Electromagnetic electron hole generation: theory and PIC simulations

Recent MMS observations (e.g. [Holmes et al, 2018, Steinvall et al., 2019]) exploring various regions of the magnetosphere have found solitary potential structures call Electron phase-space Hole (EH). These structures have kinetic scale (dozens of Debye lengths) and persist during long time (dozens of plasma frequency periods). EH are characterized by a bipolar electric field parallel to ambient magnetic field and fastly propagate along this latter (a few tenths of speed light). We have created a 3D Bernstein-Greene-Kruskal (BGK) model (as [Chen et al, 2004]) adapted to various magnetospheric ambient magnetic fields. BGK model results depend on choice of potential shape and passing distribution function at infinity (before EH potential interaction).

2D-3V Particle-In-Cell simulations have been developed with the fully kinetic code Smilei [Derouillat et al, 2017], using real magnetosphere plasma parameters. Solitary waves in the magnetotail are three-dimensional potentials which can be generated through nonlinear evolution of an electron beam instability (or bump on tail). The simulated EH are comparable to the EH observed in the magnetosphere with the same parameters.

We have also investigated the EH formation with density inhomogeneities using a BGK stability model we have developed. Indeed, density inhomogeneities exist notably in interplanetary plasmas. As a result taking into account the background density inhomogeneities, significantly alters the stability criteria. We have performed 2D-3V PIC simulations with realistic inhomogeneous density background (smaller than 10% of mean density) to understand such a type of EH formation.

References:

• Holmes et al., J. Geophys. Res. Space Phys. 123, 9963, 2018
• Steinvall et al., Phys. Rev. Lett. 123, 255101, 2019
• Chen et al., Phys. Rev. E 69, 055401, 2004
• Derouillat et al., Comput. Phys. Commun. 222, 351, 2017