Magnetic helicity (volume integral of the product of the magnetic field vector B and the vector potential A), or its proxy, the current helicity at the surface (surface integral of B·J or BzJz), is an important quantity which characterizes the helical nature of solar magnetic fields. The current helicity on the Sun shows a tendency, though with large dispersion, that it is positive in the southern hemisphere and negative in the northern hemisphere (the helicity sign rule). However, there are indications that the helicity sign rule may be reversed at activity minimum periods. We will discuss the significance of this property by focusing on the statistical distributions of helicity whether its dispersion follows Gaussian distribution or not.

We review the theoretical studies of the Alfvén wave model of spicules and coronal heating, mainly based on the papers by Kudoh & Shibata (1999), Saito et al. (2001) and Moriyasu et al. (2004) which performed MHD numerical simulations of nonlinear Alfvén waves propagating along a magnetic flux tube in the solar atmosphere. Kudoh & Shibata (1999) and Saito et al. (2001) found that, if the root mean square of the perturbation is greater than ~ 1 km s−1 in the photosphere, (1) the transition region is lifted up to more than ~ 5000 km (i.e., the spicule is produced), (2) the energy flux sufficient for heating the quiet corona (~ 3.0 × 105 ergs s−1 cm−2) is transported into the corona by Alfvén waves. Moriyasu et al. (2004) demonstrated that a hot corona is created in an initially cool loop as a result of the nonlinear Alfvén waves produced near the photosphere. We conclude that the nonlinear Alfvén wave model is the promising model of spicules and coronal heating.

A three-dimensional, time-dependent, magnetohydrodynamic (MHD) model is constructed for the study of active region (AR) evolution. The new physics included in this model is differential rotation, meridional flow, effective diffusion and cyclonic turbulence effects, which means, that the photospheric shear is automatically generated instead of prescribed as is usually done for modeling. To benchmark this newly developed model, we have used observed active region NOAA/AR-8100 (October 29 - November 3, 1997) to verify the model by computation of the total magnetic flux and magnetic field maps of that active region. Then, we apply this model to compute the non-potentiality magnetic field parameters for possible coronal mass ejection production. These parameters are: (i) magnetic flux content ($\Phi$), (ii) the length of strong shear, strong-field main neutral line, ($L_{ss}$), (iii) the net electric current ($I_N$) and (iv) the flux normalized measure of the field twist ($\alpha$ = $\mu$$\frac{I_N}{\Phi}$). These parameters are compared with the measured values which showed remarkable agreement.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html