  The paper presents the results of numerical PIC-simulation of positron bunch
focusing when acceleration in a plasma dielectric wakefield accelerator. The
wakefield was excited by drive electron bunch in quartz dielectric tube,
embedded in cylindrical metal waveguide. The internal area of dielectric tube
has been filled with radially homogeneous plasma having in general case the
vacuum channel along waveguide axis. Results of numerical PIC simulation have
shown that it is possible a simultaneous acceleration and focusing of test
positron bunch in the wakefield. The dependence of transport and acceleration
of positron bunch on size of vacuum channel and waveguide length is studied.
