Transverse Gradient Undulators and FEL operating with large energy spread

Undulators exhibiting a gradient of the field in the transverse direction have been proposed to mitigate the effects of the gain dilution in Free Electron Laser devices operating with large energy spread. The actual use of the device depends on the realization of a field distribution with quasi-vanishing quadrupolar terms in the tapering directions. We analyze the effect of a Transverse Gradient Undulator on the FEL operation and critically review the possibility of an appropriate field implementation.