  We present a theoretical analysis of Dirac magneto-plasmons in topological
insulator nanowires. We discuss a cylindrical geometry where Berry phase
effects induce the opening of a gap at the neutrality point. By taking into
account surface electron wave functions introduced in previous papers and
within the random phase approximation, we provide an analytical form of the
dynamic structure factor. Dispersions and spectral weights of Dirac plasmons
are studied with varying the radius of the cylinder, the surface doping, and
the strength of an external magnetic field. We show that, at zero surface
doping, inter-band damped plasmon-like excitations form at the surface and
survive at low electron surface dopings ($\sim 10^{10} cm^{-2} $). Then, we
point out that the plasmon excitations are sensitive to the Berry phase gap
closure when an external magnetic field close to half quantum flux is
introduced. Indeed, a well-defined magneto-plasmon peak is observed at lower
energies upon the application of the magnetic field. Finally, the increase of
the surface doping induces a crossover from damped inter-band to sharp
intra-band magneto-plasmons which, as expected for large radii and dopings
($\sim 10^{12} cm^{-2}$), approach the proper limit of a two-dimensional
surface.
