The nonlinear properties of small amplitude electron-acoustic (EA) solitary and shock waves in a homogeneous system of unmagnetized collisionless plasma with nonextensive distribution for hot electrons have been investigated. A reductive perturbation method used to obtain the Kadomstev–Petviashvili-Burgers equation. Bifurcation analysis has been discussed for non-dissipative system in the absence of Burgers term and reveals different classes of the traveling wave solutions. The obtained solutions are related to periodic and soliton waves and their behavior are shown graphically. In the presence of the Burgers term, the EXP-function method is used to solve the Kadomstev–Petviashvili-Burgers equation and the obtained solution is related to shock wave. The obtained results may be helpful in better conception of waves propagation in various space plasma environments as well as in inertial confinement fusion laboratory plasmas.
The influence of the magnetic field of the Earth's magnetotail on dusty plasmas above the sunlit surface of the Moon is studied. For this purpose, a physical-mathematical model for a self-consistent description of dust grains and photoelectrons in the presence of the magnetic field is developed. Trajectories of motion of dust grains above the lunar surface are considered. It is shown that a distinguishing feature of the trajectory of a dust grain motion is the presence of oscillations. The process of damping of these oscillations is demonstrated to be related to variations of dust grain charges that is consistent with the concept of anomalous dissipation in dusty plasmas. We clarify whether dust grains in dusty plasmas above the sunlit lunar surface are “levitated” or “lofted.” The processes of dust grain charge variations are too fast in comparison with the day duration of the Moon. In this connection, for the majority of dust grains above the sunlit lunar surface, the oscillations are damped, and these grains can be considered as levitated. Only very fine grains do not go into “levitating” grain mode during the entire day on the Moon and can be treated as lofted those. A theory of dusty plasmas above the sunlit surface of the Moon, which takes into account the lunar gravity and the electrostatic processes but does not take into account the magnetic fields, explains the existence of dusty plasmas only for rather high lunar latitudes. The magnetic fields of the Earth's magnetotail are shown to provide a possibility of dust transport above the lunar surface, which can result in the existence of positively charged dust and correspondingly dusty plasmas at the sunlit side of the Moon for the whole range of the lunar latitudes.
The nonlinear properties of small amplitude electron-acoustic ( EA) solitary and shock waves in a homogeneous system of unmagnetized collisionless plasma consisted of a cold electron fluid and superthermal hot electrons obeying superthermal distribution, and stationary ions have been investigated. A reductive perturbation method was employed to obtain the Kadomstev-Petviashvili-Burgers (KP-Brugers) equation. Some solutions of physical interest are obtained. These solutions are related to soliton, monotonic and oscillatory shock waves and their behaviour are shown graphically. The formation of these solutions depends crucially on the value of the Burgers term and the plasma parameters as well. By using the tangent hyperbolic (tanh) method, another interesting type of solution which is a combination between shock and soliton waves is obtained . The topology of phase portrait and potential diagram of the KP-Brugers equation is investigated.The advantage of using this method is that one can predict different classes of the travelling wave solutions according to different phase orbits. The obtained results may be helpful in better understanding of waves propagation in various space plasma environments as well as in inertial confinement fusion laboratory plasmas.
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