Quantifying magnetic fluxes and reconnection rates in complex fields

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.