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Further Development and Refinement of the Effective Potential Concept for Stroboscopic Samplings of Ion Coordinates and Velocities in Quadrupole RF Fields

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Abstract

We consider the concept of effective potential, that has been proposed recently based on analysis of stroboscopic sampling of coordinates and velocities of ions moving in an rf quadrupole field. Exact expressions have been obtained for the stroboscopic model of motion of ions, which are valid at any point of a stability zone. Analysis of these expressions has led to correction of some postulates of the initial effective potential concept of stroboscopic sampling, which was developed for the neighborhood of the stability zone peak.

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REFERENCES

  1. W. Paul and H. Steinwedel, Z. Naturforsch. A 8, 448 (1953).

    Article  ADS  Google Scholar 

  2. G. I. Slobodenyuk, Quadrupole Mass Spectrometers (Atomizdat, Moscow, 1974).

    Google Scholar 

  3. P. H. Dawson, in Advances in Electronics and Electron Physics, Ed. by L. Marton and C. Marton (Academic, New York, 1980), Vol. 53, p. 153.

    Google Scholar 

  4. R. E. March and R. J. Hughes, Quadrupole Storage Mass Spectrometry (Wiley, New York, 1989).

    Google Scholar 

  5. P. H. Dawson, Quadrupole Mass Spectrometry and Its Applications (American Inst. of Physics, Woodbury, 1995).

    Google Scholar 

  6. F. G. Major, V. N. Gheorghe, and G. Werth, Charged Particle Traps. Physics and Techniques of Charged Particle Field Confinement (Springer, 2005).

    Google Scholar 

  7. G. Werth, V. N. Gheorghe, and F. G. Major, Charged Particle Traps II. Applications (Springer, 2009).

    Book  Google Scholar 

  8. N. W. Mclachlan, Theory and Application Of Mathieu Functions (Oxford Univ. Press, 1951).

    Google Scholar 

  9. L. D. Landau and E. M. Lifshitz, Mechanics (Fizmatgiz, Moscow, 1958), pp. 119–123.

    MATH  Google Scholar 

  10. A. V. Gaponov and M. A. Miller, J. Exp. Theor. Phys. 7, 168 (1958).

    Google Scholar 

  11. D. Gerlich, in Advances in Chemical Physics, Ed. by C.-Y. Ng and M. Baer (Wiley, New York, 1992), Vol. LXXXII, pp. 1–197.

    Google Scholar 

  12. M. Sudakov, Int. J. Mass Spectrom. 206, 27 (2001).

    Article  Google Scholar 

  13. V. I. Baranov, D. R. Bandura, and S. D. Tanner, Int. J. Mass Spectrom. 247, 40 (2005).

    Article  Google Scholar 

  14. M. Yu. Sudakov and M. V. Apatskaya, J. Exp. Theor. Phys. 115, 194 (2012).

    Article  ADS  Google Scholar 

  15. C. Gao and D. J. Douglas, J. Am. Soc. Mass Spectrom. 24, 1848 (2013).

    Article  ADS  Google Scholar 

  16. D. J. Douglas, A. S. Berdnikov, and N. V. Konenkov, Int. J. Mass Spectrom. 377, 345 (2015).

    Article  Google Scholar 

  17. P. T. A. Reilly and G. F. Brabeck, Int. J. Mass Spectrom. 392, 86 (2015).

    Article  Google Scholar 

  18. G. F. Brabeck and P. T. A. Reilly, J. Am. Soc. Mass Spectrom. 27, 1122 (2016).

    Article  ADS  Google Scholar 

  19. A. S. Berdnikov, D. J. Douglas, and N. V. Konenkov, Int. J. Mass Spectrom. 421, 204 (2017).

    Article  Google Scholar 

  20. A. S. Berdnikov, L. N. Gall’, N. R. Gall’, and K. V. Solov’ev, Nauchno-Tekh. Vedomosti S.-Peterb. Gos. Politekh. Univ. Fiz.-Mat. Nauki 11 (3), 52 (2018).

    Google Scholar 

  21. G. Floquet, Ann. Sci. Ec. Norm. Super. 12, 47 (1883).

    Article  Google Scholar 

  22. B. P. Demidovich, Lectures on Mathematical Stability Theory (Nauka, Moscow, 1967).

    MATH  Google Scholar 

  23. N. V. Konenkov, M. Sudakov, and D. J. Douglas, J. Am. Soc. Mass Spectrom. 13, 597 (2002).

    Article  Google Scholar 

  24. A. Verentchikov, A. Berdnikov, and M. Yavor, Phys. Proc. 1, 87 (2008).

    Article  ADS  Google Scholar 

  25. A. O. Gel’fond, Calculus of Finite Differences (GIFML, Moscow, 1959).

    Google Scholar 

  26. A. S. Berdnikov, A. N. Verentchikov, and N. V. Konenkov, J. Anal. Chem. 73, 1229 (2018).

    Article  Google Scholar 

  27. A. L. Bulyanitsa and V. E. Kurochkin, Nauchn. Priborostr. 10 (2), 43 (2000).

    Google Scholar 

  28. A. A. Evstrapov, A. L. Bulyanitsa, G. E. Rudnitskaya, B. G. Belen’kii, A. O. Petryakov, and V. E. Kurochkin, Nauchn. Priborostr. 13 (2), 57 (2003).

    Google Scholar 

  29. A. L. Bulyanitsa, A. A. Evstrapov, and G. E. Rudnitskaya, Nauchn. Priborostr. 13 (4), 28 (2003).

    Google Scholar 

  30. A. L. Bulyanitsa, Nauchn. Priborostr. 15 (2), 51 (2005).

    Google Scholar 

  31. A. S. Berdnikov, A. G. Kuz’min, and S. V. Masyukevich, Nauchn. Priborostr. 28 (3), 90 (2018).

    Article  Google Scholar 

  32. A. S. Berdnikov, A. G. Kuz’min, and S. V. Masyukevich, Nauchn. Priborostr. 28 (4), 135 (2018).

    Article  Google Scholar 

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ACKNOWLEDGMENTS

The authors are grateful to the editorial board of the Journal of Technical Physics for the opportunity to continue the scientific discussion started in the Journal of Experimental and Theoretical Physics with the publication of [14]. The authors thank the reviewer of this work for a benevolent opinion and important clarifications that helped to correct some technical mistakes and to considerably improve the text of this article.

Funding

This work was performed under State assignment no. 075-00780 19-00 for the Institute for Analytical Instrumentation, Russian Academy of Sciences.

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Correspondence to A. S. Berdnikov.

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Translated by N. Wadhwa

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Berdnikov, A.S., Gall’, N.R. & Masyukevich, S.V. Further Development and Refinement of the Effective Potential Concept for Stroboscopic Samplings of Ion Coordinates and Velocities in Quadrupole RF Fields. Tech. Phys. 64, 1046–1050 (2019). https://doi.org/10.1134/S1063784219070077

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  • DOI: https://doi.org/10.1134/S1063784219070077

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