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The poloidal field and ohmic heating coils for the Next European Torus Tokamak are envisioned for operation at magnetic fields as high as 10-14 T. To increase the maximum flux sweep, present designs either use niobium tin for the superconducting coils or inset a copper coil cooled by liquid nitrogen in the NbTi coil or even both. Based on experience with the TORE SUPRA, the authors argue that cooling NbTi to a lower temperature is a highly competitive and safe alternative. Two solutions are investigated: the first uses a 40-kA cable wound in double pancakes. The second makes use of several conductors layer-wound with current supplied in parallel. The novel aspect of both solutions is that He II circulates inside the conductor itself, introducing the advantages of a force-flow-cooled conductor at the cost of the implementation of a circulating device.