Theory and computer simulation of whistler turbulence and velocity space diffusion in the magnetospheric plasma

Abstract

The nonlinear development of unstable whistler waves and their interaction with electrons in an anisotropic, collisionless, magnetospheric-type plasma is investigated by theory and computer simulation experiments. A two-component plasma is considered; a hot electron Maxwellian component with 60° loss cone is superimposed on a cold isotropic electron background. The linear and quasi-linear theory is developed, and quasi-linear theory is used to obtain equations for the temporal evolution of the parallel and perpendicular energy for the hot and cold plasma components. The computer code follows the nonrelativistic dynamics of a large number of charges in their self-consistent electromagnetic fields. Three velocity and one spatial dimension are used. The simulation automatically includes energy as well as pitch angle diffusion. The 6.5 × 104 electrons, which were followed, were distributed into the two components. Initially, the wave magnetic energy grows according to linear theory; the hot electrons diffuse into the loss cone, gaining parallel and losing perpendicular kinetic energy by both pitch angle and energy diffusion; and the cold background gains perpendicular energy nonresonantly. The quasi-linear equations for the evolution of parallel and perpendicular energy for the hot and cold components explain the partitioning of energy. A plot of hot particle density in υ⊥ versus υ∥ velocity space shows a hole developing as the particles diffuse, in agreement with theory. We observe that, as the hot electrons isotropize, the initially unstable higher mode numbers sequentially switch off; i.e., the spectrum shifts to lower k values. The growth of the wave magnetic energy saturates in a full nonlinear phase when the average growth rate is of the order of the electron trapping frequency in the whistler spectrum. At this time there exists a large residual kinetic energy anisotropy in the hot particle distribution.