Magnetic coordinates with double straightening

Magnetic (flux) coordinates are discussed where two solenoidal vector fields are represented by straight lines. It is shown how to take advantage of this selection rule within a general method of constructing magnetic coordinates based on straightening the magnetic lines and implicit prescription of the functional dependence of the Jacobian. The particular applications for MHD models describing the equilibrium of isotropic plasma, equilibrium of anisotropic plasma, and equilibrium of plasma with stationary flows are considered. In all these cases, there are at least two suitable divergence-free vector fields in the initial equations. If no additional equations are attracted, the straightening of the lines of these two vectors appears to be the only natural requirement of the optimal choice of flux coordinates. Then, an admissible freedom in the choice of such coordinates is completely used, and the two mentioned vectors are expressed in the simplest form