Magnetic (flux) coordinates are discussed where two solenoidal vector field
s are represented by straight lines. It is shown how to take advantage of t
his selection rule within a general method of constructing magnetic coordin
ates 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 con
sidered. In all these cases, there are at least two suitable divergence-fre
e vector fields in the initial equations. If no additional equations are at
tracted, the straightening of the lines of these two vectors appears to be
the only natural requirement of the optimal choice of flux coordinates. The
n, an admissible freedom in the choice of such coordinates is completely us
ed, and the two mentioned vectors are expressed in the simplest form.