Two Stream Instability as a Source of Coronal Heating
ABSTRACT
Recent observation of oscillating the two stream instability (TSI) in a solar type III radio bursts and spatial damping of Langmuir oscillations has made this instability as an important candidate to understand the coronal heating problem. This instability has been studied by several authors for cold plasma found to be stable for high frequencies (greater than plasma frequency ωp). In this paper, we prove that this instability is unstable for warm plasma for higher frequencies (greater than plasma frequency ωp) and much suitable to study the solar coronal heating problem. We have derived a general dispersion relation for warm plasma and discussed the various methods analyzing the instability conditions. Also, we derived an expression for the growth rate of TSI and analyzed the growth rate for photospheric and coronal plasmas. A very promising result is that the ion temperature is the source of this instability and shifts the growth rate to high frequency region, while the electron temperature does the reverse. TSI shows a high growth rate for a wide frequency range for photosphere plasma, suggesting that the electron precipitation by magnetic reconnection current, acceleration by flares, may be source of TSI in the photosphere. But for corona, these waves are damped to accelerate the ions and further growing of such instability is prohibited due to the high conductivity in coronal plasma. The TSI is a common instability; the theory can be easily modifiable for multi-ion plasmas and will be a useful tool to analyze all the astrophysical problems and industrial devices, too.
Recent observation of oscillating the two stream instability (TSI) in a solar type III radio bursts and spatial damping of Langmuir oscillations has made this instability as an important candidate to understand the coronal heating problem. This instability has been studied by several authors for cold plasma found to be stable for high frequencies (greater than plasma frequency ωp). In this paper, we prove that this instability is unstable for warm plasma for higher frequencies (greater than plasma frequency ωp) and much suitable to study the solar coronal heating problem. We have derived a general dispersion relation for warm plasma and discussed the various methods analyzing the instability conditions. Also, we derived an expression for the growth rate of TSI and analyzed the growth rate for photospheric and coronal plasmas. A very promising result is that the ion temperature is the source of this instability and shifts the growth rate to high frequency region, while the electron temperature does the reverse. TSI shows a high growth rate for a wide frequency range for photosphere plasma, suggesting that the electron precipitation by magnetic reconnection current, acceleration by flares, may be source of TSI in the photosphere. But for corona, these waves are damped to accelerate the ions and further growing of such instability is prohibited due to the high conductivity in coronal plasma. The TSI is a common instability; the theory can be easily modifiable for multi-ion plasmas and will be a useful tool to analyze all the astrophysical problems and industrial devices, too.
KEYWORDS
Coronal Heating, Two Stream Instability, Langmuir Waves, Ion Temperature, Drift Velocity, Photosphere, Fusion Plasma
Coronal Heating, Two Stream Instability, Langmuir Waves, Ion Temperature, Drift Velocity, Photosphere, Fusion Plasma
Cite this paper
Soosaleon, A. and Jose, B. (2015) Two Stream Instability as a Source of Coronal Heating. International Journal of Astronomy and Astrophysics, 5, 61-69. doi: 10.4236/ijaa.2015.52009.
Soosaleon, A. and Jose, B. (2015) Two Stream Instability as a Source of Coronal Heating. International Journal of Astronomy and Astrophysics, 5, 61-69. doi: 10.4236/ijaa.2015.52009.
References
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http://dx.doi.org/10.1088/2[041-8205/747/1/L1 [3] Winglee, R.M. (1989) Heating and Acceleration of Heavy Ions during Solar Flares. Astrophysical Journal, 343, 511-525.
http://dx.doi.org/10.1086/167726 [4] Brown, J.C., Karlicky, M., MacKinnon, A.L., et al. (1990) Beam Heating in Solar Flares—Electrons or Protons? Astrophysical Journal, 73, 343-348.
http://dx.doi.org/10.1086/191470 [5] Dwivedi, B.N. and Narain, U. (2006) Physics of Sun and Its Atmosphere. Proceedings of the National Workshop (India) on Recent Advances in Solar Physics, Meerut, November 2008. [6] Sturrock, P.A., Holzer, T.E., Mihalas, D.M. and Ulrich, R.K. (1986) Physics of the Sun. Vol. 2, D. Reidel Publishing Company, Dordrecht. [7] Tautz, R.C. and Schlickeiser, R. (2005) Covariant Kinetic Dispersion Theory of Linear Waves in Anisotropic Plasmas. III. Counterstreaming Plasmas. Physics of Plasmas, 12, Article ID: 072101.
http://dx.doi.org/10.1063/1.1939967 [8] Tautz, R.C. and Schlickeiser, R. (2005) Counterstreaming Magnetized Plasmas. I. Parallel Wave Propagation. Physics of Plasmas, 12, Article ID: 122901.
http://dx.doi.org/10.1063/1.2139505 [9] Tautz, R.C., Schlickeiser, R., (2006) Counterstreaming Magnetized Plasmas. II. Perpendicular Wave Propagation. Physics of Plasmas, 13, Article ID: 062901.
http://dx.doi.org/10.1063/1.2207588 [10] Chen, F.F. (1981) Introduction to Plasma Physics and Controlled Fusion. Plenum Press, New York. [11] Nicholson, D.R. (1983) Introduction to Plasma Theory. Wiley, Hoboken. [12] Treumann, R.A. and Baumjohann, W. ( 2001) Advanced Space Plasma Physics. Imperial College Press, London.
[1] Aschwanden, M.J. (2005) Physics of Solar Corona. Springer, Berlin. [2] Thejappa, G., MacDowall, R.J., Bergamo, M. and Papadopoulos, K. (2012) Evidence for the Oscillating Two Stream Instability and Spatial Collapse of Langmuir Waves in a Solar Type III Radio Burst. Astrophysical Journal, 747, L1.
http://dx.doi.org/10.1088/2[041-8205/747/1/L1 [3] Winglee, R.M. (1989) Heating and Acceleration of Heavy Ions during Solar Flares. Astrophysical Journal, 343, 511-525.
http://dx.doi.org/10.1086/167726 [4] Brown, J.C., Karlicky, M., MacKinnon, A.L., et al. (1990) Beam Heating in Solar Flares—Electrons or Protons? Astrophysical Journal, 73, 343-348.
http://dx.doi.org/10.1086/191470 [5] Dwivedi, B.N. and Narain, U. (2006) Physics of Sun and Its Atmosphere. Proceedings of the National Workshop (India) on Recent Advances in Solar Physics, Meerut, November 2008. [6] Sturrock, P.A., Holzer, T.E., Mihalas, D.M. and Ulrich, R.K. (1986) Physics of the Sun. Vol. 2, D. Reidel Publishing Company, Dordrecht. [7] Tautz, R.C. and Schlickeiser, R. (2005) Covariant Kinetic Dispersion Theory of Linear Waves in Anisotropic Plasmas. III. Counterstreaming Plasmas. Physics of Plasmas, 12, Article ID: 072101.
http://dx.doi.org/10.1063/1.1939967 [8] Tautz, R.C. and Schlickeiser, R. (2005) Counterstreaming Magnetized Plasmas. I. Parallel Wave Propagation. Physics of Plasmas, 12, Article ID: 122901.
http://dx.doi.org/10.1063/1.2139505 [9] Tautz, R.C., Schlickeiser, R., (2006) Counterstreaming Magnetized Plasmas. II. Perpendicular Wave Propagation. Physics of Plasmas, 13, Article ID: 062901.
http://dx.doi.org/10.1063/1.2207588 [10] Chen, F.F. (1981) Introduction to Plasma Physics and Controlled Fusion. Plenum Press, New York. [11] Nicholson, D.R. (1983) Introduction to Plasma Theory. Wiley, Hoboken. [12] Treumann, R.A. and Baumjohann, W. ( 2001) Advanced Space Plasma Physics. Imperial College Press, London.