Positron acceleration by plasma wake fields driven by a hollow electron beam

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.