Optimal positron-beam excited plasma wakefields in Hollow and Ion-Wake channels

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.