RECORD
Stability of an electromagnetically levitated spherical sample in a set of coaxial circular loops
Classical Physics · Submitted 14 Jun 2006
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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 $l+1$.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
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 $l+1$.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | 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. | contribution 0.99 | 0.86 | 0.07 | asserted 0.96 |
| s1 | 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. | method 0.52 | 0.92 | 0.06 | asserted 0.93 |
| s2 | We introduce an original analytical approach employing a gauge transformation for the vector potential. | method 0.67 | 0.94 | 0.03 | asserted 0.99 |
| s3 | First, we calculate the spring constants that define the frequency of small-amplitude oscillations. | method 0.97 | 0.94 | 0.03 | asserted 0.96 |
| s4 | For static stability, the spring constants must be positive. | method 0.33 | 0.23 | 0.05 | asserted 1.00 |
| s5 | Dynamic instabilities are characterized by critical ac frequencies that, when exceeded, may result either in a spin-up or oscillations with increasing amplitude. | result 0.66 | 0.54 | 0.19 | hedged possibility 0.90 |
| s6 | We found that the critical frequencies increase with the nonuniformity of the field. | result 1.00 | 0.95 | 0.19 | asserted 1.00 |
| s7 | 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 $l+1$. | result 1.00 | 0.92 | 0.36 | asserted 1.00 |
What was examined, and what was not
- arXiv listing abstract v2
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original 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 $l+1$.
Human review
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.