  We discuss a problem about magnetic collapse as a possible process for
singularity formation of the magnetic field in a finite time within ideal
magneto-hydrodynamics for incompressible fluids. This process is very important
from the point of view of various astrophysical applications, in particular, as
a mechanism of magnetic filaments formation in the convective zone of the Sun.
The collapse possibility is connected with compressibility of continuously
distributed magnetic field lines. A well-known example of the formation of
magnetic filaments in the kinematic dynamo approximation with a given velocity
field, first considered by Parker in 1963, rather indicates that the increase
in the magnetic field is exponential in time. In the case of the kinematic
approximation for the induction equation, the magnetic filaments formation is
shown to occur in areas with a hyperbolic velocity profile.
