具有时间非局部 $\alpha$ 效应的振荡发电机模型
Oscillating dynamo models with a time-nonlocal $α$ effect
- Leibniz-Institut für Astrophysik Potsdam (AIP)（波茨坦阿斯特罗物理研究所）
- University of Potsdam（波茨坦大学）
- INAF, Catania Astrophysical Observatory（意大利国家天体物理研究所，卡塔尼亚天文台）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究将传统α效应扩展为时间非局部形式，发现其能简化发电机激发、延长周期并产生锯齿状磁场轮廓，且能重现Waldmeier趋势及类似蒙德极小期的弱周期事件。
AI中文摘要：
传统的 $\alpha$ 效应通过加入时间一阶导数进行扩展，使得在湍流中，进入感应过程的磁场实际上是在过去时刻被采样的。因此，与由局部标准公式获得的解相比，发电机激发变得更容易，周期时间也得以延长。磁周期的时域形状也发生改变，上升时间变得比下降时间更短，从而使轮廓呈现出特有的“锯齿”外观。在非局部公式中，感应磁场振幅对关联时间产生了额外的依赖性。对于固定的发电机数，场振幅在某个特定的关联时间处达到最大值。当关联时间大于该峰值时，模型能够重现从太阳黑子观测中已知的Waldmeier型趋势。如果实际关联时间在该值附近波动，长期磁周期偶尔会进入弱周期事件，这些事件让人联想到诸如蒙德极小期等重大极小期。然而，对于接近临界值的较小发电机数，需要相当长的关联时间才能出现这种行为。
英文摘要：
The traditional $α$ effect is extended by the first temporal derivative, so that in turbulent flows the magnetic field entering the induction process is effectively sampled in the past. As a consequence, dynamo excitation becomes easier and cycle times are prolonged relative to solutions obtained from the local standard formulation. The temporal shape of the magnetic cycles is also modified, with rise times becoming shorter than decline times, so that the profiles acquire a characteristic ``sawtooth'' appearance. In the nonlocal formulation, the induced magnetic-field amplitudes acquire an additional dependence on the correlation time. For fixed dynamo number, the field amplitude reaches a maximum at a certain correlation time. For correlation times larger than this peak value, the model can reproduce Waldmeier-type trends known from solar sunspot observations. If the actual correlation time fluctuates around this value, the long-term magnetic cycle can occasionally enter weak-cycle episodes reminiscent of grand minima such as the Maunder minimum. For smaller dynamo numbers close to the critical one, however, rather long correlation times are required for this behaviour to occur.
