In the stellar chromospheres, radiative energy transport is dominated by only the strongest spectral lines. For these lines, the approximation of local thermodynamic equilibrium (LTE) is known to be very inaccurate, and a state of equilibrium cannot be assumed in general. To calculate the radiative energy transport under these conditions, the population evolution equation must be evaluated explicitly, including all time-dependent terms. We develop a numerical method to solve the evolution equation for the atomic-level populations in a time-implicit way, keeping all time-dependent terms to first order. We show that the linear approximation of the time dependence of the populations can handle very large time steps without losing accuracy. We reproduce the benchmark solutions from earlier, well-established works in terms of non-LTE kinetic equilibrium solutions and typical ionization/recombination timescales in the solar chromosphere.

在恒星色球层中，辐射能量传输仅由最强的谱线支配。对于这些线，局部热力学平衡 (LTE) 的近似值已知非常不准确，并且通常不能假设平衡状态。要计算这些条件下的辐射能量传输，必须明确评估种群演化方程，包括所有与时间相关的项。我们开发了一种数值方法，以时间隐式方式求解原子级种群的演化方程，将所有与时间相关的项保持为一阶。我们表明，种群时间相关性的线性近似可以处理非常大的时间步长而不会损失准确性。我们重现了之前的基准解决方案，