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 ω p ). In this paper, we prove that this instability is unstable for warm plasma for higher frequencies (greater than plasma frequency ω p ) 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.