Collisional radiative (CR) models based on ab initio atomic structure calculation have been utilized over 20 years to analyze many-electron atomic and ionic spectra. Although the population distribution of the excited states in plasmas and their emission spectra are computed using CR models, systematic and analytical understanding of the population kinetics is still lacking. In this work, we present a reduced model of the population dynamics in many-electron atomic ions, in which we approximate the dense energy structure of complex many-electron atoms by a continuum, a continuous CR model (CCRM). Using this simplification, we show an analytical population distribution of many-electron atoms in plasmas and its electron-density and temperature dependence. In particular, the CCRM shows that the population distribution of highly excited states of many-electron atoms in plasmas resembles a Boltzmann distribution but with an effective excitation temperature. We also show the existence of three typical electron-density regions and two electron-temperature regions where the parameter dependence of the excitation temperature is different. Analytical representations of the effective excitation temperature and the boundaries of these phases are also presented.

中文翻译：

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使用连续碰撞辐射模型研究电离等离子体中多电子原子的种群动力学

从头算起的碰撞辐射（CR）模型原子结构计算已使用20多年，用于分析多电子原子和离子光谱。尽管使用CR模型计算了等离子体中激发态的总体分布及其发射光谱，但仍缺乏对总体动力学的系统和分析性了解。在这项工作中，我们提出了一个简化的多电子原子离子动力学模型，其中我们通过连续的连续CR模型（CCRM）来近似复杂的多电子原子的致密能量结构。使用这种简化，我们显示了等离子体中许多电子原子的分析种群分布及其电子密度和温度依赖性。尤其是，CCRM表明，等离子体中多电子原子的高激发态的总体分布类似于玻尔兹曼分布，但具有有效的激发温度。我们还表明存在三个典型的电子密度区域和两个电子温度区域，其中激发温度的参数依赖性不同。还给出了有效激发温度和这些相界的解析表示。