Magnetic levitation is a way of using electromagnetic fields to levitate objects without any noise. It employs diamagnetism, which is an intrinsic property of many materials referring to their ability to temporarily expel a portion of an external magnetic field. As a result, diamagnetic materials are repelled by strong magnetic fields. This repulsive force, however, is very weak compared with the attractive force due to magnetic fields. Maglev is the means of floating one magnet over another. This maglev system is divided into two types attractive systems and repulsive systems, which are referred to as electromagnetic suspension and electrodynamics suspension. Thus many countries spend billions of dollars to use this maglev system.

http://ieeexplore.ieee.org/iel5/45/34572/01649010.pdf

Magnetic levitation

This paper considers the stability of a horizontal liquid-metal
 free surface in the presence of a horizontal alternating magnetic field. A weak formulation
 is used to derive a generalized Mathieu–Hill equation for the evolution of surface
 perturbations. Previous studies which rely on time-averaging the electromagnetic force
 over one field cycle have predicted a generally weak instability, but we find much larger
 growth rates near the resonances, where the surface wave frequency is an integral multiple
 of the field frequency. The method can be extended to include viscous and ohmic
 damping; the former has little effect, while the latter damps all waves except those
 whose frequency is close to the field frequency. Growth rates can be closely
 approximated by simple algebraic formulae, as can the critical magnetic field strength
 for the onset of instability.

/pdf/instability-of-a-plane-conducting-free-surface-submitted-to-5bmj09w707.pdf

Instability of a plane conducting free surface submitted to an alternating magnetic field

The influence of a uniform magnetic field on an electrically conducting fluid generally yields greater stability and delays the appearance of turbulence. Schematically, this is due to the fact that, in general, perturbations induce eddy currents, whose energy is dissipated by Joule heating. In this chapter, we intend to analyse this phenomenon specifying how the critical conditions depend on the applied magnetic field and discussing the specific features of the perturbations which can nevertheless exist in the presence of a magnetic field.

Stability and turbulence

This paper considers the stability of a horizontal liquid-metal free surface in the presence of a horizontal alternating magnetic eld. A weak formulation is used to derive a generalized Mathieu{Hill equation for the evolution of surface perturbations. Previous studies which rely on time-averaging the electromagnetic force over one eld cycle have predicted a generally weak instability, but we nd much larger growth rates near the resonances, where the surface wave frequency is an integral multiple of the eld frequency. The method can be extended to include viscous and ohmic damping; the former has little eect, while the latter damps all waves except those whose frequency is close to the eld frequency. Growth rates can be closely approximated by simple algebraic formulae, as can the critical magnetic eld strength for the onset of instability.

Instability of a plane conducting free surface submitted to an alternating magnetic eld

The stability of an interface between inviscid fluids subjected to a high-frequency magnetic field has been examined previously by Garnier & Moreau. We extend that study to include the viscosity of both fluids in order to estimate the damping rates of the perturbations. Furthermore, Garnier & Moreau made an assumption that the frequency of oscillation of the interface could be neglected compared to the frequency of the applied field; they concluded that the applied field was not destabilizing. That (apparently reasonable) assumption has been lifted in the present work and the consequence is that the magnetic field is seen to lead to instability over a significant range of wavelengths. Application of this analysis to the electromagnetic casting of aluminium is discussed

The stability of an interface between viscous fluids subjected to a high-frequency magnetic field and consequences for electromagnetic casting

High‐frequency electromagnetic (EM) fields are investigated for the levitation of thin horizontal sheets of liquid metal. A magnetic configuration is analyzed in which inductance stabilization provides global stability and magnetic flux compression provides local stability. Stability analysis indicates that frequencies greater than about 24 kHz are desirable to stably levitate 6 mm thick steel. For stability in systems without active feedback, a conducting screen is required below the metal, with a gap between the screen and the molten metal of no more than twice the metal thickness. Experiments in which 10 kHz EM fields were used to statically levitate sheets of molten tin indicate that dominant magnetohydrodynamic instabilities are of the Rayleigh–Taylor type and correspond to theory.

Tom Wiencek

Papers

Magnetohydrodynamic stability in the electromagnetic levitation of horizontal molten-metal sheets