Approximate models for the study of exponential changed quantities: Application on the plasma waves growth rate or damping

Abstract

Many physical phenomena that concern the research these days are basically complicated because of being multi-parametric. Thus, their study and understanding meets with big if not unsolved obstacles. Such complicated and multi-parametric is the plasmatic state as well, where the plasma and the physical quantities that appear along with it have chaotic behavior. Many of those physical quantities change exponentially and at most times they are stabilized by presenting wavy behavior. Mostly in the transitive state rather than the steady state, the exponentially changing quantities (Growth, Damping etc) depend on each other in most cases. Thus, it is difficult to distinguish the cause from the result. The present paper attempts to help this difficult study and understanding by proposing mathematical exponential models that could relate with the study and understanding of the plasmatic wavy instability behavior. Such instabilities are already detected, understood and presented in previous publications of our laboratory. In other words, our new contribution is the study of the already known plasmatic quantities by using mathematical models (modeling and simulation). These methods are both useful and applicable in the chaotic theory. In addition, our ambition is to also conduct a list of models useful for the study of chaotic problems, such as those that appear into the plasma, starting with this paper's examples. C 2014 Author(s)

Exponentially Changeable Quantities; An Attempt to Extend the Transition Time

“…However, as the transitive phenomenon of the luminescence proceeds to the saturation, the time for this completion is limited and at many times insufficient to reveal an extensive dating. Thus, the need for extension of this time led us to seek again another mathematical model, in order to interpret more correctly the exponential phenomena by extending their time [21][22][23]. Especially, a non constant coefficient of the conversion was taken along with two other constants, which can be found if experimental simulations are used.…”