  A scheme of wake field generation for positron acceleration using hollow or
donut shaped electron driver beams is studied. An annular shaped, electron free
region forms around a hollow driver beam creating a favorable region
(longitudinal field is accelerating and transverse field is focusing and
radially linear) for positron acceleration. Accelerating gradients of the order
of 10 GV/m are produced by a hollow electron beam driver with FACET like
parameters. The peak accelerating field increases linearly with the total
charge in the beam driver while the axial size of the favorable region ($\sim$
one plasma wavelength) remains approximately fixed. The radial size drops with
the total charge but remains large enough for the placement of a witness
positron beam. We simulate an efficient acceleration of a 23 GeV positron beam
to 35.4 GeV with a maximum energy spread of 0.4\% and very small emittance over
a plasma length of 140 cm.
