Waves and instabilities play a crucial role in space and astrophysical plasmas, governing the transport of energy, momentum, and particles. They shape the dynamics of planetary magnetospheres, solar and stellar winds, accretion disks, and interstellar and intergalactic plasmas. Instabilities occur when a small perturbation in a plasma grows over time, leading to turbulence or wave amplification. Some key instabilities include: We work on the MHD waves and the following instabilities :

• Gravitational instability: A fundamental instability responsible for structure formations in the ISM in the presence of gravitational force.

• Kelvin-Helmholtz Instability: Occurs at shear flow interfaces (e.g., Earth's magnetopause), creating vortices and turbulence.

• Rayleigh-Taylor Instability: Happens when a heavier plasma layer is supported by a lighter one in the presence of a gravitational field.

• Firehose and Mirror Instability: Driven by anisotropic ion distributions in magnetized plasmas. Arises in high-beta plasmas when the pressure along magnetic field lines exceeds a critical threshold.

• Neutrino-beam driven instabilities: High energy neutrino beam propagated through supernova explosion enters into MCs which excites several interesting features of waves and instabilities.

Dusty plasma, a complex state of matter consisting of electrons, ions, neutral particles, and charged dust grains, plays a crucial role in various astrophysical, space, and laboratory environments. Research in dusty plasma physics explores fundamental phenomena such as dust charging, wave dynamics, instabilities, transport processes, and collective interactions in strongly and weakly coupled regimes. These studies have significant implications for understanding planetary ring systems, cometary tails, interstellar clouds, and the lunar surface plasma environment. Additionally, dusty plasma research contributes to advancements in plasma propulsion, semiconductor processing, and fusion energy. 

The galactic cosmic rays (CRs) are the highly energetic charged particles (E>GeV) which interact numerously with various components of the interstellar medium (ISM). CRs are one of the significant sources of charging dust grains, interstellar gas ionization and energy transfer in the ISM. They are the dominant contributors to the ionization of molecular hydrogen in diffuse interstellar clouds and ionization of molecular clouds (MCs) cores through low-energy CRs. The energy transport of the CR particles into the plasmas plays a significant role in the waves and instabilities in astrophysical plasma and affects the star formation mechanism. We study the low-frequency MHD waves and instabilities, including the transport of galactic CRs in astrophysical plasma and dusty plasma environments.

The presence of thermal pressure anisotropy deals with the excitation of magnetohydrodynamic (MHD) waves and kinetic instabilities, such as firehose instability and mirror instability in space plasmas. Recent observations of Parker Solar Probe (PSP) have confirmed that the solar wind in the inner heliosphere exhibits thermal pressure anisotropy in the plasmas. We study the MHD wave dissipation and pressure anisotropy-driven instabilities in space plasmas. Also, in space plasmas, the non-Maxwellian distributions are typically for plasmas that are not in thermal equilibrium, which can be formulated using the kappa- distribution. The so-called kappa probability distribution function incorporates the suprathermal corrections for energetic particles. We consider the role of suprathermal particles in the excitation of waves, instabilities and transport properties of plasmas in solar wind plasmas.