Stability of an electromagnetically levitated spherical sample in a set of coaxial circular loops

Janis Priede, Gunter Gerbeth

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


This paper presents a theoretical study of oscillatory and rotational instabilities of a solid spherical body, levitated electromagnetically in axisymmetric coils made of coaxial circular loops. We apply our previous theory to analyze the static and dynamic stability of the sample depending on the ac frequency and the position of the sample in the coils for several simple configurations. We introduce an original analytical approach employing a gauge transformation for the vector potential. First, we calculate the spring constants that define the frequency of small-amplitude oscillations. For static stability, the spring constants must be positive. Dynamic instabilities are characterized by critical ac frequencies that, when exceeded, may result either in a spin-up or oscillations with increasing amplitude. We found that the critical frequencies increase with the nonuniformity of the field. We show that for a spherically harmonic field, the critical frequency for the spin-up instability in a field of degree l coincides with the critical frequency for the oscillatory instability in a field of degree I + 1.

Original languageEnglish
Pages (from-to)2089-2101
Number of pages13
JournalIEEE Transactions on Magnetics
Issue number6
Publication statusPublished - 6 Jun 2005
Externally publishedYes


  • Electromagnetic analysis
  • Electromagnetic forces
  • Electromechanical effects
  • Levitation
  • Spheres
  • Coaxial components
  • Coils
  • Frequency
  • Solids
  • Stability analysis
  • Springs
  • Eddy currents
  • Physics
  • Vectors
  • magnetic levitation
  • electromagnetic levitation
  • coaxial circular loops
  • oscillatory instabilities
  • rotational instabilities
  • solid spherical body
  • axisymmetric coils
  • static stability
  • dynamic stability
  • vector potential
  • electromagnetic forces
  • electromechanical effects

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Electrical and Electronic Engineering


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