Vol. 24 No. 1 (2014)

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

Published 12-03-2014


  • Nonlinear modes,
  • KdV system,
  • Oscillatory shocks,
  • Soliton patterns

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. https://doi.org/10.15625/0868-3166/24/1/3599


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. 


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