  A positron-beam interacting with the plasma electrons drives radial suck-in,
in contrast to an electron-beam driven blow-out in the over-dense regime,
$n_b>n_0$. In a homogeneous plasma, the electrons are radially sucked-in from
all the different radii. The electrons collapsing from different radii do not
simultaneously compress on-axis driving weak fields. A hollow-channel allows
electrons from its channel-radius to collapse simultaneously exciting coherent
fields. We analyze the optimal channel radius. Additionally, the low ion
density in the hollow allows a larger region with focusing phase which we show
is linearly focusing. We have shown the formation of an ion-wake channel behind
a blow-out electron bubble-wake. Here we explore positron acceleration in the
over-dense regime comparing an optimal hollow-plasma channel to the ion-wake
channel. The condition for optimal hollow-channel radius is also compared. We
also address the effects of a non-ideal ion-wake channel on positron-beam
excited fields.
