Quantifying magnetic fluxes and reconnection rates in complex fields

太阳的大气层和大多数恒星的大气层一样，是由一个复杂的磁场构成的热等离子体组成的。每隔一段时间，磁场的结构就会发生一次突然的局部变化，即所谓的磁重联事件，这可能引发或大或小的等离子体爆发。这些爆发会加热大气，并将太阳大气中的等离子体释放到行星际空间。人们怀疑，这些重连过程不是以单个事件的形式发生，而是更多地以雪崩的形式发生，即最初的重大事件触发一系列较小的重连事件。然而，我们无法用目前的观测方法检测到这些。本提案旨在发展理论工具，以回答重连接是以单一事件的形式发生还是以雪崩的形式发生的基本问题。其中一个主要目标是确定磁重联的特征特征。这种重新连接的“指纹”是由磁场结构的特定变化给出的，可以用磁通量来量化。为了在观测到的太阳磁场中探测到这种重联的指纹，我们还必须分析它们的结构和所涉及的磁通量。为此，我们必须定义某些度量，即所谓的拓扑通量，本提案旨在定义这些度量并提供在任意磁场中找到它们的算法。最终，这些将使我们能够回答一个主要问题，即磁重联是作为单个事件还是雪崩发生的。这个问题的答案不仅对太阳物理学很有意义，而且对其他发现类似等离子体的领域也很有意义，比如在其他恒星的大气中，在吸积盘的湍流等离子体中，在聚变装置中的等离子体中。

The Sun's atmosphere, as well as the atmospheres of most stars, consists of a hot plasma which is structured by a complex magnetic field. At random intervals the structure of this magnetic field undergoes a sudden local change, a so-called magnetic reconnection event, which can trigger minor or major outbreaks of plasma. These outbreaks heat the atmosphere and release plasma from the solar atmosphere into the interplanetary space. It is suspected that these reconnection processes occur not in the form of individual events but more in the form of an avalanche, where an initial major event triggers a series of smaller reconnection events. However, we are unable to detect these with our current observational methods. This proposal aims to develop the theoretical tools to answer the fundamental question of whether reconnection occurs in form of a singular event or as an avalanche. One of the main goals is to identify the characteristic signature of magnetic reconnection. This 'fingerprint' of reconnection is given by a specific change in the structure of the field and can be quantified in terms of magnetic flux. In order to detect this fingerprint of reconnection in the observed magnetic fields on the Sun we have to analyse these also with respect to their structure and the magnetic fluxes involved. For this we must define certain measures, so-called topological fluxes, and the proposal aims to define these measures and provide algorithms for finding them in arbitrary magnetic fields. Eventually these will allow us to answer the main question as to whether magnetic reconnection occurs as an individual event or an avalanche. An answer to this question is not only of great interest to solar physics but also to other fields where similar plasmas are found such as in the atmospheres of other stars, in the turbulent plasma in accretion disks and the plasma in fusion devices.