We have developed two strong focusing field configurations that provide high midplane accessibility and therefore are compatible with presently contemplated extraction schemes for high‐current, toroidal accelerators. When these windings are attached to a modified betatron accelerator, the bandwidth of the device is slightly smaller than the bandwidth of a modified betatron with unsplit stellarator windings. However, the bandwidth of the two new configurations is more than sufficient even for modest (20–30 kA) winding currents.