The excitation of a non-linear ion-wake by a train of ultra-relativistic
electron bubble wake [1]-[8] is modeled. The ion-wake is shown to be a driven
non-linear ion-acoustic wave in the form of a cylindrical ion-soliton
[11]-[14]. The phases of the oscillating radial electric fields of the
slowly-propagating [21] electron bubble is asymmetric in time and excites
time-averaged inertial ion motion radially. The electron compression in the
back of the bubble sucks-in the ions and the space-charge within the bubble
cavity expels them, driving a cylindrical ion-soliton structure with on-axis
and bubble-edge density-spikes [5][6]. Once formed, the channel-edge
density-spike is driven radially outwards by the thermal pressure of the wake
energy [12]. Its channel-like structure due to the flat-residue left behind by
the propagating ion-soliton, is independent of the energy-source driving the
bubble [3][4] electron wake. We explore the use of the partially- filled
channel formed by the cylindrical ion-soliton for a novel regime of positron
acceleration [18]. OSIRIS PIC [25] simulations are used to study the ion-wake
soliton structure, its driven propagation and its use for positron
acceleration.