EFFECT OF SPACE-CHARGE ON FREE-ELECTRON-LASER GAIN

The first-order correction due to space-charge effects to the small-signal gain of a free-electron laser is calculated classically. For a current density of 102 A/cm2, an interaction length of 1 m and an electron beam energy of 20 MeV, the maximum small-signal gain is reduced by about 0.5% while for 103 Amp/cm2, it is reduced by about 5%. The reduction is proportional to (ωpLc)2γ03aS, where ωp is the electron plasma frequency, L is the interaction length, c is the velocity of light, and mc2γ0 is the initial electron energy. S=0.092 in the former case and 0.92 in the latter. © 1978 The American Physical Society.