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

We investigate the interactions of charged particles with straight and bent single-walled carbon nanotubes （SWNTs） under channeling conditions in the presence of dynamic polarization of the valence electrons in carbon, This polarization is described by a cylindrical, two-fluid hydrodynamic model with the parameters taken from the recent modelling of several independent experiments on electron energy loss spectroscopy of carbon nano-structures. We use the hydrodynamic model to calculate the image potential for protons moving through four types of SWNTs at a speed of 3 atomic units. The image potential is then combined with the Doyle-Turner atomic potential to obtain the total potential in the bent carbon nanotubes. Using that potential, we also compute the spatial and angular distributions of protons channeled through the bent carbon nanotubes, and compare the results with the distributions obtained without taking into account the image potential.