Numerical simulation of the generation of electrostatic turbulence in the magnetotail

A two-dimensional plasma model is used to investigate the development of electrostatic turbulence in a magnetized plasma from plasma instabilities. The simulation consists of following the motion of 105 ions in their self-consistent electrostatic field. The electrons are treated as a constant neutralizing background. The instabilities modeled are driven by a ring-type velocity distribution and by interpenetrating ion beams in a time variable magnetic field. Instability growth times are the order of an ion gyroperiod in the case of the ring distribution and of the order of an ion plasma period in the case of the beam simulation. Maximum potential differences generated are of the order of the ion kinetic energies. These simulations demonstrate the cascade of wave energy to long wavelengths, thus showing that E x B turbulence can be generated from plasma microinstabilities. After the free energy feeding, the instabilities are exhausted, and wave energy at wavelengths less than an ion gyrodiameter decays quickly to equilibrium levels, while longer wavelength modes persist for much longer times. In one model with a time dependent, but spatially uniform, magnetic field, the electric field energy at long wavelengths appeared to increase as a result of the increase of the magnetic field