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Åström, Ernst (2011)
Publisher: Co-Action Publishing
Journal: Tellus A
Languages: English
Types: Article

Classified by OpenAIRE into

arxiv: Astrophysics::Earth and Planetary Astrophysics
Electron motion in the field from cylindrical pole pieces with the section in the shape of a rectangular hyperbola and its conjugate is treated. The accessible region is discussed. For the motion in the asymptote planes to the hyperbola the orbits are characterized by two parameters, e.g. one (k), characterizing the shape, and the other the amplitude. The solution is given in elliptic functions. The orbits may be divided into two groups, one composed of orbits resembling trochoids and the other orbits of a meander type. There exists a periodic orbit similar to the diget 8. The drift is in opposite directions on different sides of this orbit, as characterized by k. The trochoidal motion is stable if the orbit is not stretched too much. For the meander orbits the criterion used gives a main stability region. This region is bounded by the periodic orbit and the orbit the branches of which just touch each other. For both groups of orbits there exists an infinite number of stable regions.DOI: 10.1111/j.2153-3490.1956.tb01220.x
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