Image potential and stopping force in the interaction of fast ions with carbon nanotubes: The extended two-fluid hydrodynamic model

We study the interaction of charged particles with a (6, 4) single-walled carbon nanotube (SWNT) under channeling conditions by means of the linearized, two dimensional (2D), two-fluid extended hydrodynamic model. We use the model to calculate analytically and numerically the image potential and the stopping force for a proton moving parallel to the axis of the SWNT, both inside and outside the nanotube at the speeds from 0.5 a.u. to 15 a.u. The effects of different angular modes on the velocity dependence of the image potential are compared for a proton moving in different types of SWNTs. We also compute the spatial and angular distributions of protons in the 2D two-fluid extended hydrodynamic model and compare them with the 2D two-fluid hydrodynamic model with zero damping.