Dynamic polarization effects in ion channeling through single-wall carbon nanotubes

Ion channeling through a single-wall carbon nanotube is simulated by solving Newton’s equations for ion motion at intermediate energies, under the action of both the surface-atom repulsive forces and the polarization forces due to the dynamic perturbation of the nanotube electrons. The atomic repulsion is described by a continuum potential based on the Thomas-Fermi-Moliere model, whereas the dynamic polarization of the nanotube electrons is described by a two-dimensional hydrodynamic model, giving rise to the transverse dynamic image force and the longitudinal stopping force. In the absence of centrifugal forces, a balance between the image force and the atomic repulsion is found to give rise to ion trajectories which oscillate over peripheral radial regions in the nanotube, provided the ion impact position is not too close to the nanotube wall, the impact angle is sufficiently small, and the incident speed is not too high. Otherwise, the ion is found to oscillate between the nanotube walls, passing over a local maximum of the potential in the center of the nanotube, which results from the image interaction. The full statistical analysis of ${10}^3$ ion trajectories has been made to further demonstrate the actual effect of dynamic polarization on the ion channeling.

Figure 1

(a) Self-energy $E_s$ (in a.u.) and (b) stopping power $S$ (in a.u.) versus radial position $\rho$ (in a.u.) and speed $v$ (in a.u.) for proton moving paraxially in a single-wall nanotube with radius $a=20\mathrm{a}.\mathrm{u}.$

Figure 2

Dependence of total potential $E_s+U_n$ (in a.u.) on radial position $\rho$ (in a.u.) for proton moving paraxially in a single-wall nanotube with radius $a=20\mathrm{a}.\mathrm{u}.$, at several speeds: (a) $v=2$, 3, 4 and (b) $v=6$, 7, and 8 a.u.

Figure 3

Dependence of total radial force $F_{\rho }^{\left(p\right)}+F_{\rho }^{\left(n\right)}$ (in a.u.) on radial position $\rho$ (in a.u.) for proton moving paraxially in a single-wall nanotube with radius $a=20\mathrm{a}.\mathrm{u}.$, at several speeds (a) $v=2$, 3, 4 and (b) $v=6$, 7, and 8 a.u.

Figure 4

Proton trajectories in a single-wall carbon nanotube with radius $a=20\mathrm{a}.\mathrm{u}.$ at fixed initial radial position ${\rho }_0=8\mathrm{a}.\mathrm{u}.$ and incident angle ${\theta }_0=0$, for several incident speeds: $v_0=2$, 4, 6, and 8 a.u. The solid and the dashed lines correspond to numerical results with and without the dynamic polarization effect, respectively.

Figure 5

Proton trajectories in a single-wall carbon nanotube with radius $a=20\mathrm{a}.\mathrm{u}.$ at fixed initial speed $v_0=4\mathrm{a}.\mathrm{u}.$ and incident angle ${\theta }_0=0$, for several initial radial positions ${\rho }_0=2$, 5, 9, and 11 a.u. The solid and the dashed lines correspond to numerical results with and without the dynamic polarization effect, respectively.

Figure 6

Proton trajectories in a single-wall carbon nanotube with radius $a=20\mathrm{a}.\mathrm{u}.$ at fixed initial speed $v_0=8\mathrm{a}.\mathrm{u}.$ and incident angle ${\theta }_0=0$, for several initial radial positions ${\rho }_0=2$, 5, 9, and 11 a.u. The solid and the dashed lines correspond to numerical results with and without the dynamic polarization effect, respectively.

Figure 7

Proton trajectories in a single-wall carbon nanotube with radius $a=20\mathrm{a}.\mathrm{u}.$ at fixed initial radial position ${\rho }_0=9\mathrm{a}.\mathrm{u}.$, for several incident speeds $v_0=2$, 4, 6, and 8 a.u. Here, the solid, dashed, and dotted lines correspond to numerical results, obtained with the polarization effects included, for incident angles ${\theta }_0=0.01°$, 0.02°, and 0.03°, respectively.

Figure 8

The statistical distributions of the radial positions (a) with (b) without the dynamic polarization after the homogeneous beam traveled ${10}^5\mathrm{a}.\mathrm{u}.$ through a single-wall carbon nanotube. Here the radius $a=20\mathrm{a}.\mathrm{u}.$, the initial speed $v_0=4\mathrm{a}.\mathrm{u}.$, the initial angles ${\theta }_{i0}=0$, and the initial positions ${\rho }_{i0}$ are sampled randomly from $-15$ to 15 a.u.

Figure 9

The statistical distributions of the angles (a) with (b) without the dynamic polarization after the homogeneous beam traveled ${10}^5\mathrm{a}.\mathrm{u}.$ through a single-wall carbon nanotube. Here the input parameters are same as those used in Fig. 8.