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

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