Limitations of electron beam conditioning for free-electron lasers

Several ideas have been proposed to "condition" an electron beam prior to the undulator of a free-electron laser (FEL) by increasing each particle's energy in proportion to the square of its transverse betatron amplitude. This conditioning enhances FEL gain by reducing the axial velocity spread within the electron bunch. We demonstrate that for symplectic beam lines, and independent of the method, this conditioning is always accompanied by a large head-tail focusing variation which, for short-wavelength FELs, is so severe as to make conditioning completely impractical. We furthermore find that any system added to correct the head-tail focusing variation will also remove the conditioning. As an example, a new method for conditioning is presented and shown to generate exactly the same head-tail focusing problems as in previously published work.