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The use of a transverse gradient undulator (TGU) is viewed as an attractive option for free-electron lasers (FELs) driven by beams with a large energy spread. By suitably dispersing the electron beam and tilting the undulator poles, the energy spread effect can be substantially mitigated. However, adding the dispersion typically leads to electron beams with large aspect ratios. As a result, the presence of higher-order modes in the FEL radiation can become significant. To investigate this effect, we study the eigenmode properties of a TGU-based, high-gain FEL, using both an analytically-solvable model and a variational technique. Our analysis, which includes the fundamental and the higher-order FEL eigenmodes, can provide an estimate of the mode content for the output radiation. This formalism also enables us to study the trade-off between FEL gain and transverse coherence. Numerical results are presented for a representative soft X-ray, TGU FEL example

Eigenmode analysis of a high-gain free-electron laser based on a transverse gradient undulator