Interaction of a spatially uniform electron beam with a rotational magnetic hole in a form of a Harris current sheet

In this work we use particle-in-cell (PIC) numerical simulations to study interaction of a spatially uniform electron beam with a rotational magnetic hole in a form of a Harris current sheet. We vary width of the Harris current sheet to investigate how this affects the quasi-linear relaxation, i.e. plateau formation of the bump-on-tail unstable electron beam. We find that when width of the Harris current sheet approaches and becomes smaller than the electron gyro-radius, quasi-linear relaxation becomes hampered and a positive slope in the electron velocity distribution function (VDF) persists. We explain this by the effects of non-conservation of electron magnetic moment, which, as recent works suggest, can maintain the positive slope of the VDF. In part, this can explain why some electron beams in the solar wind travel much longer distances than predicted by the quasi-linear theory, at least in those cases when the electron beams slide along the current sheets that are abundant when the different-speed solar wind streams interact with each other.