Plasmonic Excitations in Carbon Nanotubes: PIC simulations vs Hydrodynamic Model

Abstract

Charged particles traveling along a carbon nanotube (CNT) may produce the collective oscillation of the free electrons within the cylindrical graphene shell that makes up the nanotube wall. The associated electromagnetic modes (called plasmonic modes) are a potential candidate to achieve ultra-high accelerating gradients for particle acceleration. The plasmonic excitations can be studied by particle simulations and with analytical models. In this chapter, we firstly review different works that employ particle-in-cell (PIC) codes to simulate plasmonic excitations in carbon nanostructures. Then, the linearized hydrodynamic model is presented to analytically describe the plasmonic modes excited by a localized point-like charge propagating along a single-walled nanotube. In this model, the free electron gas at the nanotube wall is treated as a plasma, which satisfies the linearized continuity and momentum equations with specific solid-state properties. Finally, we compare the plasmonic excitations obtained using the hydrodynamic model with those from Fourier-Bessel PIC (FBPIC) simulations. A comprehensive analysis is conducted to examine similarities, differences, and limitations of both methods. This research offers an insightful viewpoint on the potential use of CNTs to enhance particle acceleration techniques, paving the way for future progress in high-energy physics and related fields.