Electron Orbits in Hyperbolic Magnetic Fields

Article English OPEN
Åström, Ernst (2011)
  • Publisher: Co-Action Publishing
  • Journal: Tellus A (issn: 1600-0870, eissn: 0280-6495)
  • Related identifiers: doi: 10.3402/tellusa.v8i2.8955
  • Subject:
    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
  • References (10)

    A L F V ~ NH, ., 1950: Cosmicnf Elecfrodynaniics, p. 22. Oxford.

    BECKER,., 1933: Theorie der Efektrizitat, 11, § 64. Leipzig.

    CARTANL,., 1934: Sur le deplacement, en champ Clectrostatique, d'enroulements magneto-electroniques.]otrm. d. physique et 2e Radium 5, p. 257.

    GUNNR,., 1929: An electromagnetic effect of importance in solar and terrestrial magnetism, Phys. Rev. 33, p. 832.

    JAHNKEand EMDE,1948: Tajeln Hoherer Funktionen, Kap. V, VI. Leipzig.

    KREINM,. G., 1951: On certain problems on the maximum and minimum characteristic values and on the Lyapunov zones of stability, Akad. Nauk. SSSR Prikf. Mnf. Meh. 15, p. 323.

    MCLACHLANN,. W., 1947: Theory atrd application of Mathieu junctions. Oxford.

    SVARCMAAN., P., 1954: On the boundness of solutions of the differential equation y " + p ( x ) y=o. Aknd. Nauk. SSSR Pfikl. Mat. Meh. 18,p. 464.

    THIBAUJD.., 1933: etude des proprittts du positron, C.R. 197, p. 915.

    VILLARDP,., 1908: Les Rayons Cathodiques et l'aurore bodale. Journal de physique 7 , p. 429.

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