Free-electron laser (FEL) theory and experiments are reviewed. The physical mechanism responsible for the generation of coherent radiation in the FEL is described and the fundamental role of the ponderomotive wave in bunching and trapping the beam is emphasized. The relationship of the FEL interaction to the beam–plasma interaction is pointed out. Various FEL operating regimes are discussed. These include the high-gain Compton and Raman regimes, both with and without an axial guiding magnetic field. The linear and nonlinear regimes are examined in detail, with particular emphasis on techniques for achieving efficiency enhancement. The quality of the electron beam used to drive FEL’s is a critical factor in determining their gain and efficiency. The subject of electron beam quality, for different accelerators, is discussed. Key proof-of-principle experiments for FELs in an axial guiding magnetic field, as well as those driven by induction linacs, rf linacs, electrostatic accelerators, and storage rings, are reviewed. Finally, the requirements on wigglers and resonators are discussed.

The nonlinear evolution of the instability resulting from a gentle bump on the tail of the electron velocity distribution of a plasma was investigated experimentally. An electron beam with a large velocity spread was injected along the axis of a collisionless plasma column immersed in a strong magnetic field. The equilibrium wave amplitude, spectral shape, and electron velocity distribution were measured and found to be in good agreement with the predictions of quasilinear theory, providing the beam met the requirements of the theory. When the beam was too strong to be a gentle bump, deviations from quasilinear theory appeared.

By adding an I =2 stellarator field to a betatron accelerator, a new configuration is obtained which is capable of accelerating multikiloamp beams and which will tolerate a large (more than 50%) mismatch between the particle energy and the vertical magnetic field. The additional field is a twisted quadrupole which acts as a strong-focusing system. This device has been analyzed both analytically and numerically.

A free-electron laser operating in the gain-focusing regime is discussed. The variation of growth rate, radius of curvature of wave fronts, filling factor, and efficiency with emittance and energy spread is derived. The results, which are based on the Vlasov-Maxwell system of equations, are obtained by minimizing a variational functional. When plotted as a function of emittance, the efficiency at maximum growth rate peaks at a nonzero value of emittance. For small values of energy spread, the efficiency at maximum growth rate increases with energy spread, in contrast to intuitive expectations. PACS numbers: 41.60.Cr We present the results of an analytical study of the effect of emittance and energy spread [1-15] on a freeelectron laser (FEL) in the gain-focusing regime [16-19] of operation. Based on the Vlasov-Maxwell equations a differential eigenvalue equation for the wave number k of the radiation is derived and solved by a variational technique. We make use of the scaled parameters of Refs. [11,15]. However, in contrast to Refs. [11,15], our trial function depends on a variational parameter. This parameter furnishes additional information about the radiation field; namely, the spot size and the radius of curvature of radiation wave fronts [18,19]. The stationarity condition imposed on the variational functional implies that our results are insensitive to the choice of the trial function [20]. The variation of growth rate, radius of curvature of wave fronts, filling factor, and efficiency with emittance and energy spread is displayed graphically.The model consists of a matched electron beam and a matched radiation beam propagating along the z axis through a planar wiggler. The wiggler vector potential is given by A* =A W cosh(k w y)sin(k w z)e x , where A w is the amplitude, 2n/k w is the period, and c x is the unit vector along the x axis. The vector potential of the optical beam is given by A, = j A s (y)exp[i(kz -a)t)]e x +c.c, where (o is the angular frequency andA s is the amplitude. The equations of motion of an electron are derived from the Hamiltonian function -p z (y,p y U, ~~E,z) [21]: E P== -c m 2 c y IE l+^^ + ^[l+(*"^ m 2 c 2 where E = ymc 2 is the energy of an electron of rest mass m and charge -|e|, / is the time, (P x ,p y ) are the momenta conjugate to the coordinates (*,>>), a w^S Bt \e\A w^/ mc 2 , /fi = /o(^)-^i(^) is the usual difference of Bessel functions, and £-W/2)7(l +a M V2). In the absence of the optical field electrons perform betatron oscillations in the y-p y plane. The area in this plane is the action /=/fdydp y /2x m *H/kfr where H =cp 2 /2E + Ek}y 2 l2c is the Hamiltonian for the transverse motion and kp-a w k w /J2y is the betatron wave number. The electron distribution function evolves according to the Vlasov equation. For the equilibrium distribution we choose exp[-(r-ro) 2 /q?] e/w ^exp(-J2I/a w k w mc