Magnetic Vortex Acceleration (MVA) from near critical density targets is one of the promising schemes of laser-driven ion acceleration. 3D particle-in-cell simulations are used to explore a more extensive laser-target parameter space than previously reported in the literature as well as to study the laser pulse coupling to the target, the structure of the fields, and the properties of the accelerated ion beam in the MVA scheme. The efficiency of acceleration depends on the coupling of the laser energy to the self-generated channel in the target. The accelerated proton beams demonstrate a high level of collimation with achromatic angular divergence, and carry a significant amount of charge. For petawatt-class lasers, this acceleration regime provides a favorable scaling of the maximum ion energy with the laser power for the optimized interaction parameters. The megatesla-level magnetic fields generated by the laser-driven coaxial plasma structure in the target are a prerequisite for accelerating protons to the energy of several hundred mega-electron-volts.