Monte Carlo modeling of toroidal ion distributions and ion temperatures at high altitudes equatorward of the cusp: Effect of finite gyroradius

Abstract

We report that the effect of finite gyroradius is responsible for production of the H+ and O+ toroids at high altitudes equatorward of the cusp that are observed by TIDE and TIMAS ion instruments on board the polar spacecraft. The energization of charged particles, owing to interaction with electromagnetic turbulence, has an important influence on the plasma outflow in space. The effect of wave‐particle interactions (WPI) on H+ and O+ outflow at high altitudes equatorward of the cusp was investigated by using Monte Carlo method. The Monte Carlo model includes the effect of WPI, gravity, polarization electrostatic field, and the divergence of the geomagnetic field within the simulation tube (1.2–10 Earth radii, RE). As the ions drift upward along the geomagnetic field lines, they interact with the electromagnetic turbulence and consequently get heated in the direction perpendicular to the geomagnetic field. The mirror force converts some of the gained ion energy in the perpendicular direction into parallel kinetic energy. These effects combine to form an ion‐conic velocity distribution. However, as the ions are heated and move to higher altitudes, the ion gyroradius ρi may become comparable to the perpendicular wavelength of the electromagnetic turbulence λ⊥. As the ratio ρi/λ⊥ becomes >1, then the heating rate turns to be self‐limited and the ion velocity distribution displays toroidal features. A comparison has been made between the Monte Carlo calculations obtained in this study and observations of H+ and O+ ion velocity distributions and temperatures. The comparison showed a remarkably close agreement in the corresponding results for the ion velocity distribution and its temperature. As a result of the comparison, we were able to predict the characteristic value of the perpendicular wavelength of the electromagnetic turbulence λ⊥ at high altitudes equatorward of the cusp. To our knowledge, this represents the first successful comparison of observed toroids with a theoretical model.