Freezing-in condition for a magnetic field and current sheets in plasma

In the ideal magnetohydrodynamic approximation it is shown that for physically permissible boundary conditions there may exist some lines on which the freezing-in condition is not valid. Such singular lines are closed magnetic lines of force and lines with both ends on the boundary surface. By analogy with the singular lines of a potential magnetic field the conclusion is made that X-type singular lines are the place where current sheets (sheet pinches) appear in plasma, whereas on O-type singular lines quasi-cylindrical pinches of a usual type appear. (Auth.)