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Paper: Three-Dimensional Simulations of the Parker’s Model of Solar Coronal Heating: Lundquist Number Scaling due to Random Photospheric Footpoint Motion
Volume: 429, Numerical Modeling of Space Plasma Flows, Astronum-2009
Page: 201
Authors: Ng, C. S.; Lin, L.; Bhattacharjee, A.
Abstract: The model of Parker (1972) is one of the mostly discussed mechanisms for coronal heating and has generated much debate. We have recently obtained new scaling results in a two-dimensional (2D) version of this problem suggesting that the heating rate becomes independent of resistivity in a statistical steady state (Ng & Bhattacharjee 2008) Our numerical work has now been extended to 3D by means of large-scale numerical simulations. Random photospheric footpoint motion is applied for a time much longer than the correlation time of the motion to obtain converged average coronal heating rates. Simulations are done for different values of the Lundquist number to determine scaling. In the large Lundquist number limit, results obtained so far are consistent with the trend that the coronal heating rate is independent of the Lundquist number, as predicted by previous analysis as well as 2D simulations. In the same limit the average magnetic energy built up by the random footpoint motion tends to saturate at a constant level, due to the formation of strong current layers and subsequent disruption when the equilibrium becomes unstable.
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