Assessing the time dependence of reconnection with Poynting's theorem: MMS observations

We investigate the time dependence of electromagnetic-field-to-plasma energy conversion in the electron diffusion region of asymmetric magnetic reconnection. To do so, we consider the terms in Poynting's theorem. In a steady state there is a perfect balance between the divergence of the electromagnetic energy flux $\nabla \cdot \vec{S}$ and the conversion between electromagnetic field and particle energy $\vec{J} \cdot \vec{E}$. This energy balance is demonstrated with a particle-in-cell simulation of reconnection. We also evaluate each of the terms in Poynting's theorem during an observation of a magnetopause reconnection region by Magnetospheric Multiscale (MMS). We take the equivalence of both sides of Poynting's theorem as an indication that the errors associated with the approximation of each term with MMS data are small. We find that, for this event, balance between $\vec{J}\cdot\vec{E}=-\nabla\cdot\vec{S}$ is only achieved for a small fraction of the energy conversion region at/near the X-point. Magnetic energy was rapidly accumulating on either side of the current sheet at roughly three times the predicted energy conversion rate. Furthermore, we find that while $\vec{J}\cdot\vec{E}>0$ and $\nabla\cdot\vec{S}<0$ are observed, as is expected for reconnection, the energy accumulation is driven by the overcompensation for $\vec{J}\cdot\vec{E}$ by $-\nabla\cdot\vec{S}>\vec{J}\cdot\vec{E}$. We note that due to the assumptions necessary to do this calculation, the accurate evaluation of $\nabla\cdot\vec{S}$ may not be possible for every MMS-observed reconnection event; but if possible, this is a simple approach to determine if reconnection is or is not in a steady-state.