  We calculate the plasma excitations in a bundle as well as a two-dimensional
(2D) periodic array of aligned parallel multishell nanotubes on a substrate.
The carbon nanotubes are oriented perpendicular to the substrate. The model we
use for the system is an electron gas confined to the surface of an infinitely
long cylinder embedded in a background dielectric medium. Electron tunneling
between individual tubules is neglected. We include the Coulomb interaction
between electrons on the same tubule and on different tubules for the same
nanotube and neighboring nanotubes. We present a self-consistent field theory
for the dispersion equation for intrasubband and intersubband plasmon
excitations. For both the bundle and 2D array of aligned parallel nanotubes,
the dispersion relation of the collective modes is determined by a
three-dimensional wave vector with components in the direction of the nanotube
axes and in the transverse directions. The dispersion equation is solved
numerically for a singlewall nanotube 2D array as well as a bundle, and the
plasmon excitation energies are obtained as a function of wave vector. The
intertube Coulomb interaction couples plasmons with different angular momenta
in individual nanotubes, lifting the degeneracy of the single-nanotube modes.
This effect is analyzed numerically as a function of the separation between the
tubules. We show that the translational symmetry of the lattice is maintained
in the plasmon spectrum for the periodic array, and the plasmon energies have a
periodic dependence on the transverse wave vector. For the bundle, the Coulomb
interaction between nanotubes gives rise to optical plasmon excitations.
