dorsal/arxiv
View SchemaStability of an electromagnetically levitated spherical sample in a set of coaxial circular loops
| Authors | J. Priede, G. Gerbeth |
|---|---|
| Categories | |
| ArXiv ID | physics/0606125 |
| URL | https://arxiv.org/abs/physics/0606125 |
| DOI | 10.1109/TMAG.2005.848322 |
| Journal | IEEE Trans. Magn., vol. 41, no. 6, pp. 2089-2101, 2005 |
Abstract
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 $l+1$.
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"abstract": "This paper presents a theoretical study of oscillatory and rotational\ninstabilities of a solid spherical body, levitated electromagnetically in\naxisymmetric coils made of coaxial circular loops. We apply our previous theory\nto analyze the static and dynamic stability of the sample depending on the ac\nfrequency and the position of the sample in the coils for several simple\nconfigurations. We introduce an original analytical approach employing a gauge\ntransformation for the vector potential. First, we calculate the spring\nconstants that define the frequency of small-amplitude oscillations. For static\nstability, the spring constants must be positive. Dynamic instabilities are\ncharacterized by critical ac frequencies that, when exceeded, may result either\nin a spin-up or oscillations with increasing amplitude. We found that the\ncritical frequencies increase with the nonuniformity of the field. We show that\nfor a spherically harmonic field, the critical frequency for the spin-up\ninstability in a field of degree $l$ coincides with the critical frequency for\nthe oscillatory instability in a field of degree $l+1$.",
"arxiv_id": "physics/0606125",
"authors": [
"J. Priede",
"G. Gerbeth"
],
"categories": [
"physics.class-ph"
],
"doi": "10.1109/TMAG.2005.848322",
"journal_ref": "IEEE Trans. Magn., vol. 41, no. 6, pp. 2089-2101, 2005",
"title": "Stability of an electromagnetically levitated spherical sample in a set of coaxial circular loops",
"url": "https://arxiv.org/abs/physics/0606125"
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