Detailed derivations and further analysis are presented of a recent conceptfor a plasma-based accelerator scheme incorporating a strong circularly polarisedmagnetic wiggler field producing relativistic-strength diamagnetic transverse plasmacurrents. The increase in the plasma Lorentz factor leads to a substantial increase inthe longitudinal component of the wave electric field and therefore of theacceleration rate. It is also found that ultra-high acceleration gradients are possible with relatively low plasma densities and long wave lengths. It also appearspossible that the transverse wiggling motion of the electrons of the beam is able todelay the dephasing with the accelerating wave leading to much higher values of theenergy gained by the beam at saturation and even electron bunches that have beeninjected with the "wrong" phase seem to be able to reverse their motion and accelerateto very high energies in short distances.