New Aspects on Stability Analysis of a Planar Charge-varying Collisional Dust Molecular Cloud with Finite Thermal Inertia
- Nonlinear modes,
- KdV system,
- Oscillatory shocks,
- Soliton patterns
How to Cite
A theoretical evolutionary model for the nonlinear stability analysis of a planar dust molecular cloud (DMC) in quasi-neutral hydrodynamic equilibrium on the Jeans scales of space and time is developed. It is based on a self-gravitating multi-fluid model consisting of the warm electrons and ions, and the inertial cold dust grains with partial ionization. The Jeans assumption of self-gravitating uniform medium is adopted for fiducially analytical simplification by neglecting the zero-order field. So, the equilibrium is justifiably treated initially as “homogeneous”, thereby validating nonlinear local analysis. The lowest-order finite inertial correction of the thermal species (thermal inertia, which is conventionally neglected), heavier grain-charge fluctuation and all the possible collisional dynamics are included simultaneously amid non-equilibrium plasma inhomogeneities. We apply a standard multiple scaling technique methodologically to show that the eigenmodes are collectively governed by a new electrostatic driven Korteweg-de Vries (d-KdV) equation having a self-consistent nonlinear driving source, and self-gravitational Korteweg-de Vries (KdV) equation with neither a source, nor a sink. A detailed numerical shape-analysis with judicious multi-parameter variation parametrically portrays the excitation of electrostatic eigenmodes evolving as damped oscillatory shocks (nonconservative) with the increasing global amplitude due to the source, and extended two-tail compressive solitons (conservative), when the source-strength becomes very weak. In contrast, the self-gravitational counterparts grow as bell-shaped rarefactive soliton-like structures (conservative). The correlative effect of diverse plasma parameters on the amplitudes and patterns is explicitly investigated. Interestingly, this is conjectured that the grain-mass plays a key role in the eigenmode shaping (growth and decay) through the interplaying processes of pulsating gravito-electrostatic coupling. As the grain-mass increases, a new type of shock-to-soliton transition results, and so forth. The significance of the study in space, laboratory and astrophysical environments is stressed.
- Khan M, Ghosh S, Sarkar S, Gupta MR. Ion acoustic shock waves in a dusty plasma. Physica Scripta 2005;T116:53.
- Mamun AA, Shukla PK. The role of dust charge fluctuations on nonlinear dust ion- acoustic waves. IEEE Trans Plasma Sci 2002;30:720.
- Shukla PK, Silin VP. Dust ion–acoustic wave. Physica Scripta 1992;45:508.
- Vranjes J, Pandey BP, Poedts S. Effect of dust charge fluctuations on current-driven dust-ion-acoustic waves. Phys Rev E 2001;64:066404.
- Burman S, Chowdhury AR. Solitary waves in self-gravitating dusty plasma. Chaos, Solitons and Fractals 2002;13:973.
- Gupta MR, Sarkar S, Ghosh S, Debnath M, Khan M. Effect of nonadiabaticity of dust charge variation on dust acoustic waves: Generation of dust acoustic shock waves. Phys Rev E 2001;63:046406.
- Zhi-Rong G, Zeng-Quiang Y, Bao-Xiang Y, Mao-Zhu S. Nonlinear acoustic waves in collisional self-gravitating dusty plasma. Chin Phys B 2010;19:115203.
- Rao NN, Shukla PK. Nonlinear dust acoustic waves with dust charge fluctuations. Planet Space Sci 1994;42:221.
- Barkan A, Marlino RL, Angelo ND. Laboratory observation of the dust-acoustic wave. Phys Plasmas 1995;2:3563.
- Marlino RL, Heinrich JR, Hyun S-H, Meyer JK. Nonlinear dust acoustic waves and shocks. Phys Plasmas 2012;19:057301.
- Nakamura Y, Bailung H, Shukla PK. Observation of ion-acoustic shocks in a dusty plasma. Phys Rev Lett 1999;83:1602.
- Pandey BP, Vranjes J, Poedts S, Shukla P K. The pulsational mode in the presence of dust charge fluctuations. Physica Scripta 2002;65:513.
- Verheest F. Waves and instabilities in dusty space plasma. Space Sci Rev 1996;77:267.
- Verheest F, Cadez VM. Static conﬁgurations of gravitating dusty plasmas. Phys Rev E 2002;66:056404.
- Dwivedi CB, Sen AK, Bujarbarua S. Pulsational mode of gravitational collapse and its impact on the star formation. Astron Astrophys 1999;345:1049.
- Karmakar PK. Nonlinear stability of pulsational mode of gravitational collapse in a self-gravitating hydrostatically bounded dust molecular cloud. Pramana- J Phys 2011;76:945.
- Karmakar PK, Borah B. New nonlinear eigenmodes of a self-gravitating spherical charged dust molecular cloud. Physica Scripta 2012;86:025503.
- Cattaert T, Verheest F. Solitary waves in self-gravitating molecular clouds. Astron Astrophys 2005;438:23.
- Klessen RS, Krumholz MR, Heitsch F. Numerical star-formation studies-A status report. Adv Sci Lett 2011;4:258.
- Avinash K, Shukla PK. A purely growing instability in a gravitating dusty plasma. Phys Lett A 1994;189:470.
- Karmakar PK, Bora B. Nonlinear pulsational eigenmodes of a planar collisional dust molecular cloud with grain-charge fluctuation. Eur Phys J D 2013;67:187.
- Karmakar PK, Bora B. Inertia-centric stability analysis of a planar uniform dust molecular cloud with weak neutral-charged dust frictional coupling. Plasma Sci Tech 2013 (accepted).
- Dwivedi CB, Prakash R. Relaxation effect of electron inertial delay in an ion-beam plasma system. J Appl Phys 2001;90:3200.
- Karmakar PK, Deka U, Dwivedi CB. Graphical analysis of electron inertia induced acoustic instability. Phys Plasmas 2005;12:032105.
- Karmakar PK, Deka U, Dwivedi CB. Response to comments on “Graphical analysis of electron inertia-induced acoustic instability”. Phys Plasmas 2006;13:104702.
- Deka U, Dwivedi CB. Effect of electron inertial delay on Debye sheath formation. Braz J Phys 2010;40:333.
- Deka U, Sarma A, Prakash R, Karmakar PK, Dwivedi CB. Electron inertial delay effect on acoustic soliton behavior transonic region. Physica Scripta 2004;69:303.
- Mahmood S, Ur-Rehman H. Formation of electrostatic solitons, monotonic, and oscillatory shocks in pair-ion plasmas. Phys Plasmas 2010;17:072305.
- Volosevich AV, Meister C-V. Nonlinear electrostatic structures in collisional dusty plasmas. Contrib Plasma Phys 2012;42:61.
- Popel SI, Losseva TV, Golub AP, Merlino RL, Andreev SN. Dust ion-acoustic shocks in a Q machine device. Contrib Plasma Phys 2005;45:461.
- Vranjes J. Gravitational instability problem of nonuniform medium. Astrophys Space Sci 1994;213:139.
- Verheest F, Shukla PK. Nonlinear waves in multispecies self-gravitating dusty plasmas. Physica Scripta 1997;55:83.
- Pakzad HR, Javidan K. Solitary waves in dusty plasmas with variable dust charge and two temperature ions. Chaos, Solitons and Fractals 2009;42:2904.