Magnetohydrostatic equilibria, in which the Lorentz force, the plasma pressure force and the gravitational force balance out to zero, are widely adopted as the zeroth order states of many astrophysical plasma structures. A magnetic flux-current surface is a surface, in which both magnetic field lines and current lines lie. We for the first time derive the necessary and sufficient condition for existence of magnetic flux-current surfaces in magnetohydrostatic equilibria. It is also shown that the existence of flux-current surfaces is a necessary (but not sufficient) condition for the ratio of gravity-aligned components of current density and magnetic field to be constant along each field line. However, its necessary and sufficient condition is found to be very restrictive. This finding gives a significant constraint in modeling solar coronal magnetic fields as force-free fields using photospheric magnetic field observations.

Recently, various efforts to make more speedy and precision machine tool to improve productivity and also various efforts to solve environmental problem are going on, so that dry cutting in manufacturing industry, which needs environmental conscious design and development of manufacturing technique, is becoming a very important assignment to solve. Because dry cutting does not use cutting fluid, we need other methods that can be used instead of cutting fluid, which does cooling, lubricating, chip washing, and anti-corrosion. Especially, because turning is a continuous work, the consideration of tool life and surface roughness due to continuous heat and poor lubrication is important. The purposes of this paper are the consideration of how well the compressed air can work instead of cutting fluid, and also the development of the method to select the optimum machining condition by the minimum numbers of experiments through the Taguchi method.