  The paper presents the results of numerical PIC-simulation of accelerated and
drive bunches dynamics in a dielectric waveguide filled with radially
inhomogeneous plasma. The wakefield was excited by the electron bunch in a
quartz (permittivity 3.75) dielectric tube with outer and inner diameters of
1.2 mm and 1.0 mm, respectively, which was nested into a cylindrical metallic
waveguide. The drive bunch characteristics were chosen to be: 5 GeV for
electron energy, 3 nC for the charge, 0.2 mm - the bunch length, 0.9 mm - the
bunch diameter. The accelerated bunch had the same parameters, except for the
charge, which was equal to 0.3 nC. The interior of the waveguide was filled
with plasma having different transverse density profiles, viz., the density
profile formed in the capillary discharge, and the radially nonuniform density
profile with the vacuum channel along the waveguide axis. For all the cases
under study the plasma density was low, so that the plasma frequency was lower
than the fundamental dielectric mode frequency. The obtained PIC-simulation
data have shown that the vacuum channel in the inhomogeneous plasma cylinder
improves the accelerated bunch focusing. There is the optimum vacuum-channel
size value, at which the focusing turns out to be the strongest. The
improvement in the accelerated bunch focusing is accompanied by the decrease in
the accelerating gradient as compared with the full plasma filling of the drift
channel. The best acceleration takes place in the absence of plasma; however in
that case the test bunch focusing does not occur.
