Self-Organized Critical Model of Reconnection in a Coronal Loop

Mathematics – Logic

Scientific paper

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Scientific paper

Solar flares are the manifestation of a sudden, intense and spatially localized energy release in the solar atmosphere which may raise coronal temperature to 10^7 K. It is generally agreed that the energy source comes from magnetic reconnection which provides a mechanism for the topological rearrangement of the magnetic field lines that liberate thermal and kinetic energy. In 1988 E.N. Parker suggested a physical scenario for coronal heating based on the idea of "nanoflares". Parker's idea is that stochastic photospheric fluid motions shuffle the footpoints of magnetic coronal loops. The high electrical conductivity of the coronal plasma will lead to a tangled magnetic field configuration force free everywhere but in numerous small tangential discontinuities. Parker's model includes all the ingredients to produce a self-organized critical state (SOC): a slowly driven open dissipative system subject to a local instability requiring a triggering condition and an external forcing mechanism operating on a long time scale compared to the dynamical time scales. In the last decade many efforts have been made to provide a SOC model for solar flares. One of the weak points of those models is to map the model components to the physical quantities involved in the magnetic reconnection phenomena. In this work we develop a new generation of SOC models for solar flares. We construct a 2D lattice formed of parallel 'field lines' that are randomly deformed, leading to the development of tangential discontinuities. We define a instability condition in terms of the angle substended by adjacent fieldlines, and a discrete rule to reconnect and readjust these fieldlines if this criterion is met. This model can be driven to a SOC state characterized by a wide range of energy released in avalanches. This SOC model combines a very well-defined physical context with a relatively simple modeling.

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