Linear and nonlinear behaviour of two-stream instabilities in collisionless plasmas

Abstract

The transient, growth and nonlinear saturation stages in the evolution of the electrostatic two-stream instabilities as described by the Vlasov–Poisson system are reconsidered by numerically following the evolution of the total wave energy of the plasma oscillations excited from (numerical) noise. Except for peculiarities related to the necessarily finite (even though very small) magnitude of the perturbations in the numerical simulation, the existence and initial growth properties of the instabilities from the numerical results are found to be consistent with those from linear normal mode analysis and the Penrose criteria. However, contradictory to the traditional point of view, the growth of instability before saturation is not always linear. The initial stage of the growth can exhibit fine structures that can be attributed to the harmonics of the excited plasma oscillations, whose wavelengths are determined by the system size and the numerical noise. As expected, saturation of the unstable oscillations is due to electron trapping when they reach sufficiently large amplitudes.

Evolution of the electron phase space of the two-stream and bump-on-tail instabilities in collisional plasma

“…We use 513 points for x and 2001 points for v. We found that there is only little difference in the results for NLLD when we double the points in x as well as v for both with and without the Krook collisions. The simulation code has also been benchmarked by comparing its results on linear and NLLD, as well as plasma wave echoes and instabilities, 12,13,22,49,50 with that of existing numerical and analytical works. From the Vlasov-Poisson/Amp ere system and various collision models, the so-called BB model [51][52][53][54][55] was developed to study resonant wave-particle interaction in tokamak plasmas.…”

“…Instabilities can occur in collisionless plasmas with bump-ontail and two-stream electron distributions, and their nonlinear evolution has been extensively studied analytically and numerically. [14][15][16][17][18][19][20][21][22][23] With particle-in-cell (PIC) simulations, Tsiklauri and co-workers [24][25][26] showed that superhot electron beam in plasma can generate electromagnetic waves characteristic of the type III solar radio bursts. Alves et al 27 found that the electron-scale Kelvin-Helmholtz instability can generate DC magnetic field in which particles can be accelerated to form astrophysical jets.…”