An Attempt to Study on the Growth and Damping Rates with Approximate Solutions by Using Mathematical Models

As is already known, most of the plasma literature is occupied with the plasma instabilities and the inevitable plasma waves, which remain major obstacles to the thermonuclear fusion process. Many experimental data on the plasma waves (growth or damping) and their accompanied theoretical interpretations have been published during the last five decades; lots of them have been identified and justified as well, some not yet. One of these is our previous research on plasma waves, which originated in the early 80’s at the Plasma Physics Laboratory of the NCSR “Demokritos”. As the wave rising is defined by the growth rate (or the damping on the extinguishment), these important wavy quantities will be studied in detail in the present paper. Three examples are taken from our previous theoretical results, and the first observation reveals that the involved quantities are complicated enough to be studied by themselves. So, the use of suitable approach models, which may interpret the experimental wavy quantities, is the central idea of the present attempt. Furthermore, calculations with a little change of the initial conditions have been repeated in order to determine whether the plasma behaves as a chaotic medium.