A theory of self-fields in a free-electron laser with electromagnetic-wave wiggler and ion-channel guiding is presented. The equations of motion for an electron have been analyzed. This equation together with its numerical solutions shows that the first part of group I and II trajectories is unstable. The effects of self-fields on the gain for groups I and II orbits have also been investigated by deriving the gain formula and numerical calculation. A gain decrement is found due to the effects of self-fields for group I orbits, and the gain enhancement for group II orbits. The gain decrement (enhancement) arises from diamagnetic (paramagnetic) generated by the self-fields. The gain decrement (enhancement) increases by increasing the beam density.

A theoretical study of electron trajectories, harmonic generation, and gain in a free-electron laser (FEL) with a linearly polarized electromagnetic-wave wiggler is presented for axial injection of electron beam. The relativistic equation of motion for a single electron has been derived and solved numerically. It is found that the trajectories consist of two regimes. The stability of these regimes has been investigated. The results show that the trajectories are stable except for some parts of the regime one. The effects of interaction on the transverse velocity of the electron are a superposition of two oscillation terms, one at the wiggler frequency and the other at the betatron ion-channel frequency. A detailed analysis of the gain equation in the low-gain-per-pass limit has been employed to investigate FEL operation in higher harmonics generation. The possibility of wave amplification at both wiggler frequency and betatron ion-channel frequency for their odd harmonics has been illustrated.

A theory of the dispersion relation for electromagnetically pumped free-electron laser in the presence of a special tapered axial guide magnetic field is presented. An analysis of the steady-state electron trajectories is obtained by solving the equations of motion. Next an eleventh-degree polynomial equation for electromagnetic and space-charge wave is derived. Numerical solution of the polynomial equation of the dispersion relation yield the complex wave number as a function of the frequency of the waves. These results are used to illustrate the dependence of growth rate curves on the axial guide field frequency. It is found that the tapered guide field shifts electron trajectories and enhances the growth rate in the comparison of employing uniform axial magnetic field, without needing a strong guide magnetic field.

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A free-electron laser (FEL) scheme, which employs the whistler wave as a slow electromagnetic wave wiggler, was studied theoretically. Subjected to the transverse fields of whistler wave wiggler, the beam electrons are the source of the energy needed to produce electromagnetic radiation. The strength and the period of the wiggler field depend on the parameters of the magnetoplasma medium. This configuration has a higher tunability by controlling the plasma density, on top of the γ-tunability of the conventional FELs. The theory of linear gain and electron trajectories was presented and four groups (I, II, III, and IV) of electron orbits were found in the presence of an axial guide magnetic field. Using perturbation analysis, it is found that these groups of orbits were stable except small regions of group I and IV orbits. The function Φ which determines the rate of change of axial velocity with beam energy was also derived. In the case in which Φ<0 represents a negative-mass regime in which the axial velocity accelerates as the electrons lose energy. Numerical solutions showed that by increasing the cyclotron frequency, the gain for group I and III orbits increased, while a gain decrement was obtained for group II and IV orbits.

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In this article, self-focusing of an intense circularly polarized laser pulse in the presence of an external oblique magnetic field in hot magnetized plasma, using Maxwell’s equations and the relativistic fluid momentum equation, is studied. An envelope equation governing the spot size of the laser beam for both of left- and right-hand polarizations has been derived and the effects of the plasma temperature and oblique magnetic field on the electron density distribution of hot plasma with respect to variation of the normalized laser spot size has been investigated. Numerical results depict that in right-hand polarization, self-focusing of the laser pulse along the propagation direction in hot magnetized plasma becomes better and more compressed with increasing $\unicode[STIX]{x1D703}$. Inversely, in left-hand polarization, increase of $\unicode[STIX]{x1D703}$ in an oblique magnetic field leads to enhancement of the spot size and reduction self-focusing. Besides, in the plasma density profile, self-focusing of the laser pulse improves in comparison with no oblique magnetic field. Also it is shown that plasma temperature has a key role in the laser spot size, normalized laser output power and the variation of plasma density.

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