An Integral Formulation for the Electrodynamics of Metallic Carbon Nanotubes Based on a Fluid Model

An integral formulation to model, in the frequency domain, the electromagnetic response of three-dimensional (3-D) structures formed by metallic carbon nanotubes and conductors, within the framework of the classical electrodynamics, is described. The conduction electrons of the metallic nanotube are modeled as an infinitesimally thin cylindrical layer of compressible fluid, whose dynamics are described by means of the linearized hydrodynamic equations. The resulting integral equations are solved numerically by the finite element method using the facet elements and the null-pinv decomposition. The proposed formulation is applied to study carbon nanotube interconnects and dipole antennas and some related results are outlined. The solutions highlight the high-frequency effects due to the electron inertia and the fluid pressure. In particular, since the kinetic inductance matrix dominates over the magnetic one, proximity effects are negligible.