Academic Journal of Applied Mathematical Sciences ISSN(e): 2415-2188, ISSN(p): 2415-5225 Vol. 6, Issue. 5, pp: 53-57, 2020 URL: https://arpgweb.com/journal/journal/17 DOI: https://doi.org/10.32861/ajams.65.53.57 Academic Research Publishing Group 53 Original Research Open Access Hydromagnetic Stability Analysis of a Partially Ionized Medium Pardeep Kumar (Corresponding Author) Department of Mathematics, ICDEOL, Himachal Pradesh University, Summerhill, Shimla-171005, India Email: pkdureja@gmail.com Hari Mohan Department of Mathematics, ICDEOL, Himachal Pradesh University, Summerhill, Shimla-171005, India Article History Received: April 16, 2020 Revised: May 20, 2020 Accepted: May 26, 2020 Published: May 29, 2020 Copyright © 2020 ARPG & Author This work is licensed under the Creative Commons Attribution International CC BY: Creative Commons Attribution License 4.0 Abstract Rayleigh-Taylor instability of a composite medium with variable density and viscosity is considered by taking into account the frictional effect of collisions of ionized with neutral atoms in the presence of a variable horizontal magnetic field. The criteria determining stability and instability are independent of the effects of viscosity and collisional effects. The magnetic field stabilizes the system which is otherwise unstable in the absence of the magnetic field. The viscosity of the medium has stabilizing as well as destabilizing effect on the growth rates. The collisional frequency has stabilizing effect on the growth rates, but has also destabilizing effect in some region. Keywords: Rayleigh-taylor instability; Variable density; Variable horizontal magnetic field. 1. Introduction A detailed treatment of Rayleigh-Taylor instability, together with the possible extensions in various domains of interest has been given by Chandrasekhar [1]. The medium has been considered to be fully ionized. Quite often the plasma is not fully ionized and is, instead, partially ionized. Partially ionized plasma represents a state which often exists in the Universe and there are several situations when the interaction between the ionized and neutral gas components becomes important in cosmic physics. The study of partially ionized plasmas has become a hot topic because solar structures such as spicules, prominences, as well as layers of the solar atmosphere (photosphere and chromosphere), are made of partially ionized plasmas. On the other hand, considerable developments have taken place in the study of partially ionized plasmas applied to the physics of the interstellar medium, molecular clouds, the formation of protostellar discs, planetary magnetospheres/ionospheres, exoplanets atmospheres, etc. For instance, molecular clouds are mainly made up of neutral material which does not interact with magnetic fields. However, neutrals are not the only constituent of molecular clouds since there are also several types of charged species which do interact with magnetic fields. Furthermore, the charged fraction also interacts with the neutral material through collisions. These multiple interactions produce many different physical effects which may have a strong influence on star formation and molecular cloud turbulence. A further example can be found in the formation of dense cores in molecular clouds induced by MHD waves. Because of the low ionization fraction, neutrals and charged particles are weakly coupled and ambipolar diffusion plays an important role in the formation process. Even in the primeval universe, during the recombination era, when the plasma, from which all the matter of the universe was formed, evolved from fully ionized to neutral, it went through a phase of partial ionization. Partially ionized plasmas introduce physical effects which are not considered in fully ionized plasmas, for instance, Cowling’s resistivity, isotropic thermal conduction by neutrals, heating due to ion/neutral friction, heat transfer due to collisions, charge exchange, ionization energy, etc., which are crucial to fully understand the behaviour of astrophysical plasmas in different environments. Stromgren [2], has reported that ionized hydrogen is limited to certain rather sharply bounded regions in space surrounding, for example, O-type stars and clusters of such stars and that the gas outside these regions is essentially non-ionized. Other examples of the existence of such situations are given by [3] theory on the origin of the planetary system, in which a high ionization rate is suggested to appear from collisions between a plasma and a neutral-gas cloud and by the absorption of plasma waves due to ion-neutral collisions such as in the solar photosphere and chromosphere and in cool interstellar clouds [4, 5]. Lehnert [6], has found that both ion viscosity and neutral gas friction have a stabilizing influence on cosmical plasma interacting with a neutral gas. According to Hans [7] and Bhatia [8], the medium may be idealized as a composite mixture of a hydromagnetic (ionized) component and a neutral component, the two interacting through mutual collisional (frictional) effects. A stabilizing effect of collisionals on Rayleigh-Taylor configuration has been shown by Hans [7] and Bhatia [8]. But the collisional effects are found to be destabilizing for a sufficiently large collisional frequency on Kelvin-Helmholtz configuration by Rao and Kalra [9] and Hans [7]. Chhajlani, et al. [10], considered the hydromagnetic Rayleigh- Taylor instability of a composite medium in the presence of suspended particles for an exponentially varying density