Plasma wakefields driven inside a hollow-channel plasma are significantly different from those driven in a homogeneous plasma. This work investigates the scaling laws of the accelerating and focusing fields in the "crunch-in" regime. This regime is excited due to the collapse of the electron-rings from the channel walls onto the propagation axis of the energy-source, in its wake. This regime is thus the non-linearly driven hollow channel, since the electron-ring displacement is of the order of the channel radius. We present the properties of the coherent structures in the "crunch-in" regime where the channel radius is matched to the beam properties such that channel-edge to on-axis collapse time has a direct correspondence to the energy source intensity. We also investigate the physical mechanisms that underlie the "crunch-in" wakefields by tuning the channel radius. Using a theoretical framework and results from PIC simulations the possible applications of the "crunch-in" regime for acceleration of positron beams with collider-scale parameters is presented.