Theory and Applications of Electromagnetic Levitation
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THEORY AND APPLICATIONS OF ELECTROMAGNETIC LEVITATION R. T. FROST AND C. W. CHANG General Electric,
Space Systems Division, Box 8555,
Philadelphia,
PA 19101
ABSTRACT The basic theory of electromagnetic levitation of conducEmphasis ting specimens by alternating fields is reviewed. is placed upon simple approximation formulae useful in Recent planning and interpreting laboratory measurements. work involving computer solutions for forces and heating by complex field coil configurations, including those with Applications and excitation, is described. polyphase limitations of the technique both terrestrially and in a microgravity environment are discussed.
INTRODUCTION The Electromagnetic levitation techniques were patented by Muck in 1922. original German patent is interesting in that many of the subsequent developSubsequent applications have included ments were foreseen and claimed. measurement of high temperature thermophysical properties, purification of metals, homogenization of alloys, studies of metal-gas reactions, undercooling studies, and containerless formation of alloys from elements to avoid crucible contamination. The earliest, easily available theoretical treatment of a conducting sphere immersed in a uniform oscillating magnetic field is the classic work of Smythe [1]. He gave the general expressions for the magnetic vector potential We shall display the analysis and eddy current density within such a sphere. of this problem in what we believe is a simpler explicit form than given previously. Simple expressions for the currents, fields, and forces near the sphere surface can be written and give a good physical insight of what is going on for many cases of physical interest. ELECTROMAGNETIC LEVITATION:
SIMPLEST TREATMENT
First, however, we shall treat the electromagnetic levitation problem in the This rather naive treatment gives some useful ansimplest possible manner. swers; we shall show that these simple ideas are in fact borne out by the more exact treatment to be given later. The basic idea is that an alternating magnetic field Bo acting on a spherical conducting specimen will generate eddy currents. These currents will be strongest at the surface and by Lenz's law are in such a direction as to oppose the impressed field and exclude it from the interior. The circulating eddy currents will generate a magnetic dipole of moment M in This will generate a dipole field at the north pole the conducting specimen. 3 If (MKS units) where a is the specimen radius. of the sphere equal to pM/27ra this is to cancel the impressed field B at this point, we must have uM/2a 3 + B
= 0
or
0(i) M = -2a 3B o/P.
72 For an impressed magnetic field which varies slowly in the axial direction, the induced dipole moment M will adjust to a value such as to overcompensate at one pole and undercompensate by an equal amount at the other pole. Hence, to first order, the induced moment will remain the same as in the case of a uniform impressed field. The magnetic dipole will be subject to a lifting force F = M-grad Bo
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