there is only limited knowledge of random and regular parameters. Numerical simulations carried out for typical parameters demonstrate excellent agreement.

中文翻译：

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XFEL和HHG与物质的相互作用：超短脉冲和随机尖峰的影响

描述X射线自由电子激光（XFEL）脉冲和高谐波产生（HHG）辐射相互作用的光电离理论被推广到超短激光脉冲，其中费米黄金理论中每单位时间的标准电离概率的概念规则，并在爱因斯坦的理论中崩溃了。以近似阈值范围内的脉冲总持续时间的广义光电离概率进行的数值计算表明，该行为本质上是非线性的，而对于典型的XFEL和HHG脉冲，绝对值可能会发生数量级的变化。分析了XFEL自放大自发发射脉冲，以揭示随机和规则尖峰的光电离的一般特征：非线性光电离概率对载波频率和尖峰持续时间的依赖性非常相似，即使只有很少的随机和常规参数知识，也可以使用有效的分析期望值方法。对典型参数进行的数值模拟显示出极好的一致性。