Three-dimensional crescent-shaped ion velocity distributions created by magnetic reconnection in the presence of a guide field

By means of theory and particle simulations, crescent-shaped ion velocity distributions in the outflow region of symmetric magnetic reconnection in the presence of a guide magnetic field are investigated. Assuming a spatial one-dimensional electromagnetic field, a theoretical model accounting for the shape of crescents is derived. First, following the earlier theoretical models suggested by Bessho et al. [Geophys. Res. Lett. 43, 1828-1836 (2016)] and Zenitani et al. [J. Geophys. Res.: Space Phys. 122, 7396-7413 (2017)], we derive a theoretical model for 2D velocity distributions based on the conservation of the canonical momentum and the energy. The 2D theoretical model exhibits a two-dimensional structure of crescent-shaped velocity distributions and further demonstrates that no magnetic field reversal is required in the formation of crescents, although many researchers have considered that magnetic field reversal plays an essential role. Next, we construct a theoretical model for 3D velocity distributions based not only on the conservation of the canonical momentum in two directions and the energy but also on the conservation of the magnetic moment and the kinetic energy in the moving frame with the reconnection outflow speed, which are applied when the guide field ratio is high. The 3D theoretical model derives a three-dimensional structure of crescents by combination of an antiparallel magnetic field and a guide magnetic field comparable to or greater than the reconnection field. Both of the 2D and 3D theoretical models are consistent with ion velocity distributions found in our particle simulations.