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Linearity and quadrupolarity of tetragonal and cylindrical penning traps of arbitrary length-to-width ratio

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Journal of the American Society for Mass Spectrometry

Abstract

The two most popular Penning traps in use for Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometry are tetragonal (i. e., orthorhombic with square cross section) and cylindrical. Here we compare tetragonal and cylindrical traps as a function of aspect (length-to-width) ratio and position within the trap, by comparing the numerically computed (from Simion 6.0) electric potential field of a given trap relative to each of three idealized potentials required for FT-ICR experiments: dipolar one-dimensional potential for alternating current (ac) excitation/detection of cyclotron motion, azimuthal two-dimensional quadrupolar potential for ac excitation for ion axialization, and axial three-dimensional quadrupolar potential for direct current axial confinement of ions. Our numerically computed results agree well with those previously derived analytically. The numerical approach provides a simpler and more accessible means for analyzing the aforementioned potentials. Moreover, the numerical approach (unlike the analytical approach) readily extends to traps of lower symmetry. Finally, even when analytical solutions are available, the numerical method presented here is complementary, since it provides a useful check on the validity of the derived equations.

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References

  1. Lawrence, E. O.; Livingston, M. S. Phys. Rev. 1932, 40, 19–35.

    Article  CAS  Google Scholar 

  2. Guan, S.; Marshall, A. G. Int. J. Mass Spectrom. Ion Processes 1995, 146/147, 261–296.

    Article  CAS  Google Scholar 

  3. Vartanian, V. H.; Anderson, J. S.; Laude, D. A. Mass Spectrom. Rev. 1995, 14, 1–19.

    Article  CAS  Google Scholar 

  4. Brown, L. S.; Gabrielse, G. Rev. Mod. Phys. 1986, 58, 233–311.

    Article  CAS  Google Scholar 

  5. Rempel, D. L.; Grese, R. P.; Gross, M. L. Int. J. Mass Spectrom. Ion Processes 1990, 100, 381–395.

    Article  CAS  Google Scholar 

  6. Naito, Y.; Fujiwara, M.; Inoue, M. Int. J. Mass Spectrom. Ion Phys. 1992, 120, 179–192.

    Article  CAS  Google Scholar 

  7. Gorshkov, M. V.; Guan, S.; Marshall, A. G. Rapid Commun. Mass Spectrom. 1992, 6, 166–172.

    Article  CAS  Google Scholar 

  8. Rempel, D. L.; Gross, M. L. J. Am. Soc. Mass Spectrom. 1992, 3, 590–594.

    Article  CAS  Google Scholar 

  9. Jacoby, C. B.; Holliman, C. L.; Rempel, D. L.; Gross, M. L. J. Am. Soc. Mass Spectrom. 1993, 4, 186–189.

    Article  CAS  Google Scholar 

  10. Hunter, R. L.; Sherman, M. G.; McIver, R. T. Jr. Int. J. Mass Spectrom. Ion Phys. 1983, 50, 259–274.

    Article  CAS  Google Scholar 

  11. Grosshans, P. B.; Wang, M.; Ricca, T. L.; Ledford, E. B., Jr.; Marshall, A. G. Proceedings of the 36th ASMS Conference on Mass Spectrometry and Allied Topics San Francisco, CA. 1988; pp 592–593.

  12. Beu, S. C.; Laude, D. A., Jr. Anal. Chem. 1992, 64, 177–180.

    Article  CAS  Google Scholar 

  13. Wang, M.; Marshall, A. G. Anal. Chem. 1990, 62, 515–520.

    Article  CAS  Google Scholar 

  14. Hanson, C. D.; Castro, M. E.; Kerley, E. L.; Russell, D. H. Anal. Chem. 1990, 62, 520–526.

    Article  CAS  Google Scholar 

  15. Caravatti, P.; Allemann, M. Org. Mass Spectrom. 1991, 26, 514–518.

    Article  CAS  Google Scholar 

  16. Knobeler, M.; Wanczek, K. P. Int. J. Mass Spectrom. Ion Processes 1993, 125, 127.

    Article  CAS  Google Scholar 

  17. Grosshans, P. B.; Chen, R.; Marshall, A. G. Int. J. Mass Spectrom. Ion Processes 1994, 139, 169–189.

    Article  CAS  Google Scholar 

  18. Guan, S.; Huang, Y.; Marshall, A. G. J. Mass Spectrom. 1995, 30, 1593–1598.

    Article  CAS  Google Scholar 

  19. Shockley, W. J. Appl. Phys. 1938, 9, 635.

    Article  Google Scholar 

  20. Dunbar, R. C. Int. J. Mass Spectrom. Ion Processes 1984, 56, 1–9.

    Article  CAS  Google Scholar 

  21. Grosshans, P. B.; Shields, P. J.; Marshall, A. G. J. Chem. Phys. 1991, 94, 5341–5352.

    Article  CAS  Google Scholar 

  22. Comisarow, M. B. Adv. Mass Spectrom. 1980, 8, 1698–1706.

    Google Scholar 

  23. Comisarow, M. B. Int. J. Mass Spectrom. Ion Phys. 1981, 37, 251–257.

    Article  CAS  Google Scholar 

  24. Comisarow, M. B.; Marshall, A. G. U. S. Patent No. 3,937,955, 14 February 1976.

  25. Lee, S. H.; Wanczek, K.-P.; Hartmann, H. Adv. Mass Spectrom. 1980, 8B, 1645–1647.

    CAS  Google Scholar 

  26. Sharp, T. E.; Eyler, J. R.; Li, E. Int. J. Mass Spectrom. Ion Phys. 1972, 9, 421–439.

    Article  CAS  Google Scholar 

  27. Rempel, D. L.; Huang, S. K.; Gross, M. L. Int. J. Mass Spectrom. Ion Processes 1986, 70, 163–184.

    Article  CAS  Google Scholar 

  28. Kofel, P.; Allemann, M.; Kellerhals, H.; Wanczek, K.-P. Int. J. Mass Spectrom. Ion Processes 1986, 74, 1–12.

    Article  CAS  Google Scholar 

  29. van der Hart, W. J.; van de Guchte, W. J. Int. J. Mass Spectrom. Ion Processes 1988, 82, 17–31.

    Article  Google Scholar 

  30. Grosshans, P. B.; Marshall, A. G. Int. J. Mass Spectrom. Ion Processes 1990, 100, 347–379.

    Article  CAS  Google Scholar 

  31. Marshall, A. G.; Grosshans, P. B. Anal. Chem. 1991, 63, 215A-229A.

    Article  CAS  Google Scholar 

  32. Comisarow, M. B. J. Chem. Phys. 1978, 69, 4097–4104.

    Article  CAS  Google Scholar 

  33. Comisarow, M. B. In Ion Cyclotron Resonance Spectrometry II; Hartmann, H. Wanczek, K. P., Eds.; Springer-Verlag, Berlin, 1982; pp 484–513.

    Google Scholar 

  34. Limbach, P. A.; Grosshans, P. B.; Marshall, A. G. Anal. Chem. 1993, 65, 135–140.

    Article  CAS  Google Scholar 

  35. Schweikhard, L.; Marshall, A. G. J. Am. Soc. Mass Spectrom. 1993, 4, 433–452.

    Article  CAS  Google Scholar 

  36. Mitchell, D. W.; Hearn, B. A.; DeLong, S. E. Int. J. Mass Spectrom. Ion Processes 1993, 125, 95–126.

    Article  CAS  Google Scholar 

  37. Ledford, E. B., Jr.; Rempel, D. L.; Gross, M. L. Anal. Chem. 1984, 56, 2744–2748.

    Article  CAS  Google Scholar 

  38. May, M. A.; Grosshans, P. B.; Marshall, A. G. Int. J. Mass Spectrom. Ion Processes 1992, 120, 193–205.

    Article  CAS  Google Scholar 

  39. Wang, M.; Marshall, A. G. Anal. Chem. 1989, 61, 1288–1293.

    Article  CAS  Google Scholar 

  40. Savard, G.; Becker, S.; Bollen, G.; Kluge, H.-J.; Moore, R. B.; Schweikhard, L.; Stolzenberg, H.; Wiess, U. Phys. Lett. A 1991, 158, 247–252.

    Article  CAS  Google Scholar 

  41. Guan, S.; Kim, H. S.; Marshall, A. G.; Wahl, M. C.; Wood, T. D.; Xiang, X. Chem. Rev. 1994, 8, 2161–2182.

    Article  Google Scholar 

  42. Castoro, J. A.; Wilkins, C. L. Anal. Chem. 1993, 65, 2621–2627.

    Article  CAS  Google Scholar 

  43. Wang, Y.; Wanczek, K.-P. Rev. Sci. Instrum. 1993, 64, 883–889.

    Article  CAS  Google Scholar 

  44. Zeller, L. C.; Kennady, J. M.; Kenttämaa, H.; Campana, J. E. Anal. Chem. 1993, 65, 2116–2118.

    Article  CAS  Google Scholar 

  45. Gabrielse, G.; Haarsma, L.; Rolston, S. L. Int. J. Mass Spectrom. Ion Processes 1989, 88, 319–332.

    Article  CAS  Google Scholar 

  46. Beu, S. C.; Laude, D. A., Jr. Int. J. Mass Spectrom. Ion Processes 1992, 112, 215–230.

    Article  CAS  Google Scholar 

  47. Marto, J. A.; Guan, S.; Marshall, A. G. Rapid Commun. Mass Spectrom. 1994, 8, 615–620.

    Article  CAS  Google Scholar 

  48. O’Connor, P. B.; McLafferty, F. W. J. Am. Soc. Mass Spectrom. 1995, 6, 533–535.

    Article  Google Scholar 

  49. Solouki, R.; Gillig, K. J.; Russell, D. H. Anal. Chem. 1994, 66, 1583–1587.

    Article  CAS  Google Scholar 

  50. Peiris, D. M.; Cheeseman, M. A.; Ramanathan, R.; Eyler, J. R. J. Phys. Chem. 1993, 97, 7839–7843.

    Article  CAS  Google Scholar 

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Authors and Affiliations

  1. Center for Interdisciplinary Magnetic Resonance, National High Magnetic Field Laboratory, Florida State University, USA, Tallahassee, Florida

    George S. Jackson, Jesse D. Canterbury, Shenheng Guan & Alan G. Marshall

  2. Ion Cyclotron Resonance Program, National High Magnetic Field Laboratory, Florida State University, 1800 East Paul Dirac Drive, 32310, Tallahasee, FL

    George S. Jackson, Shenheng Guan & Alan G. Marshall

Authors
  1. George S. Jackson
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  2. Jesse D. Canterbury
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  3. Shenheng Guan
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  4. Alan G. Marshall
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Jackson, G.S., Canterbury, J.D., Guan, S. et al. Linearity and quadrupolarity of tetragonal and cylindrical penning traps of arbitrary length-to-width ratio. J Am Soc Mass Spectrom 8, 283–293 (1997). https://doi.org/10.1016/S1044-0305(96)00232-2

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  • DOI: https://doi.org/10.1016/S1044-0305(96)00232-2

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