In this paper we have investigated the nonlinear dielectric constant of a slightly ionized plasma showing the Ramseuder effect. Within the approximation of the Harp model for collisions (i.e., taking the collision frequency for electrons to be small below the speed v=vo and infinitely large above v=vo) the heating of low-speed-domain electrons by the field of an electromagnetic wave and their subsequent transfer to the high-speed domain is the source of nonlinearity. The nonlinearity is seen to be a saturating function of the intensity of the intensity of the beam. For a Gaussian beam this type of nonlinearity results in the self-made oscillatory waveguide propagation of the beam. The critical power for self-focusing is much smaler than that predicted by Stenflow and Yu. For a typical case of a plasma with ω2p/ω2?0.2, the self-focusing length of a beam of 400 W, ω∼1014 sec−1, vo=10c/w, comes out to be 0.2 cm. However, below certain critical values of the initial beam radius (vo<vo min), focusing cannot be obained regardless the power of the beam. For amplitude-modulated uniform plane waves, the nonlinearity results in the distortion of the amplitude envelope and the frequency broadening of the wave.
Using appropriate expressions for the nonlinear dielectric constant of a bounded fully ionized hot plasma, the propagation of high-power electromagnetic waves in the TE10 mode in a plasma-filled rectangular waveguide has been investigated; the nonlinearity in this collisionless plasma arises from the ponderomotive force due to the gradient of the field intensity. After integrating the wave equation once, numerical solution has been carried out. As the power of the beam increases, the plasma is depleted from the center of the waveguide and concentrates near the walls. This allows the transmission of the beam in the waveguide even when the average plasma frequency is much larger than the wave frequency. At very high powers the field around the center of the waveguide possesses a cosine variation but falls very rapidly as the wall is approached. The field patterns in this case are seen to be similar to the linear case of a waveguide, partially filled with plasma.
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