Decay of zero-degree focusing of channeled ions

Miletić, L.; Petrović, S.; Nešković, N.

doi:10.1016/0168-583x(95)01494-2

Cited by 25 publications

(12 citation statements)

References 7 publications

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“…Krause et al [28] and Miletic et al [30,31] investigated the periodicity of evolution of the angular distribution of channeled ions with the reduced crystal thickness, which is…”

Section: Theory Of Crystal Rainbowsmentioning

confidence: 99%

“…For A = n/2, with η = 1,2, ..., a large part of the ion beam is parallel to the channel axis, i.e., it is focused around the origin in the transmission angle plane. This is an effect of angular focusing, which is called the effect of zerodegree focusing of channeled ions [30,31]. In order to describe ion channeling in axial channels of crystals that are not necessarily very thin, Petrovic et al [27] generalized the model of Neskovic [26] and formulated the theory of crystal rainbows.…”

Section: Theory Of Crystal Rainbowsmentioning

confidence: 99%

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Rainbows in Channeling of 1 GeV Protons in a Bent Very Short (11,9) Single-wall Carbon Nanotube

Nešković¹,

Borka²,

Šopić³

et al. 2010

International Journal of Nonlinear Sciences and Numerical Simulation

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In this work we investigate theoretically the spatial and angular distributions of protons channeled in a bent very short (11,9) single-wall carbon nanotube. The initial proton kinetic energy is 1 GeV and the nanotube length 7 μηι. The nanotube bending angle is varied between 0 and 2 mrad. The calculations are performed employing the theory of crystal rainbows. The interaction of the proton and a nanotube's atom is described by the Moliere's approximation of the Thomas-Fermi interaction potential. The spatial and angular distributions of transmitted protons are generated by the computer simulation method using the numerical solution of the proton equations of motion in the transverse position plane. They are explained by the rainbow patterns in the final transverse position and transmission angle planes, being the images of the spatial and angular rainbow patterns in the impact parameter plane, respectively. These patterns are also obtained numerically. We discuss the possibility of applying bent carbon nanotubes for guiding ion beams in accelerators.

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“…Krause et al [28] and Miletic et al [30,31] investigated the periodicity of evolution of the angular distribution of channeled ions with the reduced crystal thickness, which is…”

Section: Theory Of Crystal Rainbowsmentioning

confidence: 99%

Section: Theory Of Crystal Rainbowsmentioning

confidence: 99%

Rainbows in Channeling of 1 GeV Protons in a Bent Very Short (11,9) Single-wall Carbon Nanotube

Nešković¹,

Borka²,

Šopić³

et al. 2010

International Journal of Nonlinear Sciences and Numerical Simulation

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“…The angular distribution of the transmitted ions is generated by the computer simulation method. 2,3,[14][15][16][17] The transverse components of the initial ion position, i.e., the components of its impact parameter, are chosen randomly or uniformly within the region of the channel.…”

Section: Theorymentioning

confidence: 99%

“…4,14 Also, it has been demonstrated that the evolution of the angular distribution with the reduced crystal thickness has a periodic behavior. 4,[15][16][17] The values of variable ⌳ equal to 0.0, 0.5, 1.0, . .…”

Section: Introductionmentioning

confidence: 99%

Theory of rainbows in thin crystals: The explanation of ion channeling applied toNe10+ions transmitted through a 〈100〉 Si thin crystal

2000

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The theory of crystal rainbows is presented. It enables the generation and full explanation of the angular distribution of ions transmitted through thin crystals. The angular distribution of the transmitted ions is generated by the computer simulation method. Then, the rainbow lines in the scattering angle plane are determined. These lines ensure the full explanation of the angular distribution. The theory is applied to the transmission of Ne 10ϩ ions through a ͗100͘ Si thin crystal. The ion energy is 60 MeV and the crystal thickness is varied from 105 to 632 atomic layers, i.e., from the beginning of the first rainbow cycle to the beginning of the second rainbow cycle.

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“…Since the effect was qualitatively different from the flux peaking effect after establishing the statistical equilibrium, they named it differently-the superfocusing effect in ion channeling. Following the theoretical studies of Miletić et al [20,21], those authors analyzed the spatial focusing of protons of the initial energy of 1 MeV in the 100 channel of a Si thin crystal assuming that the continuum proton-crystal interaction potential was dominantly cylindrically symmetric and harmonic. The superfocusing effect was also considered by us [22].…”

Section: Introductionmentioning

confidence: 99%

Superfocusing of channeled protons and subatomic measurement resolution

et al. 2012

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In this work we analyze the superfocusing of protons channeled in a 100 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.

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Decay of zero-degree focusing of channeled ions

Cited by 25 publications

References 7 publications

Rainbows in Channeling of 1 GeV Protons in a Bent Very Short (11,9) Single-wall Carbon Nanotube

Rainbows in Channeling of 1 GeV Protons in a Bent Very Short (11,9) Single-wall Carbon Nanotube

Theory of rainbows in thin crystals: The explanation of ion channeling applied toNe10+ions transmitted through a 〈100〉 Si thin crystal

Superfocusing of channeled protons and subatomic measurement resolution

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