Generalization of the perturbation theory by using a repeating equation: A case that reveals the plasma chaotic state

AbstractAmong the theoretical and experimental situations of interest in plasma physics are the waves that rise into the plasma and are strongly affected from the plasma parameters. Therefore, the development of strong relations between unperturbed and perturbed quantities is proved to exist both experimentally and theoretically. In the present paper, the mathematical solution ended in a relation between drift and perturbed velocities, which presupposes the perturbed velocity value to be very small in comparison with the drift velocity. However, the experiment has shown that the presupposition of the small value of the perturbations is not satisfied in many laboratory instances; as a result the use of the perturbation theory is limited. To surpass this difficulty, the big perturbed quantity was divided into small and equal parts, and by using the equation between unperturbed and perturbed velocities as a repeating relation, the perturbed theory may be extended and generalized beyond the small disturbances. In addition, calculations with a little change in the initial conditions were carried out, to determine when the plasma obtains chaotic behavior.