The effect of altitude- and velocity-dependent wave-particle interactions on the H+ and O+ outflows in the auroral region

The formation of H+ and O+ toroids at high altitudes in the auroral region are discussed in terms of altitude- and velocity-dependent wave-particle interactions (WPI), and special attention is given to the peaked nature of the velocity diffusion coefficient D⊥. The effects of altitude- and velocity-dependent WPI are taken into account by perturbing the ion velocity with random increment Δv⊥, such that 〈(Δv⊥)2〉=4D⊥Δt, where the time step is Δt. To model the heating process, we specify a model for the velocity diffusion coefficient as a function of the ion perpendicular velocity and position along the auroral geomagnetic field line. The ion velocity distribution is described by a quasi-linear diffusion equation, which is solved by the Monte Carlo technique. The Monte Carlo model includes the effects of altitude- and velocity-dependent WPI, gravity, polarization electrostatic field, and the divergence of the geomagnetic field within the simulation tube (1.2-10 earth radii, RE). These effects were included self-consistently in the computations. The peaked nature of D⊥ reflects the way in which altitude- and velocity-dependent WPI lead to the formation of H+ and O+ toroids at high altitudes in the auroral region, rather than simple bulk heating process. Because D⊥ falls to zero at small perpendicular velocities, the bulk of the ion velocity distribution is unaffected by interaction with the waves (electromagnetic turbulence). However, near the phase velocity v0, D⊥ begins to become appreciable, and the diffusion process begins to affect ions. Because there are initially more ions at lower velocities than at higher velocities, the net escape flux in velocity space is toward higher velocities, leading to the formation of ion toroids. At large perpendicular velocities, D⊥ falls to zero and consequently, the effect of WPI is negligible. As the heated ions drift upward along geomagnetic field lines due to the mirror geometry of the Earth's magnetic field, they eventually leave the primary heating region and form a ring “donuts”. The heating process is found to be self-limiting, and this explains the saturation of the ion velocity distributions at high altitudes. The altitude profiles of ion density, drift velocity, parallel and perpendicular temperatures are also discussed. We find that including the effect of velocity-dependent WPI in addition to the effect of altitude-dependent WPI produce realistic ion temperatures that are, qualitatively, comparable to the observations. The model produces simulation results similar to the observed toroids.