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

Abstract

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.

Channeling of fast ions through the bent carbon nanotubes: The extended two-fluid hydrodynamic model

“…This means that the new reference frame rotates in the yz plane along the circle of radius R b = L/α that is the radius of curvature of the nanotube. [23,24] This is a non-inertial reference frame in which one need to treat the nanotube as if it were straight and use the effective proton-nanotube interaction potential…”

“…As a consequance of the rotation of the moving frame, a centrifugal force arises that affects the particle energy, which may be described through the effective potential (5) in the direction of the bending radius. [23,24] The dynamic polarization of the nanotube by the proton is treated using the 2D extended two-fluid [25,27] hydrodynamic model of the carbon valence electrons, which is based on a jellium-like description of the nanotube ion cores. Therefore, our model for the attractive image potential given by Eq.…”

“…There are some studies of channeling through the bent carbon nanotubes, but without taking into account the image force. [22][23][24] So, it is important to study the influence of dynamic polarization of carbon nanotubes when the nanotubes are curved. Therefore, in this paper, we extend our investigation of the spatial and angular distributions of the channeled ions [19][20][21] to the cases in which the carbon nanotubes are not straight.…”

Focusing properties of a square electrostatic rainbow lens

“…As in our previous study [1], we are going to apply to the problem in question the theory of crystal rainbows [4][5][6][7][8]. It is assumed that the proton propagation angle inside the lens and in the drift space after it remains small.…”