Solar phenomena move about and can travel at a few hundred meters per second when they first appear. The solar wind is a stream of plasma released from the Sun's upper atmosphere. It consists of mostly electrons and protons with energies usually between 1.5 and 10 keV. The stream of particles varies in density, temperature and speed over time and over solar longitude. These particles can escape the Sun's gravity because of their high energy. The solar wind is divided into the slow solar wind and the fast solar wind. The slow solar wind has a velocity of about , a temperature
Two-stream instability in various limiting cases as beam-plasma instability, beam instability, or bump-on-tail instability. Consider a cold, uniform, and unmagnetized plasma, where ions are stationary and the electrons have velocity formula_1, that is, the reference frame is moving with the ion stream. Let the electrostatic waves be of the form: formula_2 Applying linearization techniques to the equation of motions for both species, to the equation of continuity, and Poisson's equation, and introducing the spatial and temporal harmonic operators formula_3, formula_4 we can get the following expression: formula_5 which represents the dispersion relation for longitudinal waves, and represents a quartic equation in formula_6.