Limitations of electron beam conditioning for free-electron lasers

The most demanding requirement for future FELs in the X-ray regime is the generation of a sufficiently small transverse electron emittance. To mitigate this problem, ideas have been proposed to ´condition´ an electron beam by increasing each particle´s energy in proportion to the square of its betatron amplitude. This conditioning enhances FEL gain by reducing the axial velocity spread within the electron bunch. We present a new conditioning scheme using solenoid magnets, which looks promising. But a strong head-tail focusing variation arises. We quantify the resulting ´projected´ (bunch-length integrated) emittance growth, relating it directly to the FEL parameters. We then present a general symplectic beam conditioner and show the unavoidable relation between conditioning and projected transverse emittance growth.