Turbulence driven by two-stream instability in a magnetized plasma - Goldman, Martin V.; Crary, Frank; Newman, David L.; Oppenheim, Meers (Physics of Plasmas, 2000)
Although the nonlinear evolution of the two-stream instability has been a subject of numerical and theoretical studies for many years, recent spacecraft measurements of nonlinear electrostatic bipolar wave structures in the auroral ionosphere have prompted new studies. Using parallel two-dimensional (2D) particle-in-cell electrostatic simulations with initially counterstreaming cold electrons in a magnetized plasma, the evolution of wave turbulence and particle distributions has been followed for over 10 000 inverse plasma frequencies. Ions are introduced in the frame of one of the electron beams (motivated by measurements). Wave turbulence evolves in at least five separate stages. After tens of ω e −1 , trapping produces bipolar wave structures with long range order across B. After hundreds of ω e −1 , the structures break up and whistlers appear. After thousands of ω e −1 , ion cyclotron waves driven by a bump-on-tail in the evolved electron distribution become prominent. After 6000 ω e −1 , the ion cyclotron waves appear to undergo parametric decay into oblique waves.