A new theory for energetic electron generation behind dipolarization front

A long-standing problem concerning dipolarization front (DF) is why energetic electrons only appear in half the DF events? By analyzing MMS measurements, here we answer this question. We find a DF structure, behind which energetic-electron fluxes are modulated by magnetosonic waves: At wave troughs (B-minimum) electron fluxes are high; at wave crests (B-maximum) electron fluxes are low. This phenomenon challenges the classical theory of betatron mechanism, so we need to propose a new theory to explain it. In our theory, there exists a magnetic bottle with time-varying belly but steady neck behind the DF. When the belly expands, a magnetic bottle is formed, and electrons are trapped; when the belly contracts, the magnetic bottle disappears, and electrons are expelled. Quantitatively, we validate the existence of this bottle and estimate its size as 2-3 R-E. Our theory can explain both the presence and absence of energetic electrons behind DFs.