The DOI matches its Crossref record; 11 of the 11 references it cites were found in a registry or an index.
Particle motion in a Penning trap
Open accessAbstract
The motion of a charged particle in an ideal Penning trap (ion trap with static electromagnetic fields) can be analysed by a large variety of methods of analytical mechanics, similar to the Kepler problem and the harmonic oscillator exact solutions can be provided. For this reason and because of its great relevance for experimental techniques the problem represents a topic of high pedagogical value for a course in theoretical mechanics. The paper briefly sketches the essential steps of various theoretical approaches.
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“Conventional treatment in Penning trap theory [28, 29, 35, 39] follows a procedure of classical canonical transformation followed by quantisation in order to diagonalise the Hamiltonian of the radially symmetric trap (3).”
From Quantisation of the elliptical Penning trap (2021) · cites this paper as [35]
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“The motion in the radial plane can be decoupled by canonical transformation [35], and the Hamiltonian written in terms of three distinct harmonicoscillators of the cyclotron ( + ), axial ( z ), and magnetron ( -) modes.”
From Quantisation of the elliptical Penning trap (2021) · cites this paper as [35]
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Citations
Cites
Electromagnetic traps for charged and neutral particles
Paul, W. (1990) · Reviews of Modern Physics · doi:10.1103/revmodphys.62.531 · Cited by 1,537
Geonium theory: Physics of a single electron or ion in a Penning trap
Brown, L. S., & Gabrielse, G. (1986) · Reviews of Modern Physics · doi:10.1103/revmodphys.58.233 · Cited by 1,367
Die glimmentladung bei niedrigem druck zwischen koaxialen zylindern in einem axialen magnetfeld
Penning, F. M. (1936) · Physica · doi:10.1016/s0031-8914(36)80313-9 · Cited by 382
Experiments with an isolated subatomic particle at rest
Dehmelt, H. (1990) · Reviews of Modern Physics · doi:10.1103/revmodphys.62.525 · Cited by 302
High-Resol Ution Spectroscopy of Stored Ions
Wineland, D. J., Itano, W. M., & Dyck, R. S. V. (1983) · Advances in atomic and molecular physics · doi:10.1016/s0065-2199(08)60253-5 · Cited by 197
Ekstrom, P. A., & Wineland, D. J. (1980) · Scientific American · doi:10.1038/scientificamerican0880-104 · Cited by 39
Analytische Geometrie spezieller ebener Kurven
Fladt, K. (1962) · Cited by 28
A Theory of Anharmonic Perturbations in a Penning Trap
Kretzschmar, M. (1990) · Zeitschrift für Naturforschung A · doi:10.1515/zna-1990-0805 · Cited by 27
Self-citationDegeneracy of Cyclotron Motion
Dulock, V. A., & McIntosh, H. V. (1966) · Journal of Mathematical Physics · doi:10.1063/1.1705049 · Cited by 26
Böck, S., Nöth, H., & Wietelmann, A. (1990) · Zeitschrift für Naturforschung B · doi:10.1515/znb-1990-0711 · Cited by 22
Epicyclic Orbits of Charged Particles
Harrison, E. R. (1959) · American Journal of Physics · doi:10.1119/1.1934843 · Cited by 7
Cited by
Sorted by citations
Single particle motion in a Penning trap: description in the classical canonical formalism
Kretzschmar, M. (1992) · Physica Scripta · doi:10.1088/0031-8949/46/6/011 · Cited by 65
Self-citationTheory of the elliptical Penning trap
Kretzschmar, M. (2008) · International Journal of Mass Spectrometry · doi:10.1016/j.ijms.2008.05.009 · Cited by 18
Self-citationThe quantum theory of the Penning trap
Crimin, F., Garraway, B. M., & Verdú, J. (2018) · Journal of Modern Optics · doi:10.1080/09500340.2017.1393570 · Cited by 10
Quantisation of the elliptical Penning trap
Crimin, F., Garraway, B. M., & Verdú, J. L. (2021) · Journal of Physics B: Atomic, Molecular and Optical Physics · doi:10.1088/1361-6455/abfeda · Cited by 1
Metadata
- Authors
- Kretzschmar, M.
- Affiliations
- Johannes Gutenberg University Mainz (DE)
- Corresponding author
- Kretzschmar, M
- ORCID
- Kretzschmar, M
- Venue
- European Journal of Physics
- Publisher
- IOP Publishing
- Published
- 1991-09-01
- Volume
- 12
- Issue
- 5
- Pages
- 240-246
- ISSN
- 0143-0807 (ISSN-L)
- 1361-6404
- OpenAlex
- W1983447610
- Semantic Scholar
- 8824677e5bfc9357492194784e559b11f96b41c5
- Cited by
- 61
- References
- 11
- Citations by year
- 2024: 5 · 2023: 2 · 2021: 3 · 2020: 1 · 2019: 3 · 2018: 4 · 2017: 1 · 2016: 4 · 2015: 3 · 2014: 4 · 2013: 2 · 2012: 3
- FWCI
- 1.59
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- European Journal of Physics (publishedVersion)
- Topics
- Social Sciences › Education › Experimental and Theoretical Physics Studies
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and Classical Electrodynamics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Quantum chaos and dynamical systems
- Keywords
- Penning trap, charged particle motion, ion trap, static electromagnetic fields, Kepler problem, harmonic oscillator, exact solutions, analytical mechanics, theoretical mechanics education
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