On Force-Free Magnetic Fields with non-constant proportionality factor and their applications to High Temperature Superconductors Theory, applying quaternmonic analysis

We review the state of the art of quaternionic solutions for the Force-Free Magnetic Field equations rot Boarr = alphaBoarr (1) div Boarr = 0, where alpha is a non-constant proportionality factor and Boarr is the magnetic induction vector, applied to the study of High Temperature Superconductors. We introduce one method for rewriting this system of equations in quaternionic form, and particularly, we review one technic for obtaining new classes of solutions when alpha is an arbitrary function of one spatial variable and one approach for obtaining solutions for one special case of alpha depending on three spatial variables.