Dust Ion Acoustic Structures in Complex Lossy Plasma
Eugene V. Martysh
Taras Shevchenko National Kyiv University,
Volodimirska str.60, Kyiv-33, 01033, Ukraine
Abstract. It is known that modified Korteweg-deVries-Burgers (mKdVB) equation can be written for a nonlinear dust
ion acoustic wave (DIAW). The main reason of this modification is nonadiabatic charge variation of the dust particles. We used
for mKdVB the well-known method based on adiabatic approximation proposed by Whitham. In the case low usual dissipation
mKdVB equation may be reduced to modified KdV (mKdV). This new equation is full analogue to cylindrical KdV and has a
slow damping soliton solution. All conclusions are in a good accordance with experimental results.
Keywords: Complex plasma, dust ion acoustic wave, charge variation, weakly dissipative soliton.
PACS: 52. 27. Lw; 52. 35. Sb
A complex (dusty) plasma is the plasma containing electrons, ions, neutrals and solid or liquid
microparticles. The remarkable property of complex plasma is the particle charging process. Usually, in lab
experiments these particles are charged negatively, due to the electron ahd ion fluxes on their surface. Any
fluctuations in plasma parameters can vary these fluxes and thus cause fluctuations of microparticles charge.
Charged dust grains are often found in space and laboratory plasma. The highly charged dust particles can
signficantly affect the system since they carry a considerable percentage of the total negative charge of the
plasma. In fact, most of the plasma waves are to some degree affected by the dust. The variable dust charge also
leads to a new plasma mode, usually referred as the charge relaxation mode (CRM), involving dust-charge
fluctuations . In most early envestigations on waves in dusty plasma are almost always thermodynamically
open was sidestepped by invoking unspecified sources or sinks, whose details are nevertheless important for a
rigorous treatment of a problem.
Nonlinear coherent and dissipative structures in complex plasmas can be formed by different means. In the
absence of dissipation the balance between nonlinear and dispersion effects can result in the formation of
soliton. Investigation of the anomalous dissipation is especially interesting at the ion acoustic times, when
heavy microparticles can be treated as motionless. The charging processes at these time-scales are not in
equilibrium and role of this dissipation can be crucial. These processes make the existence of pure steady-state
nonlinear structure impossible. The theoretical study of dust-ion-acoustic (DIA) solitons in  investigates the
possibility of their existence. There has also been an experimental investigation of DIA solitons . In this paper
we present not only the model that describes nonlinear DIA perturbations but give the methods for treatment of
It is known  that set of equations for ion-acoustic waves in complex plasma with collisions microparticles
charge variations is following:
where A is amplitude of weakly damping solitary wave at initial stage τO.
It is clear that relation (14) describes a weakly damping soliton (WDS) and its amplitude varies according to
(τO/τ)2/3 law. That is, the soliton shape, amplitude and phase are varying when soliton propagates in complex
plasmas, which is confirmed by the experiments, mentioned above. In this case, however, the shape of WDS is not
deformed as it is propagates.
In summary, the evolution of solitonlike perturbation in a complex plasmas is studied by both asymptotic method
and trasformation method. This analysis shows that WDS in the complex plasmas is governed by a cylindrical KdV
equation. The reduction to the cylindrical KdV equation may be useful to understand the dynamics of WDS and will
help to get a deeper insight into the physics of WDS.
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