A theory of wiggler pumped ion-channel free-electron laser (WPIC-FEL) and an axial magnetic field is presented. The motion of a relativistic electron is analyzed in the field configuration consisting of a helical wiggler magnetic field, a uniform axial magnetic field, and an electrostatic electric field produced by an ion-channel. An equation for the function Φ, which determines the rate of change of axial velocity with energy, is derived. Numerical calculations are made to illustrate the effects of two electron beam guiding devices on the trajectories. By means of linear fluid theory, the sixth-degree polynomial dispersion equation for electromagnetic and space-charge waves is derived. The dependence of growth rate-frequency curves on the ion-channel frequency and axial magnetic field is studied numerically.

The existence of Weibel instability for a streaming electron, counterstreaming electron-electron (e-e), and electron-positron (e-p) plasmas with intrinsic temperature anisotropy is investigated. The temperature anisotropy is included in the directions perpendicular and parallel to the streaming direction. It is shown that the beam mean speed changes the instability mode, for a streaming electron beam, from the classic Weibel to the Weibel-like mode. The analytical and numerical solutions approved that Weibel-like modes are excited for both counterstreaming e-e and e-p plasmas. The growth rates of the instabilities in e-e and e-p plasmas are compared. The growth rate is larger for e-p plasmas if the thermal anisotropy is small and the opposite is true for large thermal anisotropies. The analytical and numerical solutions are in good agreement only in the small parallel temperature and wave number limits, when the instability growth rate increases linearly with normalized wave number kc∕ωp.

Counterstreaming beams of charged particles are frequently observed in the laboratory and space plasma systems, and they are responsible for supplying the free energy of the system in the absence of temperature anisotropies. Such systems are unstable and give rise to excitation of various electrostatic and electromagnetic plasma waves. This work is intended as a supplement to the previous investigations of the Maxwell-Jüttner distributed counterstreaming plasmas on the basis of the covariant (fully relativistic) formulation. Here, we aim to find analytical solutions of the dispersion relations and investigate the properties of the growth rate for the electrostatic and electromagnetic modes propagating parallel to the background magnetic field. The influences of the important parameters of the beam, namely, velocity, temperature, the relative intensity of the two streams, and the strength of the stationary magnetic field, on the growth rates of the longitudinal and transverse modes are compared. The analytical evaluation of the parallel modes reveals several interesting results. First, for all investigated modes, the growth rate is minimum only if the particle distribution function is exactly symmetric. Second, the behavior of the electrostatic and electromagnetic instabilities by varying the beam temperature is totally opposite. Third, increasing the drift velocity, the growth rate exhibits a maximum at a certain velocity; however, beyond that, wave damping occurs. Finally, under the same conditions, the external magnetic field has a destabilizing (stabilizing) effect on the left (right)-hand branch of the transverse modes.

No abstract