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A model for the excitation of a non-linear ion-wake mode by a train of plasmaelectron oscillations in the non-linear time-asymmetric regime is developedusing analytical theory and particle-in-cell based computational solutions. Theion-wake is shown to be a driven non-linear ion-acoustic wave in the form of acylindrical ion-soliton. The near-void and radially-outwards propagatingion-wake channel of a few plasma skin-depth radius, is explored for applicationto "Crunch-in" regime of positron acceleration. The coupling from the electronwakefield mode to the ion-mode dictates the long-term evolution of the plasmaand the time for its relaxation back to an equilibrium, limiting therepetition-rate of a plasma accelerator. Using an analytical model it is shownthat it is the time asymmetric phases of the oscillating radial electric fieldsof the nearly-stationary electron bubble that excite time-averaged inertial ionmotion radially. The electron compression in the back of the bubble sucks-inthe ions whereas the space-charge within the bubble cavity expels them, drivinga cylindrical ion-soliton structure with on-axis and bubble-edgedensity-spikes. Once formed, the channel-edge density-spike is sustained overthe length of the plasma and driven radially outwards by the thermal pressureof the wake energy in electrons. Its channel-like structure is independent ofthe energy-source, electromagnetic wave or particle beam, driving the bubbleelectron wake. Particle-In-Cell simulations are used to study the ion-wakesoliton structure, its driven propagation and its use for positron accelerationin the "Crunch-in" regime.

Non-linear Ion-Wake Excitation by the Time-Asymmetric Electron Wakefields of Intense Energy Sources with applications to the Crunch-in regime