Nonlinear Longitudinal Waves Research Articles

Nonlinear Oscillations in a Weakly Ionized Plasma

A perturbation theory is developed for a nonlinear longitudinal monochromatic wave in a weakly ionized plasma. The effect of collisions between electrons and neutrals is treated by means of a relaxation term in the Boltzmann-Vlasov equation. With the distribution function developed to all orders in the amplitude E0 of the oscillating electric field (assumed exponentially damped sinusoidal in form), a constant damping decrement λ is indicated for two cases: Either (i) λ must be negligible or (ii) the collision frequency vR of the resonance electrons must be negligible in the calculation of the distribution function of the resonance electrons in terms of the electric field. With the nonlinear correction developed to lowest order, the Landau damping decrement is reduced from its linear value γk0 by the factor 1−⅛(Ω4/vR4) for case (i), and by the factor 1−116[Ω4/(|γk0|+v̄)4] for case (ii). Here v̄ is the collision frequency appropriately averaged for direct collisional damping, Ω=(eE0k0/m)1/2 is the frequency of oscillation of the resonance electrons, k0 is the wavenumber, and e and m are the electronic charge and mass, respectively.

Acceleration of particles in a plasma

The physical principles underlying a new method of linear acceleration of particles are explained; in this method the accelerating system is a plasma waveguide or an uncompensated electron or ion beam. The propagation of electromagnetic waves in a narrow plasma waveguide is considered in the nonlinear approximation. The acceleration of particles by nonlinear longitudinal waves and in a plasma and the excitation of these waves are also considered. The adia batic invariants for wave motion in plasma particle acceleration are considered. A description is given of the results of an investigation of a method of amplifying high-frequency electromagnetic waves based on the reflection of electromagnetic waves from a moving plasma.