The excitation of travelling nonlinear Langmuir waves in a plasma by a relativistic electron bunch is considered. The nonlinear excitation is described as relativistic oscillations of the momentum of plasma electrons in effective potentials produced by the bunch and by the perturbation of the electron density of the plasma. The condition for the optimal excitation of the wave yields a relation between the density of the plasma, the density of the bunch and the length of the bunch. Numerical results support the theoretical analysis and demonstrate a deep nonlinear modulation of the electron plasma density and excitation of a large-amplitude longitudinal field at realistic plasma and electron pulse parameters. The back action of the wave field on the bunch is considered. It is shown that sharp peaks develop in its density distribution.

Concepts of compact free-electron lasers that are based on beam-plasma interactions and that operate in the vacuum ultraviolet and X-ray wavelength ranges are discussed. Coherent radiation can not only be produced by periodic transverse motions of an electron beam, but also by its longitudinal motions. In this latter case, coherent transition radiation is generated when an electron beam passes through a structure with a deep periodic modulation of the plasma electron density. A number of structures are considered as short-wavelength radiators: standing Langmuir solitons or collapsing caverns, fast nonlinear longitudinal plasma waves, artificial periodical structures that can be converted into the plasma state by a powerful current generator or by a laser pulse, and periodic z-pinches produced by a thin wire.

A method of reducing the energy spread of an electron beam in a free-electron laser is suggested. The electron beam compression is based on a nonlinear mechanism of electron interactions with a ponderomotive wave in the presence of a constant and uniform magnetic field perpendicular to the electron motion. Due to this interaction the electrons slightly increase their energies; electrons with less initial energy are subject to a higher acceleration. As a result, the initial energy spread can be reduced several times.

A new construction of a free-electron laser using induced betatron oscillations to increase the FEL gain or efficiency is proposed. Induced betatron oscillations are driven by an additional space-periodic magnetic field with a period close to that of electron betatron oscillations in an undulator magnetic field. The induced oscillation amplitude proves to be sensitive to electron energy variation. In the result one more mechanism causing electron grouping in a ponderomotive wave takes place. This mechanism can cause the increase of the gain in a small-signal regime or the realization of an amplification regime close to an autoresonance when FEL efficiency grows essentially.

A theoretical interpretation is given of the effects in a free-electron laser with a longitudinal magnetic field oriented the opposite to the electron beam.

A new variant is proposed of a free-electron laser in which induced betatron oscillations of the particles are used to increase the gain or efficiency. These induced oscillations are created by an additional spatially periodic magnetic field and the period is close to that of betatron electron oscillations in the magnetic field of an undulator. The amplitude of induced oscillations is sensitive to changes in the electron energy. This gives rise to an additional electron bunching in the field of a ponderomotive force, which may increase the small-signal gain or ensure amplification conditions close to a self-resonance, which increases significantly the efficiency of a free-electron laser.

Free electron lasers with transverse synchronizing magnetic fields are considered. A constant transverse magnetic field or one with a constant longitudinal gradient makes it possible to maintain the resonance longitudinal velocity of an electron while changing its transverse velocity. The process of wave amplification in a FEL with a synchronizing magnetic field is investigated analytically and numerically. Two possible amplification regimes are considered: electron capture by the ponderomotive wave and reflection of particles by the ponderomotive potential. An expression for the gain in the small-signal regime is obtained. Comparison with other schemes of synchronized FELS is made. The self-consistent equations describing wave amplification are solved. An analysis is made of the possibility to enhance the efficiency of a FEL with a longitudinal magnetic field by a reduction of the nonisochronism parameter of the electron oscillations in a wave field.

Analyzed are the differences and similarities between three types of radiation by relativistic electrons, which are most suitable for generation of induced radiation: coherent bremsstrahlung, resonant transition radiation and Cherenkov radiation. The advantages of Cherenkov schemes and schemes with a modulated electron density in natural periodic structures (crystals) in comparison with undulator ones in the regions of the ultraviolet and the X-ray spectrum are shown.

We consider one of the FEL schemes in which the phase velocity of the electromagnetic wave (or the ponderomotive wave) is constant, but the longitudinal electron velocity is changed due to an external magnetic field. There is also an additional magnetic field which turns the electrons back before the interaction. It is shown that the efficiency of utilizing hot electron beams of large current density may be high enough in such systems with a refractive and an undulator medium.

Excitation of surface waves by a sequence of electron bunches moving above a metal surface, semiconductor or plasma, is considered. It is shown that a wake wave propagating above a surface can accelerate electrons effectively. In this case the accelerated bunch moves in vacuum.