ИСТИНА

Electron holes are a specific type of nonlinear electrostatic solitary waves, so called BGK modes. Interest in such structures is due to the fact, that they may contribute to plasma heating and provide anomalous resistivity in various space plasma regions. Multisatellite space observations of electron holes have firmly established that these structures can have speeds comparable to local ion thermal velocity. In fact, the stable persistence of such slow electron holes presents a riddle, since theory and simulations have indicated that the interaction of such slow electron holes with ions normally prevents their speeds remaining at or below the ion thermal velocity. Although the origin of these structures is still elusive, in our work we resolve the problem of existence of slow electron holes. Based on the multisatellite measurements aboard four Magnetospheric Multiscale (MMS) spacecraft, we were able to determine velocities of around one thousand electron holes in a particular interval in the Earth’s plasma sheet. Using MMS measurements of the ion velocity distribution functions (VDF) during the same time interval we were able to show these observed ion VDFs have a pronounced double-humped shape with electron holes speeds clustered near the local minimum between the two humps. New theory shows that slow electron holes can avoid the acceleration that otherwise prevents their remaining slow only under these same circumstances. In addition, we have also analyzed about one thousand slow electron holes from the dataset of Lotekar et al. and proved, that indeed the speeds of slow electron holes are always clustered around the local minimum of double-humped (more specifically, at least double-humped) ion VDF. Thus, the agreement between observation and theory about the conditions for their existence is remarkable. Although the origin of the slow electron holes is still elusive, this analysis resolves the problem of existence of slow electron holes. This work was supported by the Russian Scientific Foundation, Project No. 19–12-00313