The DOI matches its Crossref record; 17 of the 17 references it cites were found in a registry or an index.
Single particle motion in a Penning trap: description in the classical canonical formalism
Open accessAbstract
This paper aims at the development of methods for the calculation of the characteristic frequencies of a Penning trap, taking into account deviations of the actual geometry from the ideal one, anharmonicities of the electric potential, misalignments and inhomogeneities of the magnetic field, additional time dependent electromagnetic fields, and so on. The paper starts by describing the motion of a single charged particle in an ideal hyperbolic Penning trap using the formalism of classical hamiltonian mechanics. The usefulness of rotating coordinates is pointed out, and the importance of conservation of canonical angular momentum is stressed. After transformation to action-angle variables the ideal hyperbolic Penning trap can be considered as a 0-th approximation for a systematic classical hamiltonian perturbation approach to "real" Penning traps, as they are used in the laboratory. It is explained how a given problem has to be set up and prepared for the perturbation calculation, then the general principles of the method are outlined. Finally the application of the method is illustrated on hand of a number of worked out examples.
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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 [39]
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Citations
Cites
Goldstein, H. (1951) · UCLA - Biblioteca de Ciencias y Tecnologia Felix Morales Bueno · Cited by 9,832
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
Les méthodes nouvelles de la mécanique céleste
Poincaré, H. (1892) · doi:10.3931/e-rara-421 · Cited by 1,078
Mathieusche Funktionen und Sphäroidfunktionen
Meixner, J., & Schäfke, F. W. (1954) · Springer eBooks · doi:10.1007/978-3-662-00941-3 · Cited by 553
Die dreidimensionale Stabilisierung von Ladungstr�gern in einem Vierpolfeld
Fischer, E. (1959) · The European Physical Journal A · doi:10.1007/bf01332512 · Cited by 388
Bollen, G., Moore, R. B., Savard, G., & Stolzenberg, H. (1990) · Journal of Applied Physics · doi:10.1063/1.346185 · Cited by 314
Exchange-Collision Technique for the rf Spectroscopy of Stored Ions
Major, F. G., & DEHMELT, H. G. (1968) · Physical Review · doi:10.1103/physrev.170.91 · Cited by 298
Precision spectroscopy of a charged particle in an imperfect Penning trap
Brown, L. S., & Gabrielse, G. (1982) · Physical Review A · doi:10.1103/physreva.25.2423 · Cited by 237
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
Born, M. (1925) · Springer eBooks · doi:10.1007/978-3-642-61898-7 · Cited by 143
Research works printed but not linked: 2
- Born M, 1976, Vorlesungen über Atommechanik
- Fues E, 1927, Störungsrechnung, in Handbuch der Physik (Grundlagen der Mechanik, Mechanik der Punkte und Starren Körper), 5
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High-accuracy mass spectrometry with stored ions
Blaum, K. (2006) · Physics Reports · doi:10.1016/j.physrep.2005.10.011 · Cited by 685
Electron g‐factor determinations in Penning traps
Sturm, S., Werth, G., & Blaum, K. (2013) · Annalen der Physik · doi:10.1002/andp.201300052 · Cited by 33
Theory 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
“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).”
Method
Metadata
- Authors
- Kretzschmar, M.
- Affiliations
- Johannes Gutenberg University Mainz (DE)
- Corresponding author
- Kretzschmar, Martin
- ORCID
- Kretzschmar, Martin
- Venue
- Physica Scripta
- Publisher
- IOP Publishing
- Published
- 1992-12-01
- Volume
- 46
- Issue
- 6
- Pages
- 544-554
- ISSN
- 0031-8949 (ISSN-L)
- 1402-4896
- OpenAlex
- W2019005726
- Semantic Scholar
- 618233342dcc253cf38d4fdc973d6af330987418
- Cited by
- 65
- References
- 17
- Citations by year
- 2025: 1 · 2024: 2 · 2022: 1 · 2021: 1 · 2019: 1 · 2018: 1 · 2017: 2 · 2016: 4 · 2015: 6 · 2014: 3 · 2013: 4 · 2012: 3
- FWCI
- 18.49
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Physica Scripta (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Particle accelerators and beam dynamics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Quantum chaos and dynamical systems
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Fusion and Plasma Physics Studies
- Keywords
- Penning trap, charged particle motion, characteristic frequency, Hamiltonian mechanics, canonical angular momentum, rotating coordinates, action-angle variables, perturbation theory, magnetic field inhomogeneity, time-dependent electromagnetic fields
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