ON THE STABILITY OF A PARTIALLY IONIZED PLASMA

Abstract

The Rayleigh-Taylor instability of an infinitely conducting plasma of variable density in the presence of a horizontal magnetic field is considered when the effects of finite ion Larmor radius (FLR) and collisions with neutral atoms simultaneously present. Here we considered the perturbations propagating along the ambient magnetic field. It is observed that, real part of n is negative, where n is the growth rate of disturbance, so that instability does not arise in the form of increasing amplitude, i.e. overstability. To obtain an approximate solution of the problem, a variational principle is used. The case of two semi-infinitely extending plasmas of constant densities separated by a horizontal interface is also considered, where it is found that the system is stable (for some wave numbers) for potentially stable configuration and unstable (for other wave numbers) for potentially unstable configuration even if there are collisions with dust particles. Also it is observed that the criteria determining stability and instability are independent of FLR effects.

Keywords

• Rayleigh-Taylor instability
• conducting plasma
• horizontal magnetic field

References

1. Alfven, H., On the Origin of the Solar System, Oxford University Press, Oxford, 1954.
2. Ariel, P.D., Effect of finite Larmor radius on the gravitational instability of a conducting plasma layer of finite thickness surrounded by a non-conducting matter, Astrophys. Space Sci., vol. 141, pp. 141-149, 1988.
3. Ariel, P.D., Rayleigh-Taylor instability of a plasma with finite ion Larmor radius effects, Astrophys. Space Sci., vol. 196, pp. 153-166, 1992.
4. Bhatia, P.K., Collisional effects on the Rayleigh-Taylor instability in a composite medium, Nucl. Fusion, vol. 10, pp. 383-386, 1970.
5. Chandrasekhar, S., Hydrodynamic and Hydromagnetic Stability, Clarendon Press, Oxford, UK, 1981.
6. Chhajlani, R.K., Sanghvi, R.K. and Purohit, P., Rayleigh-Taylor instability of a stratified magnetized medium in the presence of suspended particles, Z. Naturforsch., vol. 39a, pp. 939-944, 1984.
7. El-Sayed, M.F. and Mohamed, R.A., Gravitational instability of rotating viscoelastic partially ionized plasma in the presence of an oblique magnetic field and hall current, ISRN Mechanical Engng., Article ID 597172, 8 pages, 2011.
8. Hans, H.K., Larmor radius and collisional effects on the combined Taylor and Kelvin instabilities in a composite medium, Nucl. Fusion, vol. 8, pp. 89-92, 1968.

9. Hoshoudy, G.A., Rayleigh-Taylor instability in magnetized plasma, World J. Mechanics, vol. 4, pp. 260-272, 2014.
10. Lehnert, B., Plasma physics on cosmical and laboratory scale, Suppl. Nuovo Cimento, vol. 13, pp. 59-62, 1959.
11. Lehnert, B., R. Inst. Technol. Stockholm Rep. Nos. TRITAEPP-70-05.06; Proceedings of the V European Conference on Controlled Fusion and Plasma Physics, Grenoble, France, August 21-25, 1972.
12. Piddington, J.H., Electromagnetic field equation for a moving medium with hall conductivity, Mon. Not. R. Astron. Soc., vol. 114, pp. 638-650, 1954.
13. Rao, S.S. and Kalra, G.L., Hydromagnetic Kelvin instability in the presence of neutral particles, Canad. J. Phys., vol. 45, pp. 2779-2785, 1967.
14. Sharma, R.C. and Prakash, K., Thermal instability in plasma with finite Larmor radius, Z. Naturforsch., vol. 30A, pp. 461-465, 1975.
15. Sharma, R.C. and Rani, N., Finite Larmor radius and compressibility effects on thermosolutal instability of a plasma, Z. Naturforsch., vol. 41A, pp. 724-728, 1986.
16. Sharma, R.C. and Sharma, K.N., Finite Larmor radius effects on thermosolutal instability of a plasma, Phys. Fluids, vol. 24, pp. 2242-2244, 1981.
17. Sharma, R.C. and Sunil, Rayleigh-Taylor instability of a partially ionized plasma in a porous medium in presence of a variable magnetic field, Z. Naturforsch., vol. 47a, pp. 1227-1231, 1992.
18. Sharma, P.K., Tiwari, A., Prajapati, R.P. and Chhajlani, R.K., Rayleigh-Taylor instability in dusty magnetized fluids with surface tension flowing through porous medium, Thermal Sci., vol. 20, pp. 119-130, 2016.
19. Stromgren, B., The physical state of interstellar hydrogen, Astrophys. J., vol. 89, pp. 526-528, 1939.