Using the Fourier transform in time and space and expressing any perturbations to vary with ~[e.sup.i(kx-[omega]t) where k and [omega] are the electrostatic wave number and angular frequency in units of [[lambda].sup.-1.sub.3] and [f.sub.pe], respectively, we have the dimension-free potential perturbation as follows:
In the above, the [omega]-k relation is determined by the dispersion relation obtained from solving the electrostatic wave equations of electrons: (27)
While for the small amplitude electrostatic waves, a reductive perturbation theory (RPT) can be employed to extract the evolution equation .
Through Sections 3 and 4, RPT is appointed to deduce the evolution equations that describe electrostatic waves propagate in the system.
The topics include linear wave dynamics, natural occurrences of plasmas, electrostatic waves
in warm homogeneous and isotropic plasmas, weakly nonlinear electrostatic drift waves, and kinetic plasma sound waves.
NASA's ARTEMIS mission has now also seen both the electron beams and the ion plumes, plus newly identified electromagnetic and electrostatic waves
in the plasma ahead of the Moon, at much greater distances from the Moon.
It is well known that for not bounded plasma case the frequencies of the low frequency waves (electrostatic waves
) are proportional to the plasma density [1, 5].
During the approach to the comet, Scarf's instrument detected high-frequency electrostatic waves
of the sort familiar from spacecraft studies of planets such as Jupiter and Saturn, where bow shocks are clearly present.