Proton the particles in the solar wind are electrons and protons, in approximately equal numbers. Protons also have extrasolar origin from galactic cosmic rays, where they make up about 90% of the total particle flux. These protons often have higher energy than solar wind protons, and their intensity is far more uniform and less variable than protons coming from the Sun, the production of which is heavily affected by solar proton events such as coronal mass ejections. Research has been performed on the dose-rate effects of protons, as typically found in space travel, on human health. To be more specific, there
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.