New Aspects on Stability Analysis of a Planar Charge-varying Collisional Dust Molecular Cloud with Finite Thermal Inertia


  • P. K. Karmakar Department of Physics, Tezpur University, Napaam, Tezpur-784028, Assam, India
  • B. Borah Department of Physics, Tezpur University, Napaam, Tezpur-784028, Assam, India



Nonlinear modes, KdV system, Oscillatory shocks, Soliton patterns


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. 


Download data is not yet available.


Metrics Loading ...

Author Biography

P. K. Karmakar, Department of Physics, Tezpur University, Napaam, Tezpur-784028, Assam, India

Associate Professor, Department of Physics



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.




How to Cite

Karmakar, P. K., & Borah, B. (2014). New Aspects on Stability Analysis of a Planar Charge-varying Collisional Dust Molecular Cloud with Finite Thermal Inertia. Communications in Physics, 24(1), 45.