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Complex and catastrophic ion beam focusing with a very thin electrostatic square rainbow lens

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Abstract

The focusing properties of a very thin electrostatic square rainbow lens are investigated theoretically with a parallel proton beam of energy of 10 keV. The lens electrodes lie on a circle of diameter of d = 10 mm, and the electrode voltage is 1 kV. The calculations are performed using the momentum approximation. It is shown that the spatial and angular distributions of transmitted ions are fully determined by the rainbow effect, which emerges from the interference of the contributions of the electrodes to the ion differential transmission cross-section. This makes it a complex effect. It is also demonstrated that the shape of the rainbow line in the central region of the transverse position plane far from the lens can be very accurately reproduced using catastrophe theory. Thus, the effect is a catastrophic effect too. The transmitted ion beam far from the lens contains only a strong central sub-beam. Special attention is devoted to the characteristics of this beam, which might find use in materials science and technology.

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Data availability statement

The datasets generated and analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

The research presented in this paper has been funded by the Ministry of Education, Science and Technological Development of Serbia.

Funding

Funding by Ministry of Education, Science and Technological Development of Serbia.

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Authors and Affiliations

  1. Vinča Institute of Nuclear Sciences – National Institute of Serbia, University of Belgrade, Belgrade, Serbia

    S. Grujović Zdolšek, I. Telečki & M. Ćosić

  2. World Academy of Art and Science, Napa, CA, USA

    N. Nešković

Authors
  1. S. Grujović Zdolšek
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  2. N. Nešković
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  3. I. Telečki
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  4. M. Ćosić
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Correspondence to M. Ćosić.

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Grujović Zdolšek, S., Nešković, N., Telečki, I. et al. Complex and catastrophic ion beam focusing with a very thin electrostatic square rainbow lens. Eur. Phys. J. Plus 137, 477 (2022). https://doi.org/10.1140/epjp/s13360-022-02686-8

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  • DOI: https://doi.org/10.1140/epjp/s13360-022-02686-8

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