TY  - CONF
AU  - Jovanović, Zoran
AU  - Balvanović, Roman V.
AU  - Ćosić, Marko
AU  - Nešković, Nebojša B.
AU  - Telečki, Igor N.
PY  - 2021
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/10280
AB  - FAMA is a user facility for materials science with low-energy ion beams in the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. It includes a heavy ion source, a light ion source, two channels for modification of materials, and two channels for analysis of materials. Recently, the designing of a channel for transmission studies within FAMA has begun. The initial studies to be undertaken in this channel are related to the rainbow e ffects with very thin electrostatic lenses and two-dimensional materials.
C3  - 27th Russian Particle Accelerator Conference (RuPAC'21) : 27 September-01 October 2021, Alushta, Russi
T1  - Transmission Studies With Ion Beams Within FAMA
SP  - 127
EP  - 128
DO  - 10.18429/JACoW-RuPAC2021-FRB07
ER  - 

@conference{
author = "Jovanović, Zoran and Balvanović, Roman V. and Ćosić, Marko and Nešković, Nebojša B. and Telečki, Igor N.",
year = "2021",
abstract = "FAMA is a user facility for materials science with low-energy ion beams in the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. It includes a heavy ion source, a light ion source, two channels for modification of materials, and two channels for analysis of materials. Recently, the designing of a channel for transmission studies within FAMA has begun. The initial studies to be undertaken in this channel are related to the rainbow e ffects with very thin electrostatic lenses and two-dimensional materials.",
journal = "27th Russian Particle Accelerator Conference (RuPAC'21) : 27 September-01 October 2021, Alushta, Russi",
title = "Transmission Studies With Ion Beams Within FAMA",
pages = "127-128",
doi = "10.18429/JACoW-RuPAC2021-FRB07"
}

Jovanović, Z., Balvanović, R. V., Ćosić, M., Nešković, N. B.,& Telečki, I. N.. (2021). Transmission Studies With Ion Beams Within FAMA. in 27th Russian Particle Accelerator Conference (RuPAC'21) : 27 September-01 October 2021, Alushta, Russi, 127-128.
https://doi.org/10.18429/JACoW-RuPAC2021-FRB07

Jovanović Z, Balvanović RV, Ćosić M, Nešković NB, Telečki IN. Transmission Studies With Ion Beams Within FAMA. in 27th Russian Particle Accelerator Conference (RuPAC'21) : 27 September-01 October 2021, Alushta, Russi. 2021;:127-128.
doi:10.18429/JACoW-RuPAC2021-FRB07 .

Jovanović, Zoran, Balvanović, Roman V., Ćosić, Marko, Nešković, Nebojša B., Telečki, Igor N., "Transmission Studies With Ion Beams Within FAMA" in 27th Russian Particle Accelerator Conference (RuPAC'21) : 27 September-01 October 2021, Alushta, Russi (2021):127-128,
https://doi.org/10.18429/JACoW-RuPAC2021-FRB07 . .

TY  - CHAP
AU  - Petrović, Srđan M.
AU  - Starčević, Nikola
AU  - Ćosić, Marko
AU  - Nešković, Nebojša B.
PY  - 2021
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/10309
AB  - This work shows how recent experimental results of angular distributions of 2 MeV protons channeled in a 55-nm-thick (001) silicon crystal tilted away from the [001] direction can be explained by the very accurate rainbow ion-atom interaction potential. The obtained results are compared with the ones applying universal ZBL interaction ion-atom potential, which is mainly used in the literature. © 2021 Walter de Gruyter GmbH, Berlin/Boston.
T2  - Advanced Ceramics and Applications
T1  - On the doughnut effect and the rainbow proton-silicon interaction potential
SP  - 271
EP  - 276
DO  - 10.1515/9783110627992-019
ER  - 

@inbook{
author = "Petrović, Srđan M. and Starčević, Nikola and Ćosić, Marko and Nešković, Nebojša B.",
year = "2021",
abstract = "This work shows how recent experimental results of angular distributions of 2 MeV protons channeled in a 55-nm-thick (001) silicon crystal tilted away from the [001] direction can be explained by the very accurate rainbow ion-atom interaction potential. The obtained results are compared with the ones applying universal ZBL interaction ion-atom potential, which is mainly used in the literature. © 2021 Walter de Gruyter GmbH, Berlin/Boston.",
journal = "Advanced Ceramics and Applications",
booktitle = "On the doughnut effect and the rainbow proton-silicon interaction potential",
pages = "271-276",
doi = "10.1515/9783110627992-019"
}

Petrović, S. M., Starčević, N., Ćosić, M.,& Nešković, N. B.. (2021). On the doughnut effect and the rainbow proton-silicon interaction potential. in Advanced Ceramics and Applications, 271-276.
https://doi.org/10.1515/9783110627992-019

Petrović SM, Starčević N, Ćosić M, Nešković NB. On the doughnut effect and the rainbow proton-silicon interaction potential. in Advanced Ceramics and Applications. 2021;:271-276.
doi:10.1515/9783110627992-019 .

Petrović, Srđan M., Starčević, Nikola, Ćosić, Marko, Nešković, Nebojša B., "On the doughnut effect and the rainbow proton-silicon interaction potential" in Advanced Ceramics and Applications (2021):271-276,
https://doi.org/10.1515/9783110627992-019 . .

TY  - JOUR
AU  - Ćosić, Marko
AU  - Nešković, Nebojša B.
AU  - Petrović, Srđan M.
PY  - 2019
UR  - https://linkinghub.elsevier.com/retrieve/pii/S0168583X19300758
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/8049
AB  - This is a theoretical study of the superfocusing and zero-degree focusing effects appearing in channeling of protons of energy of 2 MeV in the {1 1 0} channel of a thin silicon crystal. We prove that the ultimate origin of these effects is the crystal rainbow effect, which has been discovered and explored in ion transmission through axial crystal channels, nanotubes and graphene. Moreover, the effect is the origin of the shapes of the whole spatial and angular distributions of channeled protons. The incident proton velocity vector is taken to be parallel to the channel midplane. We use the Molière's approximation of the Thomas-Fermi proton-atom interaction potential and the continuum approximation. The effect of thermal vibrations of the crystal's atoms is included. We solve numerically the proton equation of motion and analyze the spatial and angular proton transmission functions. The extrema of these functions are the spatial and angular rainbow points, respectively. When the whole proton beam is taken into account, a spatial rainbow pattern, composed of the lines emerging from the superfocusing points, and an angular rainbow pattern, consisting of the lines emerging from the origin and the zero-degree focusing points, appear along the channel. We consider the region of crystal thickness comprising the first, second and third superfocusing and zero-degree focusing points. When the effect of thermal vibrations is neglected, each of these rainbow lines look like the bifurcation set of the cusp catastrophe, and when the effect is included, the line resembles the bifurcation set of the butterfly catastrophe. We demonstrate that the spatial and angular distributions of transmitted protons are fully determined by the spatial and angular rainbow lines, respectively. The superfocusing and zero-degree focusing effects weaken with the increase of the crystal thickness. This is a consequence of the anharmonicity of the continuum proton-crystal interaction potential, which makes the proton beam propagation through the channel incoherent. We also explore the influence of the effect of proton collisions with the crystal's electrons on the beam dynamics in the channel. This effect additionally contributes to the incoherence of the beam motion along the channel. Our opinion is that the peaks of the spatial and angular distributions of ions transmitted through the planar channels lying off the origin registered before were in fact the rainbow peaks. © 2019 Elsevier B.V.
T2  - Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms
T1  - Superfocusing and zero-degree focusing in planar channeling of protons in a thin silicon crystal
VL  - 444
SP  - 10
EP  - 22
DO  - 10.1016/j.nimb.2019.02.004
ER  - 

@article{
author = "Ćosić, Marko and Nešković, Nebojša B. and Petrović, Srđan M.",
year = "2019",
abstract = "This is a theoretical study of the superfocusing and zero-degree focusing effects appearing in channeling of protons of energy of 2 MeV in the {1 1 0} channel of a thin silicon crystal. We prove that the ultimate origin of these effects is the crystal rainbow effect, which has been discovered and explored in ion transmission through axial crystal channels, nanotubes and graphene. Moreover, the effect is the origin of the shapes of the whole spatial and angular distributions of channeled protons. The incident proton velocity vector is taken to be parallel to the channel midplane. We use the Molière's approximation of the Thomas-Fermi proton-atom interaction potential and the continuum approximation. The effect of thermal vibrations of the crystal's atoms is included. We solve numerically the proton equation of motion and analyze the spatial and angular proton transmission functions. The extrema of these functions are the spatial and angular rainbow points, respectively. When the whole proton beam is taken into account, a spatial rainbow pattern, composed of the lines emerging from the superfocusing points, and an angular rainbow pattern, consisting of the lines emerging from the origin and the zero-degree focusing points, appear along the channel. We consider the region of crystal thickness comprising the first, second and third superfocusing and zero-degree focusing points. When the effect of thermal vibrations is neglected, each of these rainbow lines look like the bifurcation set of the cusp catastrophe, and when the effect is included, the line resembles the bifurcation set of the butterfly catastrophe. We demonstrate that the spatial and angular distributions of transmitted protons are fully determined by the spatial and angular rainbow lines, respectively. The superfocusing and zero-degree focusing effects weaken with the increase of the crystal thickness. This is a consequence of the anharmonicity of the continuum proton-crystal interaction potential, which makes the proton beam propagation through the channel incoherent. We also explore the influence of the effect of proton collisions with the crystal's electrons on the beam dynamics in the channel. This effect additionally contributes to the incoherence of the beam motion along the channel. Our opinion is that the peaks of the spatial and angular distributions of ions transmitted through the planar channels lying off the origin registered before were in fact the rainbow peaks. © 2019 Elsevier B.V.",
journal = "Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms",
title = "Superfocusing and zero-degree focusing in planar channeling of protons in a thin silicon crystal",
volume = "444",
pages = "10-22",
doi = "10.1016/j.nimb.2019.02.004"
}

Ćosić, M., Nešković, N. B.,& Petrović, S. M.. (2019). Superfocusing and zero-degree focusing in planar channeling of protons in a thin silicon crystal. in Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms, 444, 10-22.
https://doi.org/10.1016/j.nimb.2019.02.004

Ćosić M, Nešković NB, Petrović SM. Superfocusing and zero-degree focusing in planar channeling of protons in a thin silicon crystal. in Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms. 2019;444:10-22.
doi:10.1016/j.nimb.2019.02.004 .

Ćosić, Marko, Nešković, Nebojša B., Petrović, Srđan M., "Superfocusing and zero-degree focusing in planar channeling of protons in a thin silicon crystal" in Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms, 444 (2019):10-22,
https://doi.org/10.1016/j.nimb.2019.02.004 . .

TY  - JOUR
AU  - Ćosić, Marko
AU  - Petrović, Srđan M.
AU  - Nešković, Nebojša B.
PY  - 2019
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/8226
AB  - Here we report the results of the theoretical investigation of the transmission of channeled positrons through various short chiral single walled carbon nanotubes (SWCNT). The main question answered by this study is “What are the manifestations of the rainbow effect in the channeling of quantum particles that happens during the channeling of classical particles?” To answer this question, the corresponding classical and quantum problems were solved in parallel, critically examined, and compared with each other. Positron energies were taken to be 1 MeV when the quantum approach was necessary. The continuum positron-nanotube potential was constructed from the thermally averaged Molière’s positron-carbon potential. In the classical approach, a positron beam is considered as an ensemble of noninteracting particles. In the quantum approach, it is considered as an ensemble of noninteracting wave packages. Distributions of transmitted positrons were constructed from the numerical solutions of Newton’s equation and the time-dependent Schrödinger equation. For the transmission of 1-MeV positrons through 200-nm long SWCNT (14; 4), in addition to the central maximum, the quantum angular distribution has a prominent peak pair (close to the classical rainbows) and two smaller peaks pairs. We have shown that even though the semiclassical approximation is not strictly applicable it is useful for explanation of the observed behavior. In vicinity of the most prominent peak, i.e., the primary rainbow peak, rays interfere constructively. On one of its sides, rays become complex, which explains the exponential decay of the probability density in that region. On the other side, the ray interference alternates between constructive and destructive, thus generating two observed supernumerary rainbow peaks. The developed model was then applied for the explanation of the angular distributions of 1-MeV positrons transmitting through 200 nm long (7, 3), (8, 5), (9, 7), (14, 4), (16, 5) and (17, 7) SWCNTs. It has been shown that this explains most but not all rainbow patterns. Therefore, a new method for the identification and classification of quantum rainbows was developed relying only on the morphological properties of the positron wave function amplitude and the phase function families. This led to a detailed explanation of the way the quantum rainbows are generated. All wave packets wrinkle due to their internal focusing in a mutually coordinated way and are concentrated near the position of the corresponding classical rainbow. This explanation is general and applicable to the investigations of quantum effects occurring in various other atomic collision processes.
T2  - Atoms
T1  - Quantum Rainbows in Positron Transmission through Carbon Nanotubes
VL  - 7
IS  - 1
SP  - 16
DO  - 10.3390/atoms7010016
ER  - 

@article{
author = "Ćosić, Marko and Petrović, Srđan M. and Nešković, Nebojša B.",
year = "2019",
abstract = "Here we report the results of the theoretical investigation of the transmission of channeled positrons through various short chiral single walled carbon nanotubes (SWCNT). The main question answered by this study is “What are the manifestations of the rainbow effect in the channeling of quantum particles that happens during the channeling of classical particles?” To answer this question, the corresponding classical and quantum problems were solved in parallel, critically examined, and compared with each other. Positron energies were taken to be 1 MeV when the quantum approach was necessary. The continuum positron-nanotube potential was constructed from the thermally averaged Molière’s positron-carbon potential. In the classical approach, a positron beam is considered as an ensemble of noninteracting particles. In the quantum approach, it is considered as an ensemble of noninteracting wave packages. Distributions of transmitted positrons were constructed from the numerical solutions of Newton’s equation and the time-dependent Schrödinger equation. For the transmission of 1-MeV positrons through 200-nm long SWCNT (14; 4), in addition to the central maximum, the quantum angular distribution has a prominent peak pair (close to the classical rainbows) and two smaller peaks pairs. We have shown that even though the semiclassical approximation is not strictly applicable it is useful for explanation of the observed behavior. In vicinity of the most prominent peak, i.e., the primary rainbow peak, rays interfere constructively. On one of its sides, rays become complex, which explains the exponential decay of the probability density in that region. On the other side, the ray interference alternates between constructive and destructive, thus generating two observed supernumerary rainbow peaks. The developed model was then applied for the explanation of the angular distributions of 1-MeV positrons transmitting through 200 nm long (7, 3), (8, 5), (9, 7), (14, 4), (16, 5) and (17, 7) SWCNTs. It has been shown that this explains most but not all rainbow patterns. Therefore, a new method for the identification and classification of quantum rainbows was developed relying only on the morphological properties of the positron wave function amplitude and the phase function families. This led to a detailed explanation of the way the quantum rainbows are generated. All wave packets wrinkle due to their internal focusing in a mutually coordinated way and are concentrated near the position of the corresponding classical rainbow. This explanation is general and applicable to the investigations of quantum effects occurring in various other atomic collision processes.",
journal = "Atoms",
title = "Quantum Rainbows in Positron Transmission through Carbon Nanotubes",
volume = "7",
number = "1",
pages = "16",
doi = "10.3390/atoms7010016"
}

Ćosić, M., Petrović, S. M.,& Nešković, N. B.. (2019). Quantum Rainbows in Positron Transmission through Carbon Nanotubes. in Atoms, 7(1), 16.
https://doi.org/10.3390/atoms7010016

Ćosić M, Petrović SM, Nešković NB. Quantum Rainbows in Positron Transmission through Carbon Nanotubes. in Atoms. 2019;7(1):16.
doi:10.3390/atoms7010016 .

Ćosić, Marko, Petrović, Srđan M., Nešković, Nebojša B., "Quantum Rainbows in Positron Transmission through Carbon Nanotubes" in Atoms, 7, no. 1 (2019):16,
https://doi.org/10.3390/atoms7010016 . .

TY  - JOUR
AU  - Ćosić, Marko
AU  - Petrović, Srđan M.
AU  - Nešković, Nebojša B.
PY  - 2018
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/7640
AB  - This article studies the rainbow scattering of 5-key protons by the single sheet of free-standing graphene and its possible use as a tool for investigation of the ion-graphene interaction. The proton-graphene interaction potential was constructed by using the Doyle-Turner, ZBL, and Moliere proton-carbon interaction potentials. The thermal motion of carbon atoms was included by averaging the potentials according to the Debye model. Proton trajectories were obtained by numerical solution of the corresponding Newton equations of motion. They were used to obtain the mapping of the proton initial positions to their scattering angles. Morphological properties of the introduced mapping including its multiplicity and the rainbow singularities were used to explain important features of the obtained angular distributions of transmitted protons.
T2  - Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms
T1  - The forward rainbow scattering of low energy protons by a graphene sheet
VL  - 422
SP  - 54
EP  - 62
DO  - 10.1016/j.nimb.2018.02.028
ER  - 

@article{
author = "Ćosić, Marko and Petrović, Srđan M. and Nešković, Nebojša B.",
year = "2018",
abstract = "This article studies the rainbow scattering of 5-key protons by the single sheet of free-standing graphene and its possible use as a tool for investigation of the ion-graphene interaction. The proton-graphene interaction potential was constructed by using the Doyle-Turner, ZBL, and Moliere proton-carbon interaction potentials. The thermal motion of carbon atoms was included by averaging the potentials according to the Debye model. Proton trajectories were obtained by numerical solution of the corresponding Newton equations of motion. They were used to obtain the mapping of the proton initial positions to their scattering angles. Morphological properties of the introduced mapping including its multiplicity and the rainbow singularities were used to explain important features of the obtained angular distributions of transmitted protons.",
journal = "Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms",
title = "The forward rainbow scattering of low energy protons by a graphene sheet",
volume = "422",
pages = "54-62",
doi = "10.1016/j.nimb.2018.02.028"
}

Ćosić, M., Petrović, S. M.,& Nešković, N. B.. (2018). The forward rainbow scattering of low energy protons by a graphene sheet. in Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms, 422, 54-62.
https://doi.org/10.1016/j.nimb.2018.02.028

Ćosić M, Petrović SM, Nešković NB. The forward rainbow scattering of low energy protons by a graphene sheet. in Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms. 2018;422:54-62.
doi:10.1016/j.nimb.2018.02.028 .

Ćosić, Marko, Petrović, Srđan M., Nešković, Nebojša B., "The forward rainbow scattering of low energy protons by a graphene sheet" in Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms, 422 (2018):54-62,
https://doi.org/10.1016/j.nimb.2018.02.028 . .

TY  - JOUR
AU  - Efremov, Andrey
AU  - Bogomolov, Sergey
AU  - Bekhterev, Vladimir
AU  - Dobrosavljević, Aleksandar S.
AU  - Nešković, Nebojša B.
AU  - Trajić, Ivan
AU  - Ćirić, Dragana
PY  - 2018
UR  - http://www.doiserbia.nb.rs/Article.aspx?ID=1451-39941801047E
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/7786
AB  - Recent upgrading of the Facility for Modification and Analysis of Materials with Ion Beams-FAMA, in the Laboratory of Physics of the Vinca Institute of Nuclear Sciences, included the modernization of its electron cyclotron resonance ion source. Since the old ion source was being extensively used for more than 15 years for production of multiply charged ions from gases and solid substances, its complete reconstruction was needed. The main goal was to reconstruct its plasma and injection chambers and magnetic structure, and thus intensify the production of multiply charged ions. Also, it was decided to refurbish its major subsystems the vacuum system, the microwave system, the gas inlet system, the solid substance inlet system, and the control system. All these improvements have resulted in a substantial increase of ion beam currents, especially in the case of high charge states, with the operation of the ion source proven to be stable and reproducible.
T2  - Nuclear Technology and Radiation Protection
T1  - Upgrading the ECR ion source within FAMA
VL  - 33
IS  - 1
SP  - 47
EP  - 52
DO  - 10.2298/NTRP1801047E
ER  - 

@article{
author = "Efremov, Andrey and Bogomolov, Sergey and Bekhterev, Vladimir and Dobrosavljević, Aleksandar S. and Nešković, Nebojša B. and Trajić, Ivan and Ćirić, Dragana",
year = "2018",
abstract = "Recent upgrading of the Facility for Modification and Analysis of Materials with Ion Beams-FAMA, in the Laboratory of Physics of the Vinca Institute of Nuclear Sciences, included the modernization of its electron cyclotron resonance ion source. Since the old ion source was being extensively used for more than 15 years for production of multiply charged ions from gases and solid substances, its complete reconstruction was needed. The main goal was to reconstruct its plasma and injection chambers and magnetic structure, and thus intensify the production of multiply charged ions. Also, it was decided to refurbish its major subsystems the vacuum system, the microwave system, the gas inlet system, the solid substance inlet system, and the control system. All these improvements have resulted in a substantial increase of ion beam currents, especially in the case of high charge states, with the operation of the ion source proven to be stable and reproducible.",
journal = "Nuclear Technology and Radiation Protection",
title = "Upgrading the ECR ion source within FAMA",
volume = "33",
number = "1",
pages = "47-52",
doi = "10.2298/NTRP1801047E"
}

Efremov, A., Bogomolov, S., Bekhterev, V., Dobrosavljević, A. S., Nešković, N. B., Trajić, I.,& Ćirić, D.. (2018). Upgrading the ECR ion source within FAMA. in Nuclear Technology and Radiation Protection, 33(1), 47-52.
https://doi.org/10.2298/NTRP1801047E

Efremov A, Bogomolov S, Bekhterev V, Dobrosavljević AS, Nešković NB, Trajić I, Ćirić D. Upgrading the ECR ion source within FAMA. in Nuclear Technology and Radiation Protection. 2018;33(1):47-52.
doi:10.2298/NTRP1801047E .

Efremov, Andrey, Bogomolov, Sergey, Bekhterev, Vladimir, Dobrosavljević, Aleksandar S., Nešković, Nebojša B., Trajić, Ivan, Ćirić, Dragana, "Upgrading the ECR ion source within FAMA" in Nuclear Technology and Radiation Protection, 33, no. 1 (2018):47-52,
https://doi.org/10.2298/NTRP1801047E . .

TY  - CONF
AU  - Efremov, Andrey
AU  - Bogomolov, Sergey
AU  - Bekhterev, Vladimir
AU  - Dobrosavljević, Aleksandar S.
AU  - Vujović, Velibor V.
AU  - Nešković, Nebojša B.
AU  - Trajić, Ivan
PY  - 2018
UR  - http://aip.scitation.org/doi/abs/10.1063/1.5053291
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/7900
AB  - The CAPRICE-type ECR ion source mVINIS has been upgraded by increasing its magnetic field to improve a plasma confinement and thereby enhance the source performance. This modification made it also possible to increase the internal diameter of the plasma chamber and to replace the coaxial microwave input by a waveguide. Some major subsystems such as: the vacuum system, the microwave system, the gas inlet system, the solid substance inlet system, and the control system have been also refurbished. All these improvements have resulted in a substantial increase of ion beam currents, especially in the case of high charge states, with the operation of the ion source proven to be stable and reproducible. This modification can be applied to other CAPRICE-type ion sources. © 2018 Author(s).
C3  - AIP Conference Proceedings
T1  - Upgrading of the CAPRICE type ECR ion source
VL  - 2011
SP  - 040017
DO  - 10.1063/1.5053291
ER  - 

@conference{
author = "Efremov, Andrey and Bogomolov, Sergey and Bekhterev, Vladimir and Dobrosavljević, Aleksandar S. and Vujović, Velibor V. and Nešković, Nebojša B. and Trajić, Ivan",
year = "2018",
abstract = "The CAPRICE-type ECR ion source mVINIS has been upgraded by increasing its magnetic field to improve a plasma confinement and thereby enhance the source performance. This modification made it also possible to increase the internal diameter of the plasma chamber and to replace the coaxial microwave input by a waveguide. Some major subsystems such as: the vacuum system, the microwave system, the gas inlet system, the solid substance inlet system, and the control system have been also refurbished. All these improvements have resulted in a substantial increase of ion beam currents, especially in the case of high charge states, with the operation of the ion source proven to be stable and reproducible. This modification can be applied to other CAPRICE-type ion sources. © 2018 Author(s).",
journal = "AIP Conference Proceedings",
title = "Upgrading of the CAPRICE type ECR ion source",
volume = "2011",
pages = "040017",
doi = "10.1063/1.5053291"
}

Efremov, A., Bogomolov, S., Bekhterev, V., Dobrosavljević, A. S., Vujović, V. V., Nešković, N. B.,& Trajić, I.. (2018). Upgrading of the CAPRICE type ECR ion source. in AIP Conference Proceedings, 2011, 040017.
https://doi.org/10.1063/1.5053291

Efremov A, Bogomolov S, Bekhterev V, Dobrosavljević AS, Vujović VV, Nešković NB, Trajić I. Upgrading of the CAPRICE type ECR ion source. in AIP Conference Proceedings. 2018;2011:040017.
doi:10.1063/1.5053291 .

Efremov, Andrey, Bogomolov, Sergey, Bekhterev, Vladimir, Dobrosavljević, Aleksandar S., Vujović, Velibor V., Nešković, Nebojša B., Trajić, Ivan, "Upgrading of the CAPRICE type ECR ion source" in AIP Conference Proceedings, 2011 (2018):040017,
https://doi.org/10.1063/1.5053291 . .

TY  - BOOK
AU  - Nešković, Nebojša B.
AU  - Petrović, Srđan M.
AU  - Ćosić, Marko
PY  - 2017
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/10495
AB  - Authors are experts in the field, having discovered the phenomena and formulated the theory of crystal rainbows;

Describes both analytical and numerical approaches to ion channeling;

Covers the latest advances, including rainbow effects in crystals and nanotubes, crystal rainbows as catastrophes, and ion beam bending with nanotubes.
T2  - Lecture Notes in Nanoscale Science and Technology
T1  - Rainbows in Channeling of Charged Particles in Crystals and Nanotubes
VL  - 25
DO  - 10.1007/978-3-319-61524-0
ER  - 

@book{
author = "Nešković, Nebojša B. and Petrović, Srđan M. and Ćosić, Marko",
year = "2017",
abstract = "Authors are experts in the field, having discovered the phenomena and formulated the theory of crystal rainbows;

Describes both analytical and numerical approaches to ion channeling;

Covers the latest advances, including rainbow effects in crystals and nanotubes, crystal rainbows as catastrophes, and ion beam bending with nanotubes.",
journal = "Lecture Notes in Nanoscale Science and Technology",
title = "Rainbows in Channeling of Charged Particles in Crystals and Nanotubes",
volume = "25",
doi = "10.1007/978-3-319-61524-0"
}

Nešković, N. B., Petrović, S. M.,& Ćosić, M.. (2017). Rainbows in Channeling of Charged Particles in Crystals and Nanotubes. in Lecture Notes in Nanoscale Science and Technology, 25.
https://doi.org/10.1007/978-3-319-61524-0

Nešković NB, Petrović SM, Ćosić M. Rainbows in Channeling of Charged Particles in Crystals and Nanotubes. in Lecture Notes in Nanoscale Science and Technology. 2017;25.
doi:10.1007/978-3-319-61524-0 .

Nešković, Nebojša B., Petrović, Srđan M., Ćosić, Marko, "Rainbows in Channeling of Charged Particles in Crystals and Nanotubes" in Lecture Notes in Nanoscale Science and Technology, 25 (2017),
https://doi.org/10.1007/978-3-319-61524-0 . .

TY  - JOUR
AU  - Ćosić, Marko
AU  - Petrović, Srđan M.
AU  - Nešković, Nebojša B.
PY  - 2017
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/1575
AB  - We describe here the dynamic behaviors of a quantum ensemble of particles in a one-dimensional anharmonic potential well and of the corresponding classical ensemble in the vicinity of a focusing point. The anharmonicity of the interaction is chosen to be very small and small. Accordingly, the perturbation theory is used, and the accurate analytical solutions of the problem in both the quantum and classical cases are obtained. The dynamics of the quantum ensemble is considered through a detailed morphological analysis of the families of amplitudes squared and phases of the particle wave functions. We explore the dependence of the quantum solution of the problem on the anharmonicity and its relation to the classical solution. In addition, a solution of the problem based on catastrophe theory is given and compared with the quantum solution. It has been proven that an effective quantum dynamics of the ensemble can be clearly observed. In addition, we have concluded that, when the anharmonicity increases, the difference between the effective quantum behavior and classical behavior becomes larger. (C) 2017 Elsevier B.V. All rights reserved.
T2  - Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms
T1  - Effective quantum dynamics in a weakly anharmonic interaction in the vicinity of a focusing point
VL  - 399
SP  - 1
EP  - 11
DO  - 10.1016/j.nimb.2017.03.001
ER  - 

@article{
author = "Ćosić, Marko and Petrović, Srđan M. and Nešković, Nebojša B.",
year = "2017",
abstract = "We describe here the dynamic behaviors of a quantum ensemble of particles in a one-dimensional anharmonic potential well and of the corresponding classical ensemble in the vicinity of a focusing point. The anharmonicity of the interaction is chosen to be very small and small. Accordingly, the perturbation theory is used, and the accurate analytical solutions of the problem in both the quantum and classical cases are obtained. The dynamics of the quantum ensemble is considered through a detailed morphological analysis of the families of amplitudes squared and phases of the particle wave functions. We explore the dependence of the quantum solution of the problem on the anharmonicity and its relation to the classical solution. In addition, a solution of the problem based on catastrophe theory is given and compared with the quantum solution. It has been proven that an effective quantum dynamics of the ensemble can be clearly observed. In addition, we have concluded that, when the anharmonicity increases, the difference between the effective quantum behavior and classical behavior becomes larger. (C) 2017 Elsevier B.V. All rights reserved.",
journal = "Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms",
title = "Effective quantum dynamics in a weakly anharmonic interaction in the vicinity of a focusing point",
volume = "399",
pages = "1-11",
doi = "10.1016/j.nimb.2017.03.001"
}

Ćosić, M., Petrović, S. M.,& Nešković, N. B.. (2017). Effective quantum dynamics in a weakly anharmonic interaction in the vicinity of a focusing point. in Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms, 399, 1-11.
https://doi.org/10.1016/j.nimb.2017.03.001

Ćosić M, Petrović SM, Nešković NB. Effective quantum dynamics in a weakly anharmonic interaction in the vicinity of a focusing point. in Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms. 2017;399:1-11.
doi:10.1016/j.nimb.2017.03.001 .

Ćosić, Marko, Petrović, Srđan M., Nešković, Nebojša B., "Effective quantum dynamics in a weakly anharmonic interaction in the vicinity of a focusing point" in Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms, 399 (2017):1-11,
https://doi.org/10.1016/j.nimb.2017.03.001 . .

TY  - JOUR
AU  - Ćosić, Marko
AU  - Petrović, Srđan M.
AU  - Nešković, Nebojša B.
PY  - 2016
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/1029
AB  - This paper is devoted to a quantum mechanical consideration of the transmission of positrons of a kinetic energy of 1 MeV through very short (11, 9) single-wall chiral carbon nanotubes. The nanotube lengths are between 50 and 320 nm. The transmission process is determined by the rainbow effects. The interaction potential of a positron and the nanotube is deduced from the Molires interaction potential of the positron and a nanotube atom using the continuum approximation. We solve numerically the time-dependent Schrodinger equation, and calculate the spatial and angular distributions of transmitted positrons. The initial positron beam is assumed to be an ensemble of non-interacting Gaussian wave packets. We generate the spatial and angular distributions using the computer simulation method. The examination is focused on the spatial and angular primary rainbows. It begins with an analysis of the corresponding classical rainbows, and continues with a detailed investigation of the amplitudes and phases of the wave functions of transmitted positrons. These analyses enable one to identify the principal and supernumerary primary rainbows appearing in the spatial and angular distributions. They also result in a detailed explanation of the way of their generation, which includes the effects of wriniding of each wave packet during its deflection from the nanotube wall, and of its concentration just before a virtual barrier lying close to the corresponding classical rainbow. The wrinkling of the wave packets occurs due to their internal focusing. In addition, the wave packets wrinkle in a mutually coordinated way. This explanation may induce new theoretical and experimental investigations of quantum rainbows occurring in various atomic collision processes.
PB  - Elsevier
T2  - Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms
T1  - Quantum primary rainbows in transmission of positrons through very short carbon nanotubes
VL  - 373
SP  - 52
EP  - 62
DO  - 10.1016/j.nimb.2016.03.019
ER  - 

@article{
author = "Ćosić, Marko and Petrović, Srđan M. and Nešković, Nebojša B.",
year = "2016",
abstract = "This paper is devoted to a quantum mechanical consideration of the transmission of positrons of a kinetic energy of 1 MeV through very short (11, 9) single-wall chiral carbon nanotubes. The nanotube lengths are between 50 and 320 nm. The transmission process is determined by the rainbow effects. The interaction potential of a positron and the nanotube is deduced from the Molires interaction potential of the positron and a nanotube atom using the continuum approximation. We solve numerically the time-dependent Schrodinger equation, and calculate the spatial and angular distributions of transmitted positrons. The initial positron beam is assumed to be an ensemble of non-interacting Gaussian wave packets. We generate the spatial and angular distributions using the computer simulation method. The examination is focused on the spatial and angular primary rainbows. It begins with an analysis of the corresponding classical rainbows, and continues with a detailed investigation of the amplitudes and phases of the wave functions of transmitted positrons. These analyses enable one to identify the principal and supernumerary primary rainbows appearing in the spatial and angular distributions. They also result in a detailed explanation of the way of their generation, which includes the effects of wriniding of each wave packet during its deflection from the nanotube wall, and of its concentration just before a virtual barrier lying close to the corresponding classical rainbow. The wrinkling of the wave packets occurs due to their internal focusing. In addition, the wave packets wrinkle in a mutually coordinated way. This explanation may induce new theoretical and experimental investigations of quantum rainbows occurring in various atomic collision processes.",
publisher = "Elsevier",
journal = "Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms",
title = "Quantum primary rainbows in transmission of positrons through very short carbon nanotubes",
volume = "373",
pages = "52-62",
doi = "10.1016/j.nimb.2016.03.019"
}

Ćosić, M., Petrović, S. M.,& Nešković, N. B.. (2016). Quantum primary rainbows in transmission of positrons through very short carbon nanotubes. in Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms
Elsevier., 373, 52-62.
https://doi.org/10.1016/j.nimb.2016.03.019

Ćosić M, Petrović SM, Nešković NB. Quantum primary rainbows in transmission of positrons through very short carbon nanotubes. in Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms. 2016;373:52-62.
doi:10.1016/j.nimb.2016.03.019 .

Ćosić, Marko, Petrović, Srđan M., Nešković, Nebojša B., "Quantum primary rainbows in transmission of positrons through very short carbon nanotubes" in Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms, 373 (2016):52-62,
https://doi.org/10.1016/j.nimb.2016.03.019 . .

TY  - JOUR
AU  - Motapothula, Mallikarjuna Rao
AU  - Petrović, Srđan M.
AU  - Nešković, Nebojša B.
AU  - Breese, Mark B.H.
PY  - 2016
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/1205
AB  - Sub-Angstrom focusing of megaelectronvolt (MeV) ions within axial channels was predicted over 10 years ago, but evidence proved elusive. We present experimental angular distributions of axially channeled MeV protons in a 55-nm-thick (001) silicon membrane through which multiple scattering is negligible. Fine angular structure is in excellent agreement with Monte Carlo simulations based on three interaction potentials, providing indirect evidence of the existence of the superfocusing effect with flux enhancement of around 800 within a focused beam width of similar to 20 pm.
T2  - Physical Review B: Condensed Matter and Materials Physics
T1  - Experimental evidence of the superfocusing effect for axially channeled MeV protons
VL  - 94
IS  - 7
DO  - 10.1103/PhysRevB.94.075415
ER  - 

@article{
author = "Motapothula, Mallikarjuna Rao and Petrović, Srđan M. and Nešković, Nebojša B. and Breese, Mark B.H.",
year = "2016",
abstract = "Sub-Angstrom focusing of megaelectronvolt (MeV) ions within axial channels was predicted over 10 years ago, but evidence proved elusive. We present experimental angular distributions of axially channeled MeV protons in a 55-nm-thick (001) silicon membrane through which multiple scattering is negligible. Fine angular structure is in excellent agreement with Monte Carlo simulations based on three interaction potentials, providing indirect evidence of the existence of the superfocusing effect with flux enhancement of around 800 within a focused beam width of similar to 20 pm.",
journal = "Physical Review B: Condensed Matter and Materials Physics",
title = "Experimental evidence of the superfocusing effect for axially channeled MeV protons",
volume = "94",
number = "7",
doi = "10.1103/PhysRevB.94.075415"
}

Motapothula, M. R., Petrović, S. M., Nešković, N. B.,& Breese, M. B.H.. (2016). Experimental evidence of the superfocusing effect for axially channeled MeV protons. in Physical Review B: Condensed Matter and Materials Physics, 94(7).
https://doi.org/10.1103/PhysRevB.94.075415

Motapothula MR, Petrović SM, Nešković NB, Breese MB. Experimental evidence of the superfocusing effect for axially channeled MeV protons. in Physical Review B: Condensed Matter and Materials Physics. 2016;94(7).
doi:10.1103/PhysRevB.94.075415 .

Motapothula, Mallikarjuna Rao, Petrović, Srđan M., Nešković, Nebojša B., Breese, Mark B.H., "Experimental evidence of the superfocusing effect for axially channeled MeV protons" in Physical Review B: Condensed Matter and Materials Physics, 94, no. 7 (2016),
https://doi.org/10.1103/PhysRevB.94.075415 . .

TY  - CONF
AU  - Nešković, Nebojša B.
PY  - 2015
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/10892
AB  - Carbon nanotubes are the sheets of carbon atoms rolled up into cylinders with the atoms lying at the hexagonal crystal lattice sites. It has been predicted that they can be used to channel positively charged particles. This means that nanotubes could be used for guiding such beams. It has been also shown that the rainbow effect plays an important role in proton and positron channeling in nanotubes. This plenary speech is devoted to channeling of positrons of kinetic energy of 1 MeV in (11, 9) chiral single-wall carbon nanotubes of lengths between 50 and 200 nm. We present the classical and quantum spatial and angular distributions of transmitted positrons. In the classical calculations, the approach is via the equations of motion, and in the quantum calculations, the time-dependent Schrödinger equations is solved. The solutions of these quations are obtained numerically. In the quantum calculations, the initial beam is taken to be an ensemble on noninteracting Gaussian wave packets. The spatial and angular distributions are generated using the computer simulation method. The analysis is concentrated on the rainbow effects, which is clearly seen in the spatial and angular distributions. The obtained classical and quantum rainbows are analyzed in detail and compared with each other. We give a full quantum mechanical explanation of the quantum rainbows.
PB  - Belgrade : Serbian Ceramic Society
C3  - Advanced Ceramics and Application : 4th Serbian Ceramic Society Conference : program and the book of abstracts; September 21-23, 2015; Belgrade
T1  - Quantum rainbows in positron channeling in carbon nanotubes
SP  - 31
EP  - 32
UR  - https://hdl.handle.net/21.15107/rcub_vinar_10892
ER  - 

@conference{
author = "Nešković, Nebojša B.",
year = "2015",
abstract = "Carbon nanotubes are the sheets of carbon atoms rolled up into cylinders with the atoms lying at the hexagonal crystal lattice sites. It has been predicted that they can be used to channel positively charged particles. This means that nanotubes could be used for guiding such beams. It has been also shown that the rainbow effect plays an important role in proton and positron channeling in nanotubes. This plenary speech is devoted to channeling of positrons of kinetic energy of 1 MeV in (11, 9) chiral single-wall carbon nanotubes of lengths between 50 and 200 nm. We present the classical and quantum spatial and angular distributions of transmitted positrons. In the classical calculations, the approach is via the equations of motion, and in the quantum calculations, the time-dependent Schrödinger equations is solved. The solutions of these quations are obtained numerically. In the quantum calculations, the initial beam is taken to be an ensemble on noninteracting Gaussian wave packets. The spatial and angular distributions are generated using the computer simulation method. The analysis is concentrated on the rainbow effects, which is clearly seen in the spatial and angular distributions. The obtained classical and quantum rainbows are analyzed in detail and compared with each other. We give a full quantum mechanical explanation of the quantum rainbows.",
publisher = "Belgrade : Serbian Ceramic Society",
journal = "Advanced Ceramics and Application : 4th Serbian Ceramic Society Conference : program and the book of abstracts; September 21-23, 2015; Belgrade",
title = "Quantum rainbows in positron channeling in carbon nanotubes",
pages = "31-32",
url = "https://hdl.handle.net/21.15107/rcub_vinar_10892"
}

Nešković, N. B.. (2015). Quantum rainbows in positron channeling in carbon nanotubes. in Advanced Ceramics and Application : 4th Serbian Ceramic Society Conference : program and the book of abstracts; September 21-23, 2015; Belgrade
Belgrade : Serbian Ceramic Society., 31-32.
https://hdl.handle.net/21.15107/rcub_vinar_10892

Nešković NB. Quantum rainbows in positron channeling in carbon nanotubes. in Advanced Ceramics and Application : 4th Serbian Ceramic Society Conference : program and the book of abstracts; September 21-23, 2015; Belgrade. 2015;:31-32.
https://hdl.handle.net/21.15107/rcub_vinar_10892 .

Nešković, Nebojša B., "Quantum rainbows in positron channeling in carbon nanotubes" in Advanced Ceramics and Application : 4th Serbian Ceramic Society Conference : program and the book of abstracts; September 21-23, 2015; Belgrade (2015):31-32,
https://hdl.handle.net/21.15107/rcub_vinar_10892 .

TY  - JOUR
AU  - Petrović, Srđan M.
AU  - Nešković, Nebojša B.
AU  - Ćosić, Marko
AU  - Motapothula, Mallikarjuna Rao
AU  - Breese, Mark B.H.
PY  - 2015
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/752
AB  - This study provides a way to produce very accurate ion atom interaction potentials. We present the high-resolution measurements of angular distributions of protons of energies between 2.0 and 0.7 MeV channeled in a 55 nm thick (0 0 1) silicon membrane. Analysis is performed using the theory of crystal rainbows in which the Molieres interaction potential is modified to make it accurate both close to the channel axis and close to the atomic strings defining the channel. This modification is based on adjusting the shapes of the rainbow lines appearing in the transmission angle plane, with the resulting theoretical angular distributions of transmitted protons being in excellent agreement with the corresponding experimental distributions.
T2  - Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms
T1  - Proton-silicon interaction potential extracted from high-resolution measurements of crystal rainbows
VL  - 360
SP  - 23
EP  - 29
DO  - 10.1016/j.nimb.2015.07.104
ER  - 

@article{
author = "Petrović, Srđan M. and Nešković, Nebojša B. and Ćosić, Marko and Motapothula, Mallikarjuna Rao and Breese, Mark B.H.",
year = "2015",
abstract = "This study provides a way to produce very accurate ion atom interaction potentials. We present the high-resolution measurements of angular distributions of protons of energies between 2.0 and 0.7 MeV channeled in a 55 nm thick (0 0 1) silicon membrane. Analysis is performed using the theory of crystal rainbows in which the Molieres interaction potential is modified to make it accurate both close to the channel axis and close to the atomic strings defining the channel. This modification is based on adjusting the shapes of the rainbow lines appearing in the transmission angle plane, with the resulting theoretical angular distributions of transmitted protons being in excellent agreement with the corresponding experimental distributions.",
journal = "Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms",
title = "Proton-silicon interaction potential extracted from high-resolution measurements of crystal rainbows",
volume = "360",
pages = "23-29",
doi = "10.1016/j.nimb.2015.07.104"
}

Petrović, S. M., Nešković, N. B., Ćosić, M., Motapothula, M. R.,& Breese, M. B.H.. (2015). Proton-silicon interaction potential extracted from high-resolution measurements of crystal rainbows. in Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms, 360, 23-29.
https://doi.org/10.1016/j.nimb.2015.07.104

Petrović SM, Nešković NB, Ćosić M, Motapothula MR, Breese MB. Proton-silicon interaction potential extracted from high-resolution measurements of crystal rainbows. in Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms. 2015;360:23-29.
doi:10.1016/j.nimb.2015.07.104 .

Petrović, Srđan M., Nešković, Nebojša B., Ćosić, Marko, Motapothula, Mallikarjuna Rao, Breese, Mark B.H., "Proton-silicon interaction potential extracted from high-resolution measurements of crystal rainbows" in Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms, 360 (2015):23-29,
https://doi.org/10.1016/j.nimb.2015.07.104 . .

TY  - JOUR
AU  - Telečki, Igor N.
AU  - Beličev, Petar
AU  - Petrović, Srđan M.
AU  - Nešković, Nebojša B.
PY  - 2015
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/938
AB  - This is a study on the properties of a square electrostatic rainbow lens doublet. The said optical element consists of two square electrostatic rainbow lenses with the second lens axially rotated for 45 degrees with respect to the first one. The propagation of a proton beam with a kinetic energy of 10 keV through the doublet is in the focus of our analysis. The potential of the electrodes of both lenses is 2 kV. The electrostatic potential and the electric field components of the lens doublet are calculated using a 3-D computer code based on the method of moments. Spatial and angular distributions of protons propagating through the lens doublet, as well as the parameters defining beam quality, are investigated. As in the case of the single square electrostatic rainbow lens, the evolution of these distributions is determined by the evolution of corresponding rainbow lines, generated by the use of the theory of crystal rainbows. Our study shows that a beam core in the shape of a cusped square is formed by the spatial rainbow line that appears first. This rainbow line occurs during proton propagation through the first lens. The beam core retains the cusped square shape during the propagation through the second lens. The electrostatic field of the second lens causes the appearance of an additional spatial rainbow line, which encompasses the beam core and defines the outer border of the beam. This rainbow line constitutes the main difference between the cases of the lens doublet and a single lens.
T2  - Nuclear technology and radiation protection
T1  - Focusing Properties of a Square Electrostatic Rainbow Lens Doublet
VL  - 30
IS  - 4
SP  - 239
EP  - 248
DO  - 10.2298/NTRP1504239T
ER  - 

@article{
author = "Telečki, Igor N. and Beličev, Petar and Petrović, Srđan M. and Nešković, Nebojša B.",
year = "2015",
abstract = "This is a study on the properties of a square electrostatic rainbow lens doublet. The said optical element consists of two square electrostatic rainbow lenses with the second lens axially rotated for 45 degrees with respect to the first one. The propagation of a proton beam with a kinetic energy of 10 keV through the doublet is in the focus of our analysis. The potential of the electrodes of both lenses is 2 kV. The electrostatic potential and the electric field components of the lens doublet are calculated using a 3-D computer code based on the method of moments. Spatial and angular distributions of protons propagating through the lens doublet, as well as the parameters defining beam quality, are investigated. As in the case of the single square electrostatic rainbow lens, the evolution of these distributions is determined by the evolution of corresponding rainbow lines, generated by the use of the theory of crystal rainbows. Our study shows that a beam core in the shape of a cusped square is formed by the spatial rainbow line that appears first. This rainbow line occurs during proton propagation through the first lens. The beam core retains the cusped square shape during the propagation through the second lens. The electrostatic field of the second lens causes the appearance of an additional spatial rainbow line, which encompasses the beam core and defines the outer border of the beam. This rainbow line constitutes the main difference between the cases of the lens doublet and a single lens.",
journal = "Nuclear technology and radiation protection",
title = "Focusing Properties of a Square Electrostatic Rainbow Lens Doublet",
volume = "30",
number = "4",
pages = "239-248",
doi = "10.2298/NTRP1504239T"
}

Telečki, I. N., Beličev, P., Petrović, S. M.,& Nešković, N. B.. (2015). Focusing Properties of a Square Electrostatic Rainbow Lens Doublet. in Nuclear technology and radiation protection, 30(4), 239-248.
https://doi.org/10.2298/NTRP1504239T

Telečki IN, Beličev P, Petrović SM, Nešković NB. Focusing Properties of a Square Electrostatic Rainbow Lens Doublet. in Nuclear technology and radiation protection. 2015;30(4):239-248.
doi:10.2298/NTRP1504239T .

Telečki, Igor N., Beličev, Petar, Petrović, Srđan M., Nešković, Nebojša B., "Focusing Properties of a Square Electrostatic Rainbow Lens Doublet" in Nuclear technology and radiation protection, 30, no. 4 (2015):239-248,
https://doi.org/10.2298/NTRP1504239T . .

TY  - JOUR
AU  - Ćosić, Marko
AU  - Petrović, Srđan M.
AU  - Nešković, Nebojša B.
PY  - 2014
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/5932
AB  - In this work, we present a study of the quantum angular distributions of 1 MeV positrons channeled through the chiral (7, 3), (8, 5), (9, 7), (14, 4), (16,5) and (17,7) single walled carbon nanotubes (SWCNTs), having the same length of 200 nm and the corresponding nanotube radiuses of 0.35, 0.45, 0.55, 0.65, 0.75 and 0.85 nm, respectively. The continuum positron-nanotube interaction potential was obtained using the thermally averaged Molieres positron-carbon interaction potential. A positron beam is treated as an ensemble of non-interacting quantum particles each represented by a Gaussian wave packet. Evolution of a channeled positron was obtained from the numerical solution of the corresponding time-dependent Schrodinger equation. For the comparison, the classical angular rainbows for cases under the consideration are investigated as well. They were obtained using the numerical solution of the corresponding Newtons equations of positron motion in the transverse plane of carbon nanotube. We show that the quantum angular transmission patterns can be successfully used for the characterization of short chiral carbon nanotubes.
T2  - Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms
T1  - Quantum rainbow characterization of short chiral carbon nanotubes
VL  - 323
SP  - 30
EP  - 35
DO  - 10.1016/j.nimb.2014.01.017
ER  - 

@article{
author = "Ćosić, Marko and Petrović, Srđan M. and Nešković, Nebojša B.",
year = "2014",
abstract = "In this work, we present a study of the quantum angular distributions of 1 MeV positrons channeled through the chiral (7, 3), (8, 5), (9, 7), (14, 4), (16,5) and (17,7) single walled carbon nanotubes (SWCNTs), having the same length of 200 nm and the corresponding nanotube radiuses of 0.35, 0.45, 0.55, 0.65, 0.75 and 0.85 nm, respectively. The continuum positron-nanotube interaction potential was obtained using the thermally averaged Molieres positron-carbon interaction potential. A positron beam is treated as an ensemble of non-interacting quantum particles each represented by a Gaussian wave packet. Evolution of a channeled positron was obtained from the numerical solution of the corresponding time-dependent Schrodinger equation. For the comparison, the classical angular rainbows for cases under the consideration are investigated as well. They were obtained using the numerical solution of the corresponding Newtons equations of positron motion in the transverse plane of carbon nanotube. We show that the quantum angular transmission patterns can be successfully used for the characterization of short chiral carbon nanotubes.",
journal = "Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms",
title = "Quantum rainbow characterization of short chiral carbon nanotubes",
volume = "323",
pages = "30-35",
doi = "10.1016/j.nimb.2014.01.017"
}

Ćosić, M., Petrović, S. M.,& Nešković, N. B.. (2014). Quantum rainbow characterization of short chiral carbon nanotubes. in Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms, 323, 30-35.
https://doi.org/10.1016/j.nimb.2014.01.017

Ćosić M, Petrović SM, Nešković NB. Quantum rainbow characterization of short chiral carbon nanotubes. in Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms. 2014;323:30-35.
doi:10.1016/j.nimb.2014.01.017 .

Ćosić, Marko, Petrović, Srđan M., Nešković, Nebojša B., "Quantum rainbow characterization of short chiral carbon nanotubes" in Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms, 323 (2014):30-35,
https://doi.org/10.1016/j.nimb.2014.01.017 . .

TY  - JOUR
AU  - Ćosić, Marko
AU  - Petrović, Srđan M.
AU  - Nešković, Nebojša B.
PY  - 2014
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/6030
AB  - This work reports on the computational method for the long time propagation of the quantum channeled particles in infinite and finite harmonic interaction wells and in a realistic carbon nanotube interaction potential well. This method is based on the Chebyshev global propagation method for solving of the corresponding time dependent Schrodinger equation. For comparison, the computational method based on the Crank-Nicolson propagation method is also presented. In the case of quantum particle motion in infinite harmonic potential well, when the analytical solution of the corresponding time-dependent Schrodinger equation exists, we show that the obtained propagation method is efficient, very accurate and numerically stable. It is superior with respect to the method based on the Crank Nicolson propagation method. A detailed study of the long time quantum particle motion in the finite harmonic interaction potential well shows that the obtained computational method based on the Chebyshev global propagation method can be successfully applied for following of the channeled quantum particle in crystals and carbon nanotubes. This is demonstrated in the case of quantum particle motion in a realistic carbon nanotube interaction potential well.
T2  - Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms
T1  - Computational method for the long time propagation of quantum channeled particles in crystals and carbon nanotubes
VL  - 330
SP  - 33
EP  - 41
DO  - 10.1016/j.nimb.2014.03.015
ER  - 

@article{
author = "Ćosić, Marko and Petrović, Srđan M. and Nešković, Nebojša B.",
year = "2014",
abstract = "This work reports on the computational method for the long time propagation of the quantum channeled particles in infinite and finite harmonic interaction wells and in a realistic carbon nanotube interaction potential well. This method is based on the Chebyshev global propagation method for solving of the corresponding time dependent Schrodinger equation. For comparison, the computational method based on the Crank-Nicolson propagation method is also presented. In the case of quantum particle motion in infinite harmonic potential well, when the analytical solution of the corresponding time-dependent Schrodinger equation exists, we show that the obtained propagation method is efficient, very accurate and numerically stable. It is superior with respect to the method based on the Crank Nicolson propagation method. A detailed study of the long time quantum particle motion in the finite harmonic interaction potential well shows that the obtained computational method based on the Chebyshev global propagation method can be successfully applied for following of the channeled quantum particle in crystals and carbon nanotubes. This is demonstrated in the case of quantum particle motion in a realistic carbon nanotube interaction potential well.",
journal = "Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms",
title = "Computational method for the long time propagation of quantum channeled particles in crystals and carbon nanotubes",
volume = "330",
pages = "33-41",
doi = "10.1016/j.nimb.2014.03.015"
}

Ćosić, M., Petrović, S. M.,& Nešković, N. B.. (2014). Computational method for the long time propagation of quantum channeled particles in crystals and carbon nanotubes. in Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms, 330, 33-41.
https://doi.org/10.1016/j.nimb.2014.03.015

Ćosić M, Petrović SM, Nešković NB. Computational method for the long time propagation of quantum channeled particles in crystals and carbon nanotubes. in Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms. 2014;330:33-41.
doi:10.1016/j.nimb.2014.03.015 .

Ćosić, Marko, Petrović, Srđan M., Nešković, Nebojša B., "Computational method for the long time propagation of quantum channeled particles in crystals and carbon nanotubes" in Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms, 330 (2014):33-41,
https://doi.org/10.1016/j.nimb.2014.03.015 . .

TY  - CHAP
AU  - Nešković, Nebojša B.
AU  - Beličev, Petar
AU  - Telečki, Igor N.
AU  - Petrović, Srđan M.
PY  - 2014
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/7028
AB  - This review paper is devoted to transmission of protons through rainbow lenses, being novel ion beam optical elements analogous to crystal channels. We begin with a brief description of the crystal rainbow effect, which has proven to be the basic effect in ion channeling in thin crystals. Then, we concentrate on the transmission of a parallel proton beam through a square electrostatic rainbow lens. The initial proton kinetic energy is 10 keV and the potential of the electrodes is chosen to be between 10 and 100 kV. It is demonstrated that the evolution of the spatial distribution of transmitted protons is determined by the evolution of the corresponding rainbow pattern. The beam after the lens is clearly separated into the bright and dark components, corresponding to the bright and dark sides of the rainbow, respectively. All the focused protons are confined within the rainbow line. After that, we explore more accurately the focusing properties of the same electrostatic rainbow lens. This is done with the parallel and nonparallel initial beams of the kinetic energy of 10 keV. The electrode potential is chosen to be 2 kV. In the continuation of the paper, we analyze the acceleration properties of a square radiofrequency rainbow lens. This is done with a nonparallel initial beam of the kinetic energy of 10 keV. The lens electrodes excitation potential is a harmonic function of time of the amplitude of 20 keV and frequency of about 3 MHz. We explain the spatial, angular, and kinetic energy distributions of protons propagating through the lens. The transmitted proton beam contains a squarelike core, which is defined by the focused protons. Finally, we discuss the possible applications of rainbow lenses.
T2  - Advances in Imaging and Electron Physics
T1  - Rainbow Lenses
VL  - 182
SP  - 123
EP  - 186
DO  - 10.1016/B978-0-12-800146-2.00003-5
ER  - 

@inbook{
author = "Nešković, Nebojša B. and Beličev, Petar and Telečki, Igor N. and Petrović, Srđan M.",
year = "2014",
abstract = "This review paper is devoted to transmission of protons through rainbow lenses, being novel ion beam optical elements analogous to crystal channels. We begin with a brief description of the crystal rainbow effect, which has proven to be the basic effect in ion channeling in thin crystals. Then, we concentrate on the transmission of a parallel proton beam through a square electrostatic rainbow lens. The initial proton kinetic energy is 10 keV and the potential of the electrodes is chosen to be between 10 and 100 kV. It is demonstrated that the evolution of the spatial distribution of transmitted protons is determined by the evolution of the corresponding rainbow pattern. The beam after the lens is clearly separated into the bright and dark components, corresponding to the bright and dark sides of the rainbow, respectively. All the focused protons are confined within the rainbow line. After that, we explore more accurately the focusing properties of the same electrostatic rainbow lens. This is done with the parallel and nonparallel initial beams of the kinetic energy of 10 keV. The electrode potential is chosen to be 2 kV. In the continuation of the paper, we analyze the acceleration properties of a square radiofrequency rainbow lens. This is done with a nonparallel initial beam of the kinetic energy of 10 keV. The lens electrodes excitation potential is a harmonic function of time of the amplitude of 20 keV and frequency of about 3 MHz. We explain the spatial, angular, and kinetic energy distributions of protons propagating through the lens. The transmitted proton beam contains a squarelike core, which is defined by the focused protons. Finally, we discuss the possible applications of rainbow lenses.",
journal = "Advances in Imaging and Electron Physics",
booktitle = "Rainbow Lenses",
volume = "182",
pages = "123-186",
doi = "10.1016/B978-0-12-800146-2.00003-5"
}

Nešković, N. B., Beličev, P., Telečki, I. N.,& Petrović, S. M.. (2014). Rainbow Lenses. in Advances in Imaging and Electron Physics, 182, 123-186.
https://doi.org/10.1016/B978-0-12-800146-2.00003-5

Nešković NB, Beličev P, Telečki IN, Petrović SM. Rainbow Lenses. in Advances in Imaging and Electron Physics. 2014;182:123-186.
doi:10.1016/B978-0-12-800146-2.00003-5 .

Nešković, Nebojša B., Beličev, Petar, Telečki, Igor N., Petrović, Srđan M., "Rainbow Lenses" in Advances in Imaging and Electron Physics, 182 (2014):123-186,
https://doi.org/10.1016/B978-0-12-800146-2.00003-5 . .

TY  - JOUR
AU  - Petrović, Srđan M.
AU  - Ćosić, Marko
AU  - Nešković, Nebojša B.
PY  - 2013
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/5585
AB  - This is a theoretical study of transmission of positrons of kinetic energies of 1 and 10 MeV through very short (11,9) single-wall carbon nanotubes of lengths of 200 and 560 nm, respectively. The needed continuum interaction potential of the positron and nanotube is obtained starting from the Molieres approximation of the Thomas-Fermi interaction potential of a positron and a nanotube atom. We calculate the classical and quantum angular distributions of transmitted positrons. In the classical calculations, the approach is via the equations of motion, and in the quantum calculations, the time-dependent Schrodinger equation is solved. The solutions of these equations are obtained numerically. In the quantum calculations, the initial beam is taken to be an ensemble of noninteracting Gaussian wave packets. The angular distributions are generated using the computer simulation method. Our analysis is concentrated on the rainbow effect, which is clearly seen in the angular distributions. The obtained classical and quantum rainbows are analyzed in detail and compared with each other.
T2  - Physical Review A
T1  - Quantum rainbow channeling of positrons in very short carbon nanotubes
VL  - 88
IS  - 1
DO  - 10.1103/PhysRevA.88.012902
ER  - 

@article{
author = "Petrović, Srđan M. and Ćosić, Marko and Nešković, Nebojša B.",
year = "2013",
abstract = "This is a theoretical study of transmission of positrons of kinetic energies of 1 and 10 MeV through very short (11,9) single-wall carbon nanotubes of lengths of 200 and 560 nm, respectively. The needed continuum interaction potential of the positron and nanotube is obtained starting from the Molieres approximation of the Thomas-Fermi interaction potential of a positron and a nanotube atom. We calculate the classical and quantum angular distributions of transmitted positrons. In the classical calculations, the approach is via the equations of motion, and in the quantum calculations, the time-dependent Schrodinger equation is solved. The solutions of these equations are obtained numerically. In the quantum calculations, the initial beam is taken to be an ensemble of noninteracting Gaussian wave packets. The angular distributions are generated using the computer simulation method. Our analysis is concentrated on the rainbow effect, which is clearly seen in the angular distributions. The obtained classical and quantum rainbows are analyzed in detail and compared with each other.",
journal = "Physical Review A",
title = "Quantum rainbow channeling of positrons in very short carbon nanotubes",
volume = "88",
number = "1",
doi = "10.1103/PhysRevA.88.012902"
}

Petrović, S. M., Ćosić, M.,& Nešković, N. B.. (2013). Quantum rainbow channeling of positrons in very short carbon nanotubes. in Physical Review A, 88(1).
https://doi.org/10.1103/PhysRevA.88.012902

Petrović SM, Ćosić M, Nešković NB. Quantum rainbow channeling of positrons in very short carbon nanotubes. in Physical Review A. 2013;88(1).
doi:10.1103/PhysRevA.88.012902 .

Petrović, Srđan M., Ćosić, Marko, Nešković, Nebojša B., "Quantum rainbow channeling of positrons in very short carbon nanotubes" in Physical Review A, 88, no. 1 (2013),
https://doi.org/10.1103/PhysRevA.88.012902 . .

TY  - JOUR
AU  - Stojanov, Nace
AU  - Petrović, Srđan M.
AU  - Nešković, Nebojša B.
PY  - 2013
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/5535
AB  - A detailed study of the energy loss distributions of the relativistic protons axially channeled in the bent LT 100 GT Si crystals is presented in this work. The bending angle was varied from 0 to 20 mu rad, while the crystal thickness was equal to 1 mm. The proton energy was chosen to be 7 TeV in accordance with the Large Hadron Collider (LHC) project, at the European Organization for Nuclear Research (CERN), in Geneva, Switzerland. The energy loss distributions of the channeled protons were generated using the numerical solution of the proton equations of motion in the transverse plane and the computer simulation method. An accurate energy loss model was used, which takes into account the trajectory dependence of the energy loss of protons during their motion through the crystal channels. Further, the dispersion of the protons scattering angle caused by its collisions with the electrons of the crystal and the divergence of the proton beam were taken into account. The calculated dependence of the number of dechanneled protons on the bending angle was excellently fitted by the Gompertz type dechanneling function.
T2  - Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms
T1  - Energy loss distributions of relativistic protons axially channeled in a bent silicon crystal
VL  - 302
SP  - 9
EP  - 13
DO  - 10.1016/j.nimb.2013.03.036
ER  - 

@article{
author = "Stojanov, Nace and Petrović, Srđan M. and Nešković, Nebojša B.",
year = "2013",
abstract = "A detailed study of the energy loss distributions of the relativistic protons axially channeled in the bent LT 100 GT Si crystals is presented in this work. The bending angle was varied from 0 to 20 mu rad, while the crystal thickness was equal to 1 mm. The proton energy was chosen to be 7 TeV in accordance with the Large Hadron Collider (LHC) project, at the European Organization for Nuclear Research (CERN), in Geneva, Switzerland. The energy loss distributions of the channeled protons were generated using the numerical solution of the proton equations of motion in the transverse plane and the computer simulation method. An accurate energy loss model was used, which takes into account the trajectory dependence of the energy loss of protons during their motion through the crystal channels. Further, the dispersion of the protons scattering angle caused by its collisions with the electrons of the crystal and the divergence of the proton beam were taken into account. The calculated dependence of the number of dechanneled protons on the bending angle was excellently fitted by the Gompertz type dechanneling function.",
journal = "Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms",
title = "Energy loss distributions of relativistic protons axially channeled in a bent silicon crystal",
volume = "302",
pages = "9-13",
doi = "10.1016/j.nimb.2013.03.036"
}

Stojanov, N., Petrović, S. M.,& Nešković, N. B.. (2013). Energy loss distributions of relativistic protons axially channeled in a bent silicon crystal. in Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms, 302, 9-13.
https://doi.org/10.1016/j.nimb.2013.03.036

Stojanov N, Petrović SM, Nešković NB. Energy loss distributions of relativistic protons axially channeled in a bent silicon crystal. in Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms. 2013;302:9-13.
doi:10.1016/j.nimb.2013.03.036 .

Stojanov, Nace, Petrović, Srđan M., Nešković, Nebojša B., "Energy loss distributions of relativistic protons axially channeled in a bent silicon crystal" in Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms, 302 (2013):9-13,
https://doi.org/10.1016/j.nimb.2013.03.036 . .

TY  - JOUR
AU  - Stojanov, Nace
AU  - Petrović, Srđan M.
AU  - Nešković, Nebojša B.
PY  - 2013
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/5423
AB  - The energy loss distributions of relativistic protons axially channeled through the bent LT 100 GT Si crystals, with the constant curvature radius, R = 50 m, are studied here. The proton energy is 7 TeV and the thickness of the crystal is varied from 1 mm to 5 mm, which corresponds to the reduced crystal thickness, Lambda, from 2.1 to 10.6, respectively. The proton energy was chosen in accordance with the large hadron collider project, at the European Organization for Nuclear Research, in Geneva, Switzerland. The energy loss distributions of the channeled protons were generated by the computer simulation method using the numerical solution of the proton equations of motion in the transverse plane. Dispersion of the proton scattering angle caused by its collisions with the crystals electrons was taken into account.
T2  - Nuclear technology and radiation protection
T1  - Energy loss distributions of 7 TeV protons channeled in a bent silicon crystals
VL  - 28
IS  - 1
SP  - 31
EP  - 35
DO  - 10.2298/NTRP1301031S
ER  - 

@article{
author = "Stojanov, Nace and Petrović, Srđan M. and Nešković, Nebojša B.",
year = "2013",
abstract = "The energy loss distributions of relativistic protons axially channeled through the bent LT 100 GT Si crystals, with the constant curvature radius, R = 50 m, are studied here. The proton energy is 7 TeV and the thickness of the crystal is varied from 1 mm to 5 mm, which corresponds to the reduced crystal thickness, Lambda, from 2.1 to 10.6, respectively. The proton energy was chosen in accordance with the large hadron collider project, at the European Organization for Nuclear Research, in Geneva, Switzerland. The energy loss distributions of the channeled protons were generated by the computer simulation method using the numerical solution of the proton equations of motion in the transverse plane. Dispersion of the proton scattering angle caused by its collisions with the crystals electrons was taken into account.",
journal = "Nuclear technology and radiation protection",
title = "Energy loss distributions of 7 TeV protons channeled in a bent silicon crystals",
volume = "28",
number = "1",
pages = "31-35",
doi = "10.2298/NTRP1301031S"
}

Stojanov, N., Petrović, S. M.,& Nešković, N. B.. (2013). Energy loss distributions of 7 TeV protons channeled in a bent silicon crystals. in Nuclear technology and radiation protection, 28(1), 31-35.
https://doi.org/10.2298/NTRP1301031S

Stojanov N, Petrović SM, Nešković NB. Energy loss distributions of 7 TeV protons channeled in a bent silicon crystals. in Nuclear technology and radiation protection. 2013;28(1):31-35.
doi:10.2298/NTRP1301031S .

Stojanov, Nace, Petrović, Srđan M., Nešković, Nebojša B., "Energy loss distributions of 7 TeV protons channeled in a bent silicon crystals" in Nuclear technology and radiation protection, 28, no. 1 (2013):31-35,
https://doi.org/10.2298/NTRP1301031S . .

TY  - JOUR
AU  - Telečki, Igor N.
AU  - Petrović, Srđan M.
AU  - Beličev, Petar
AU  - Radenovic, B.
AU  - Balvanović, Roman V.
AU  - Bojović, Boško
AU  - Nešković, Nebojša B.
PY  - 2012
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/5158
AB  - This paper is devoted to the focusing properties of a square electrostatic rainbow lens, which is a novel ion beam optical element. We consider the transmission of parallel and non-parallel proton beams of the initial kinetic energy of 10 keV through this lens. The potential of the electrodes of the lens is chosen to be 2 kV. The electrostatic potential and components of the electric field in the region of the lens are calculated using a three-dimensional finite element computer code. We investigate the spatial and angular distributions of protons propagating through the lens and in the drift space after it. It is confirmed that the evolutions of these distributions are determined by the evolutions of the corresponding rainbow lines, generated using the theory of crystal rainbows. The beam is separated into two components. One beam component, appearing as a beam core, is generated dominantly by the focused protons. Its boundary line in the transverse position plane can be very well approximated by a hypotrochoid. The other beam component is generated dominantly by the defocused protons. We present the focusing coefficient of the lens, the confining coefficients of the lens for the focused and defocused protons, the density of the beam core, the vertical or horizontal emittance of the beam core, and the brightness of the beam core. (C) 2012 Elsevier B.V. All rights reserved.
T2  - Nuclear Instruments and Methods in Physics Research. Section A: Accelerators, Spectrometers, Detectors, and Associated Equipment
T1  - Focusing properties of a square electrostatic rainbow lens
VL  - 694
SP  - 224
EP  - 233
DO  - 10.1016/j.nima.2012.08.051
ER  - 

@article{
author = "Telečki, Igor N. and Petrović, Srđan M. and Beličev, Petar and Radenovic, B. and Balvanović, Roman V. and Bojović, Boško and Nešković, Nebojša B.",
year = "2012",
abstract = "This paper is devoted to the focusing properties of a square electrostatic rainbow lens, which is a novel ion beam optical element. We consider the transmission of parallel and non-parallel proton beams of the initial kinetic energy of 10 keV through this lens. The potential of the electrodes of the lens is chosen to be 2 kV. The electrostatic potential and components of the electric field in the region of the lens are calculated using a three-dimensional finite element computer code. We investigate the spatial and angular distributions of protons propagating through the lens and in the drift space after it. It is confirmed that the evolutions of these distributions are determined by the evolutions of the corresponding rainbow lines, generated using the theory of crystal rainbows. The beam is separated into two components. One beam component, appearing as a beam core, is generated dominantly by the focused protons. Its boundary line in the transverse position plane can be very well approximated by a hypotrochoid. The other beam component is generated dominantly by the defocused protons. We present the focusing coefficient of the lens, the confining coefficients of the lens for the focused and defocused protons, the density of the beam core, the vertical or horizontal emittance of the beam core, and the brightness of the beam core. (C) 2012 Elsevier B.V. All rights reserved.",
journal = "Nuclear Instruments and Methods in Physics Research. Section A: Accelerators, Spectrometers, Detectors, and Associated Equipment",
title = "Focusing properties of a square electrostatic rainbow lens",
volume = "694",
pages = "224-233",
doi = "10.1016/j.nima.2012.08.051"
}

Telečki, I. N., Petrović, S. M., Beličev, P., Radenovic, B., Balvanović, R. V., Bojović, B.,& Nešković, N. B.. (2012). Focusing properties of a square electrostatic rainbow lens. in Nuclear Instruments and Methods in Physics Research. Section A: Accelerators, Spectrometers, Detectors, and Associated Equipment, 694, 224-233.
https://doi.org/10.1016/j.nima.2012.08.051

Telečki IN, Petrović SM, Beličev P, Radenovic B, Balvanović RV, Bojović B, Nešković NB. Focusing properties of a square electrostatic rainbow lens. in Nuclear Instruments and Methods in Physics Research. Section A: Accelerators, Spectrometers, Detectors, and Associated Equipment. 2012;694:224-233.
doi:10.1016/j.nima.2012.08.051 .

Telečki, Igor N., Petrović, Srđan M., Beličev, Petar, Radenovic, B., Balvanović, Roman V., Bojović, Boško, Nešković, Nebojša B., "Focusing properties of a square electrostatic rainbow lens" in Nuclear Instruments and Methods in Physics Research. Section A: Accelerators, Spectrometers, Detectors, and Associated Equipment, 694 (2012):224-233,
https://doi.org/10.1016/j.nima.2012.08.051 . .

TY  - JOUR
AU  - Petrović, Srđan M.
AU  - Nešković, Nebojša B.
AU  - Berec, Vesna I.
AU  - Ćosić, Marko
PY  - 2012
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/4730
AB  - In this work we analyze the superfocusing of protons channeled in a LT 100 GT Si thin crystal using the theory of crystal rainbows. The initial proton energy is 68 MeV and the proton beam incident angle is increased gradually from zero up to 30% of the critical angle for proton channeling. The reduced crystal thickness is varied around 0.250, the corresponding crystal thickness being 481.8 nm. The spatial distributions of channeled protons, obtained by the numerical solution of the proton equations of motion in the transverse position plane and a Monte Carlo computer simulation code, are explored as functions of the beam incident angle and reduced crystal thickness. They are analyzed via the corresponding mappings of the impact parameter plane to the transverse position plane, which are characterized by the rainbow effect. The performed analysis shows that it is possible to focus the beam within the region of the radius considerably below the Bohr radius. The obtained results provide the theoretical basis for the possible development of a measurement technique with the picometer resolution-the rainbow subatomic microscopy.
T2  - Physical Review A
T1  - Superfocusing of channeled protons and subatomic measurement resolution
VL  - 85
IS  - 3
DO  - 10.1103/PhysRevA.85.032901
ER  - 

@article{
author = "Petrović, Srđan M. and Nešković, Nebojša B. and Berec, Vesna I. and Ćosić, Marko",
year = "2012",
abstract = "In this work we analyze the superfocusing of protons channeled in a LT 100 GT Si thin crystal using the theory of crystal rainbows. The initial proton energy is 68 MeV and the proton beam incident angle is increased gradually from zero up to 30% of the critical angle for proton channeling. The reduced crystal thickness is varied around 0.250, the corresponding crystal thickness being 481.8 nm. The spatial distributions of channeled protons, obtained by the numerical solution of the proton equations of motion in the transverse position plane and a Monte Carlo computer simulation code, are explored as functions of the beam incident angle and reduced crystal thickness. They are analyzed via the corresponding mappings of the impact parameter plane to the transverse position plane, which are characterized by the rainbow effect. The performed analysis shows that it is possible to focus the beam within the region of the radius considerably below the Bohr radius. The obtained results provide the theoretical basis for the possible development of a measurement technique with the picometer resolution-the rainbow subatomic microscopy.",
journal = "Physical Review A",
title = "Superfocusing of channeled protons and subatomic measurement resolution",
volume = "85",
number = "3",
doi = "10.1103/PhysRevA.85.032901"
}

Petrović, S. M., Nešković, N. B., Berec, V. I.,& Ćosić, M.. (2012). Superfocusing of channeled protons and subatomic measurement resolution. in Physical Review A, 85(3).
https://doi.org/10.1103/PhysRevA.85.032901

Petrović SM, Nešković NB, Berec VI, Ćosić M. Superfocusing of channeled protons and subatomic measurement resolution. in Physical Review A. 2012;85(3).
doi:10.1103/PhysRevA.85.032901 .

Petrović, Srđan M., Nešković, Nebojša B., Berec, Vesna I., Ćosić, Marko, "Superfocusing of channeled protons and subatomic measurement resolution" in Physical Review A, 85, no. 3 (2012),
https://doi.org/10.1103/PhysRevA.85.032901 . .

TY  - JOUR
AU  - Motapothula, Mallikarjuna Rao
AU  - Petrović, Srđan M.
AU  - Nešković, Nebojša B.
AU  - Dang, Z. Y.
AU  - Breese, Mark B.H.
AU  - Rana, Mukhtar Ahmed
AU  - Osman, A.
PY  - 2012
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/5177
AB  - Using the theory of crystal rainbows, we prove that the well-known doughnut patterns observed in ion channeling in thin crystal membranes are manifestations of the rainbow effect. This is done by a detailed morphological study of the high-resolution experimental angular distributions of 2 MeV protons channeled in a 55-nm-thick (001) silicon crystal tilted away from the [001] direction. The inner side of the doughnut is the dark side of the rainbow, analogous to the Alexanders dark band, occurring between the primary and secondary meteorological rainbows.
T2  - Physical Review B: Condensed Matter and Materials Physics
T1  - Origin of ringlike angular distributions observed in rainbow channeling in ultrathin crystals
VL  - 86
IS  - 20
DO  - 10.1103/PhysRevB.86.205426
ER  - 

@article{
author = "Motapothula, Mallikarjuna Rao and Petrović, Srđan M. and Nešković, Nebojša B. and Dang, Z. Y. and Breese, Mark B.H. and Rana, Mukhtar Ahmed and Osman, A.",
year = "2012",
abstract = "Using the theory of crystal rainbows, we prove that the well-known doughnut patterns observed in ion channeling in thin crystal membranes are manifestations of the rainbow effect. This is done by a detailed morphological study of the high-resolution experimental angular distributions of 2 MeV protons channeled in a 55-nm-thick (001) silicon crystal tilted away from the [001] direction. The inner side of the doughnut is the dark side of the rainbow, analogous to the Alexanders dark band, occurring between the primary and secondary meteorological rainbows.",
journal = "Physical Review B: Condensed Matter and Materials Physics",
title = "Origin of ringlike angular distributions observed in rainbow channeling in ultrathin crystals",
volume = "86",
number = "20",
doi = "10.1103/PhysRevB.86.205426"
}

Motapothula, M. R., Petrović, S. M., Nešković, N. B., Dang, Z. Y., Breese, M. B.H., Rana, M. A.,& Osman, A.. (2012). Origin of ringlike angular distributions observed in rainbow channeling in ultrathin crystals. in Physical Review B: Condensed Matter and Materials Physics, 86(20).
https://doi.org/10.1103/PhysRevB.86.205426

Motapothula MR, Petrović SM, Nešković NB, Dang ZY, Breese MB, Rana MA, Osman A. Origin of ringlike angular distributions observed in rainbow channeling in ultrathin crystals. in Physical Review B: Condensed Matter and Materials Physics. 2012;86(20).
doi:10.1103/PhysRevB.86.205426 .

Motapothula, Mallikarjuna Rao, Petrović, Srđan M., Nešković, Nebojša B., Dang, Z. Y., Breese, Mark B.H., Rana, Mukhtar Ahmed, Osman, A., "Origin of ringlike angular distributions observed in rainbow channeling in ultrathin crystals" in Physical Review B: Condensed Matter and Materials Physics, 86, no. 20 (2012),
https://doi.org/10.1103/PhysRevB.86.205426 . .

TY  - JOUR
AU  - Nešković, Nebojša B.
AU  - Petrović, Srđan M.
PY  - 2012
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/5236
AB  - This review paper is devoted to the crystal rainbow effect, which occurs in ion channeling in crystals and nanotubes. We begin with a description of crystal rainbows. Then, we analyze the evolution of the angular distribution of channeled ions with the crystal thickness. The analysis includes the rainbow cycles, and the effects of spatial focusing and angular focusing of channeled ions. This leads us to the theory of crystal rainbows. It is shown that it is the proper theory of ion channeling. After that, we describe how the effect of spatial focusing of channeled ions can be used for a subatomic microscopy. Further, the rainbow effect occurring with carbon nanotubes is considered. Finally, we demonstrate how an ion beam can be guided by a bent carbon nanotube.
T2  - Nanoscience and Nanotechnology Letters
T1  - Rainbows with Crystals and Nanotubes
VL  - 4
IS  - 11
SP  - 1033
EP  - 1043
DO  - 10.1166/nnl.2012.1466
ER  - 

@article{
author = "Nešković, Nebojša B. and Petrović, Srđan M.",
year = "2012",
abstract = "This review paper is devoted to the crystal rainbow effect, which occurs in ion channeling in crystals and nanotubes. We begin with a description of crystal rainbows. Then, we analyze the evolution of the angular distribution of channeled ions with the crystal thickness. The analysis includes the rainbow cycles, and the effects of spatial focusing and angular focusing of channeled ions. This leads us to the theory of crystal rainbows. It is shown that it is the proper theory of ion channeling. After that, we describe how the effect of spatial focusing of channeled ions can be used for a subatomic microscopy. Further, the rainbow effect occurring with carbon nanotubes is considered. Finally, we demonstrate how an ion beam can be guided by a bent carbon nanotube.",
journal = "Nanoscience and Nanotechnology Letters",
title = "Rainbows with Crystals and Nanotubes",
volume = "4",
number = "11",
pages = "1033-1043",
doi = "10.1166/nnl.2012.1466"
}

Nešković, N. B.,& Petrović, S. M.. (2012). Rainbows with Crystals and Nanotubes. in Nanoscience and Nanotechnology Letters, 4(11), 1033-1043.
https://doi.org/10.1166/nnl.2012.1466

Nešković NB, Petrović SM. Rainbows with Crystals and Nanotubes. in Nanoscience and Nanotechnology Letters. 2012;4(11):1033-1043.
doi:10.1166/nnl.2012.1466 .

Nešković, Nebojša B., Petrović, Srđan M., "Rainbows with Crystals and Nanotubes" in Nanoscience and Nanotechnology Letters, 4, no. 11 (2012):1033-1043,
https://doi.org/10.1166/nnl.2012.1466 . .

TY  - JOUR
AU  - Ilić, Anđelija Z.
AU  - Ristić-Đurović, Jasna L.
AU  - Cirkovic, Sasa
AU  - Nešković, Nebojša B.
PY  - 2012
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/4805
AB  - A novel method for efficient analysis of ion beam acceleration in an isochronous cyclotron is proposed. Numerical simulation is used to perform multiple beam dynamics analyses on the conveniently chosen subsets of data; consequently, the total quantity of studied data is significantly reduced. The obtained results provide direct insight into beam behavior and quality of acceleration. Therefore, the analysis is not only efficient, but detailed and systematic as well. It is used to assess the impact of the accelerated orbit optimization to the enhancement of acceleration efficiency when study is extended from a single test ion to the complete ion beam consideration.
T2  - IEEE Transactions on Nuclear Science
T1  - Enhancement of Ion Beam Acceleration Efficiency in Isochronous Cyclotrons
VL  - 59
IS  - 2
SP  - 272
EP  - 280
DO  - 10.1109/TNS.2011.2180737
ER  - 

@article{
author = "Ilić, Anđelija Z. and Ristić-Đurović, Jasna L. and Cirkovic, Sasa and Nešković, Nebojša B.",
year = "2012",
abstract = "A novel method for efficient analysis of ion beam acceleration in an isochronous cyclotron is proposed. Numerical simulation is used to perform multiple beam dynamics analyses on the conveniently chosen subsets of data; consequently, the total quantity of studied data is significantly reduced. The obtained results provide direct insight into beam behavior and quality of acceleration. Therefore, the analysis is not only efficient, but detailed and systematic as well. It is used to assess the impact of the accelerated orbit optimization to the enhancement of acceleration efficiency when study is extended from a single test ion to the complete ion beam consideration.",
journal = "IEEE Transactions on Nuclear Science",
title = "Enhancement of Ion Beam Acceleration Efficiency in Isochronous Cyclotrons",
volume = "59",
number = "2",
pages = "272-280",
doi = "10.1109/TNS.2011.2180737"
}

Ilić, A. Z., Ristić-Đurović, J. L., Cirkovic, S.,& Nešković, N. B.. (2012). Enhancement of Ion Beam Acceleration Efficiency in Isochronous Cyclotrons. in IEEE Transactions on Nuclear Science, 59(2), 272-280.
https://doi.org/10.1109/TNS.2011.2180737

Ilić AZ, Ristić-Đurović JL, Cirkovic S, Nešković NB. Enhancement of Ion Beam Acceleration Efficiency in Isochronous Cyclotrons. in IEEE Transactions on Nuclear Science. 2012;59(2):272-280.
doi:10.1109/TNS.2011.2180737 .

Ilić, Anđelija Z., Ristić-Đurović, Jasna L., Cirkovic, Sasa, Nešković, Nebojša B., "Enhancement of Ion Beam Acceleration Efficiency in Isochronous Cyclotrons" in IEEE Transactions on Nuclear Science, 59, no. 2 (2012):272-280,
https://doi.org/10.1109/TNS.2011.2180737 . .