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Motion of ions in the Kingdon trap
dc.contributor.authorLewis, R. R.en_US
dc.date.accessioned2010-05-06T22:27:40Z
dc.date.available2010-05-06T22:27:40Z
dc.date.issued1982-06en_US
dc.identifier.citationLewis, R. R. (1982). "Motion of ions in the Kingdon trap." Journal of Applied Physics 53(6): 3975-3980. <http://hdl.handle.net/2027.42/70628>en_US
dc.identifier.urihttps://hdl.handle.net/2027.42/70628
dc.description.abstractThe classical and quantum motion of ions in a Kingdon trap (Orbitron) is studied for nearly circular orbits. The frequencies of small axial and radial oscillations are derived for both the logarithmic potential and the actual potential. A numerical comparison with the asymptotic approximation and with exact energy eigenvalues shows that the small oscillation method is adequate for most purposes.en_US
dc.format.extent3102 bytes
dc.format.extent444620 bytes
dc.format.mimetypetext/plain
dc.format.mimetypeapplication/pdf
dc.publisherThe American Institute of Physicsen_US
dc.rights© The American Institute of Physicsen_US
dc.titleMotion of ions in the Kingdon trapen_US
dc.typeArticleen_US
dc.subject.hlbsecondlevelPhysicsen_US
dc.subject.hlbtoplevelScienceen_US
dc.description.peerreviewedPeer Revieweden_US
dc.contributor.affiliationumDepartment of Physics, University of Michigan, Ann Arbor, Michigan 48109en_US
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/70628/2/JAPIAU-53-6-3975-1.pdf
dc.identifier.doi10.1063/1.331285en_US
dc.identifier.sourceJournal of Applied Physicsen_US
dc.identifier.citedreferenceK. H. Kingdon, Phys. Rev. 21, 408 (1923).en_US
dc.identifier.citedreferenceP. R. Brooks and D. R. Herschbach, Rev. Sci. Instrum. 35, 1528 (1964).en_US
dc.identifier.citedreferenceRoss A. Douglas, J. Zabritski, and R. G. Herb, Rev. Sci. Instrum. 36, 1 (1965).en_US
dc.identifier.citedreferenceC. R. Vane, M. H. Prior, and Richard Marrus, Phys. Rev. Lett. 46, 107 (1981).en_US
dc.identifier.citedreferenceRandall Knight, Smithsonian Astrophysical Observatory, 1981 (unpublished).en_US
dc.identifier.citedreferenceR. H. Hooverman, J. Appl. Phys. 34, 3505 (1963).en_US
dc.identifier.citedreferenceNonrelativistic dynamics are assumed. Using the virial theorem, we can calculate the mean‐square velocity for any orbit in the logarithmic potential ⟨υ∕c⟩2 = V0∕mc2,⟨υ∕c⟩2 = V0∕mc2, which is assumed small.en_US
dc.identifier.citedreferenceD. M. Dennison and T. H. Berlin, Phys. Rev. 70, 58 (1946). Since L = mρ2θL = mρ2θ is constant, the small oscillations in θ can be related to the oscillations in ρ and are not another independent variable. There are phase oscillations at the frequency ωρ,ωρ, but they are of no particular interest to us.en_US
dc.identifier.citedreferenceR. H. Hooverman, J. Appl. Phys. 34, 3505 (1963).en_US
dc.identifier.citedreferenceWe have been unable to evaluate the turning points and the integral in a closed form, except in the case M = 0,M = 0, for which x1 = 0,x1 = 0, x2 = eϵ,x2 = eϵ, and ϵ(N) = ln[(2n+1)].ϵ(N) = ln[ϕ̄(2n+1)].en_US
dc.identifier.citedreferenceThis feature of logarithmic potentials has been discussed for quark confinement models by C. Quigg and J. L. Rosner, Phys. Lett. B 71, 153 (1977).en_US
dc.identifier.citedreferenceA corresponding result for the classical orbits has been found by Hooverman, see Sec. IV. The orbits do not depend on the constants E, L separately, but only on the single parameter λ≡{E∕V0−ln[L∕a(2mV0)1∕2]}.λ≡{E∕V0−ln[L∕a(2mV0)1∕2]}.en_US
dc.identifier.citedreferenceCharlotte Froese, Can. J. Phys. 41, 1895 (1963).en_US
dc.owningcollnamePhysics, Department of


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