Magnetic levitation in two-dimensional geometry with translational invariance

Abstract

The development of activities in space and of the corresponding technologies requires research on the behavior of both matter and biological organisms under weightless conditions. Various methods have been invented in order to simulate weightlessness, for example, drop towers, sounding rockets, or parabolic flights. Magnetic field ground-based devices have also been developed. This paper introduces an optimization method of the magnetic field so as to obtain magnetic levitation in a two-dimensional cylindrical geometry.

Vibrations of a diamagnetically levitated water droplet

“…We first discuss how close to spherical it is possible to make the potential trap; that is, how small the coefficients c j , j > 0 can be made. Lorin and Mailfert have considered the relationship between the coil geometry (the distribution of the current density) and the shape of the potential trap [14]. Although we cannot alter the coil geometry, we can alter We now consider the effect on the droplet's eigenfrequencies of adding a harmonic component c j , j ≥ 2 to the potential trap.…”

Magnetogravitational potential revealed near a liquid-vapor critical point

“…This kind of restriction also occurs for magnetic compensation that can only be strictly performed in a space of lower dimensionality than the sample. [11][12][13][14] Depending on the magnetic field configuration, exact compensation can be achieved in a plane, a line, or a point; in a two-dimensional space, exact compensation can be obtained on a point or on a line.…”

Magnetic-Field Modulation of Gravity: Martian, Lunar, and Time-Varying Gravity

“…1a)-and in 2D-axisymmetric geometry-with rotational invariance ( Fig. 1b): When the magnetic field is made up of the first two harmonics, the radial and tangential components can be expressed in cylindrical geometry by (Lorin and Mailfert 2008a):…”

“…Leads us to define an inhomogeneity vector ε describing the relative precision of the compensation (Lorin and Mailfert 2008a):…”

“…The present theoretical work deals with this strategic point. Indeed, a magnetic force density can be created in a para-or dia-magnetic substance with only the help of the first two spatial harmonics of the magnetic field, whether it be in cylindrical geometry (translational invariance) (Lorin and Mailfert 2008a) or in axisymmetric geometry (rotational invariance) (Lorin and Mailfert 2008b). The cylindrical-geometry calculations done in this paper are based on a magnetic field distribution already explored in another way in previous work (combination of magnetic, gravitational and centrifugal forces) .…”