Collision coalescence and mutual penetration of electron phase space holes

As a universal nonlinear structure in space plasma, electron phase space holes, also named as electrostatic solitary waves (ESWs), have a 60-year research history. An important challenge has been to reveal the microscopic evolutionary process of ESWs. Previous simulations have shown that collision coalescences determine whether several weak ESWs can evolve into a strong one. However, the simulated collision coalescence has not yet been demonstrated in observations. Here, we employ coordinated observations from the MMS multi-satellite mission to unveil two distinct evolutionary processes: collision coalescence and mutual penetration of ESWs in space plasmas. Subsequently, collision simulations reveal that the conditions for coalescence are closely linked to the ratio of the maximum capture velocity of the trapped electrons to the hole velocity, consistent with the findings of energy balance analysis based on the virial theorem and successfully explaining the observed collision coalescence and mutual penetration of ESWs. Therefore, we provide a direct observational evidence to collision coalescence and mutual penetration of ESWs for the first time.