Relation between the magnetic free energy and relative magnetic helicity in the MHD extreme state of solar corona

<p>Magnetic helicity is a quantity describing the twist, writhe, and torsion of magnetic field lines and magnetic configurations . The concept of magnetic helicity has successfully been applied to characterize solar coronal processes. A conjecture about one approximation relation between free magnetic free energy and relative magnetic helicity in the MHD extreme state of solar corona has been proposed by using the concept of magnetic helicity conservation and Lie-Poisson mechanical structure of MHD. We use constant α force-free filed extrapolation to check out this relation. We also apply this relation to analyze the results from the simulations and observations. Such relation may be helpful to predict the solar activity like the solar flares and CMEs</p>

Relative magnetic helicity dissipation during the major flares

<p>    Magnetic helicity is conserved in ideal magnetic fluid and is still approximately conserved in the process of fast magnetic reconnection when the magnetic Reynolds number is large enough. We can derive the magnetic helicity injecting into corona from the magnetic helicity flux through photoshpere. A statistical research is carried out to investigate the dissipation of magnetic helicity during the major flares. We choose 69M-up flares from 16 major flare-productive active regions in 24th cycle to research the helicity in corona. Among these flares, 19 is X-up flares. We utilize Differential Affine Velocity Estimator for Vector Magnetograms (DAVE4VM) and 12-min successive vector magnetograms from Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) to derive the flux of magnetic helicity through photosphere. At the same time, we extrapolate the vector magnetic field in corona to calculate the relative helicity by the suppose of Non-linear Force Free Field (NLFFF). The calculation window is 12-18 minutes before and after flares. A well correlation is shown between the magnetic free energy and magnetic helicity, the threshold of triggering M-up flare is the change of magnetic helicity above 2×10<sup>42</sup>Mx<sup>2</sup> and the change of magnetic free energy above 3 × 10<sup>31</sup>erg . Considering one fifth of magnetic helicity injecting into corona, the dissipation of magnetic helicity during the flares is 6-7 % , which is corresponding to the result of previous numerical simulation results, which strongly support that the magnetic helicity is approximate conserved during the major flares.</p>