A Van der Pol–Mathieu equation for the dynamics of dust grain charge in dusty plasmas (original) (raw)
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Journal of Physics A-mathematical and Theoretical, 2007
The chaotic profile of dust grain dynamics associated with dust-acoustic oscillations in a dusty plasma is considered. The collective behaviour of the dust plasma component is described via a multi-fluid model, comprising Boltzmann distributed electrons and ions, as well as an equation of continuity possessing a source term for the dust grains, the dust momentum and Poisson's equations. A Van der Pol-Mathieu-type nonlinear ordinary differential equation for the dust grain density dynamics is derived. The dynamical system is cast into an autonomous form by employing an averaging method. Critical stability boundaries for a particular trivial solution of the governing equation with varying parameters are specified. The equation is analysed to determine the resonance region, and finally numerically solved by using a fourth-order Runge-Kutta method. The presence of chaotic limit cycles is pointed out.
Parametric excitation and chaos through dust-charge fluctuation in a dusty plasma
Arxiv preprint arXiv:0708.0684, 2007
We consider a van der Pol-Mathieu (vdPM) equation with parametric forcing, which arises in a simplified model of duty plasma with dust-charge fluctuation [1]. We make a detailed numerical investigation and show that the system can be driven to chaos either through a period doubling cascade or though a subcritical pitchfork bifurcation over an wide range of parameter space. We also discuss the frequency entrainment or frequency-locked phase of the dust-charge fluctuation dynamics and show that the system exhibits 2:1 parametric resonance away from the chaotic regime.
Lagrangian description of nonlinear dust-ion acoustic waves in dusty plasmas
European Physical Journal D, 2004
An analytical model is presented for the description of nonlinear dust-ion-acoustic waves propagating in an unmagnetized, collisionless, three component plasma composed of electrons, ions and inertial dust grains. The formulation relies on a Lagrangian approach of the plasma fluid model. The modulational stability of the wave amplitude is investigated. Different types of localized envelope electrostatic excitations are shown to exist.
Small-amplitude nonlinear dust acoustic wave a magnetized dusty plasma with charge fluctuation
IEEE Transactions on Plasma Science, 2001
Some properties of nonlinear dust acoustic waves in magnetized dusty plasma with variable charges by reductive perturbation technique have been studied. The effect of adiabatic dust charge variations under the assumption that the ratio of dust charging time to the dust hydrodynamical time is very small, and the nonadiabatic dust charges variations under the assumption that the same ratio is small but finite, are also incorporated. It is seen that the magnetic field and the dust charge variations significantly modify the wave amplitude. It is also seen that in case of adiabatic charge variations, the Korteweg-de Vries (KdV) equation governs the nonlinear dust acoustic wave, whereas in case of nonadiabatic dust charge variations, the wave is governed by the KdV Burger equation. Nonadiabaticity generated anomalous dissipative effect causes generation of the dust acoustic shock wave. Numerical integration of KdV Burger equation shows that the dust acoustic wave admits oscillatory (dispersion dominant) or monotone (dissipation dominant) shock solutions depending on the magnitude of the coefficient of the Burger term. Index Terms-Charge fluctuations, magnetized dusty plasma, nonlinear dust acoustic waves.
Results in Physics, 2017
The propagation of nonlinear waves in unmagnetized strongly coupled dusty plasma with Boltzmann distributed electrons, iso-nonthermal distributed ions and negatively charged dust grains is considered. The basic set of fluid equations is reduced to the Schamel Kadomtsev-Petviashvili (S-KP) equation by using the reductive perturbation method. The variational principle and conservation laws of S-KP equation are obtained. It is shown that the S-KP equation is non-integrable using Painlevé analysis. A set of new exact solutions are obtained by auto-Bäcklund transformations. The stability analysis is discussed for the existence of dust acoustic solitary waves (DASWs) and it is found that the physical parameters have strong effects on the stability criterion. In additional to, the electric field and the true Mach number of this solution are investigated. Finally, we will study the physical meanings of solutions.
Oscillations in a Dusty Plasma Medium
2002
Novel properties introduced by charged particulates in a plasma medium and how they influence excitation and propagation of waves are discussed. Such a medium, commonly known as dusty plasma, is generated in the near Earth environment by dust and other debris of meteoric origin and exhausts and effluents from space platforms. A novel feature of dusty plasma is that the charge to mass ratio can become a dynamical variable and represent an additional degree of freedom unavailable to a classical plasma. Charged dust particles in a plasma introduce unique potential structures and significantly alter the short and long range forces which can affect the short and long range ordering of the dust grains.
Dust acoustic and drift waves in a non-Maxwellian dusty plasma with dust charge fluctuation
Journal of Plasma Physics, 2015
The properties of dust acoustic and drift waves are investigated in a charge varying magnetized dusty plasma. The plasma is composed of non-thermal electrons and ions with dynamic dust particles. The mathematical expression which describes the dust charge fluctuation is obtained using${\it\kappa}$-distribution for both the electrons and ions. A dispersion relation is derived and analysed numerically by choosing space plasma parameters. It is found that the inclusion of variable dust charge along with the non-thermal effects of electrons and ions significantly affect linear/nonlinear properties of the dust acoustic and dust drift waves. The effects of different physical parameters including spectral index (${\it\kappa}$), dust charge number ($Z_{d}$), electron density ($n_{e}$) and ion temperature ($T_{i}$) on the wave dispersion and instability are presented. It is found that the presence of the non-thermal electron and ion populations reduce the growth rate of the instability which...
Journal of Theoretical and Applied Physics, 2015
The propagation of linear and nonlinear dust acoustic waves in a homogeneous unmagnetized, collisionless and dissipative dusty plasma consisted of extremely massive, micron-sized, negative dust grains has been investigated. The Boltzmann distribution is suggested for electrons whereas vortex-like distribution for ions. In the linear analysis, the dispersion relation is obtained, and the dependence of damping rate of the waves on the carrier wave number k, the dust kinematic viscosity coefficient g d and the ratio of the ions to the electrons temperatures r i is discussed. In the nonlinear analysis, the modified Korteweg-de Vries-Burgers (mKdV-Burgers) equation is derived via the reductive perturbation method. Bifurcation analysis is discussed for non-dissipative system in the absence of Burgers term. In the case of dissipative system, the tangent hyperbolic method is used to solve mKdV-Burgers equation, and yield the shock wave solution. The obtained results may be helpful in better understanding of waves propagation in the astrophysical plasmas as well as in inertial confinement fusion laboratory plasmas.