# Dynamic evolution of current sheets, ideal tearing, plasmoid formation and generalized fractal reconnection scaling relations

## TL;DR

This paper derives generalized scaling relations for fractal magnetic reconnection, showing that ideal tearing leads to universal aspect ratios and plasmoid formation, advancing understanding of explosive solar phenomena.

## Contribution

It introduces a unified framework for recursive tearing in current sheets, revealing universal aspect ratios and scaling laws independent of current profile details.

## Key findings

- Universal aspect ratio for ideal tearing in current sheets.
- Scaling relations for plasmoid number at realistic Lundquist numbers.
- Fractal cascade model explains rapid energy release in solar eruptions.

## Abstract

Magnetic reconnection may be the fundamental process allowing energy stored in magnetic fields to be released abruptly, solar flares and coronal mass ejection (CME) being archetypal natural plasma examples. Magnetic reconnection is much too slow a process to be efficient on the large scales, but accelerates once small enough scales are formed in the system. For this reason, the fractal reconnection scenario was introduced (Shibata and Tanuma 2001) to explain explosive events in the solar atmosphere: it was based on the recursive triggering and collapse via tearing instability of a current sheet originally thinned during the rise of a filament in the solar corona. Here we compare the different fractal reconnection scenarios that have been proposed, and derive generalized scaling relations for the recursive triggering of fast, `ideal' - i.e. Lundquist number independent - tearing in collapsing current sheet configurations with arbitrary current profile shapes. An important result is that the Sweet-Parker scaling with Lundquist number, if interpreted as the aspect ratio of the singular layer in an ideally unstable sheet, is universal and does not depend on the details of the current profile in the sheet. Such a scaling however must not be interpreted in terms of stationary reconnection, rather it defines a step in the accelerating sequence of events of the ideal tearing mediated fractal cascade. We calculate scalings for the expected number of plasmoids for such generic profiles and realistic Lundquist numbers.