|
Abstract
|
In this paper, we study the nonlinear harmonic generation effect in different oscillator models. For
weakly nonlinear systems, we use the generalized forced Korteweg de Vries Burgers (KdVB) and
modified KdVB (mKdVB) models in order to classify three fundamentally different harmonic
structures in a nonlinear dynamical system. The first is called the internal harmonic structure which
exists due to the self oscillation of the system in the absence of dissipation effect and is shown to
follow either relations of nf or (2n – 1)f depending on the symmetry of oscillator potential in which n
is an integer number and f is the fundamental frequency which is exactly obtained for the Helmholtz
oscillator. The second structure is the resonant harmonics which appears in the presence of damping
and follows the harmonic structure nf0 in which f0 is the linear resonance frequency. Finally, the last
harmonic structure appears in the presence of dissipation and external periodic forcing effects which
we call the external harmonic pattern. It is shown that the external harmonic pattern, in which f1 is the
driving frequency, always follows the nf1 rule regardless of the potential symmetry. We then extend
our analysis to study the harmonic generation in the fully nonlinear generalized Sagdeev potential for
real plasmas with isothermal and adiabatic ion fluids and investigate the effects of different plasma
parameters such as the fractional ion temperature and normalized ion acoustic speed on all three kinds
of harmonic generation.
|