  The interactions of charged particles moving paraxially in multi-walled
carbon nanotubes (MWCNTs) may excite electromagnetic modes. This wake effect
has recently been proposed as a potential novel method of short-wavelength
high-gradient particle acceleration. In this work, the excitation of wakefields
in double-walled carbon nanotubes (DWCNTs) is studied by means of the
linearized hydrodynamic theory. General expressions have been derived for the
excited longitudinal and transverse wakefields and related to the resonant
wavenumbers which can be obtained from the dispersion relation. In the absence
of friction, the stopping power of the wakefield driver, modelled here as a
charged macroparticle, can be written solely as a function of these resonant
wavenumbers. The dependencies of the wakefields on the radii of the DWCNT and
the driving velocity have been studied. DWCNTs with inter-wall distances much
smaller than the internal radius may be a potential option to obtain higher
wakefields for particle acceleration compared to single-walled carbon nanotubes
(SWCNTs).
