The Current Tension Electric Field in the Generalized Ohm's Law

In the prevailing form of the generalized Ohm's law (GOL), -me/e(J/en)& sdot; backward difference (J/en) ${-}\left({m}_{e}/e\right)\left[(\boldsymbol{J}/en)\cdot \nabla \right](\boldsymbol{J}/en)$ is often neglected. Because of the resemblance to the magnetic tension, we refer to this term as the current tension electric field (ECT). Our theoretical analysis reveals that ECT with a characteristic length of mi/me1/6 lambda e ${\left({m}_{i}/{m}_{e}\right)}<^>{1/6}{\lambda }_{e}$ dominates the electron inertia terms in the electron diffusion region (EDR) and is comparable to the electron pressure term in low-beta e conditions. Using particle-in-cell simulations, we demonstrate that ECT can contribute significantly to the reconnection electric field and energy dissipation at the boundaries of the inner EDR and in the outer EDR. Positive and negative J & sdot; ECT can be used to identify inner and outer electron diffusion regions, respectively. Magnetic reconnection is a fundamental physical process which allows for the explosive release of magnetic energy into thermal and kinetic energy. It underlies many dynamic phenomena in the universe, including solar eruptions, geomagnetic substorms and tokamak disruptions. In collisionless plasma, the generalized Ohm's law (GOL) introduces collisionless effects which break the frozen-in constraint and enable reconnection to occur. The term, -me/e(J/en)& sdot; backward difference (J/en) ${-}\left({m}_{e}/e\right)\left[(\boldsymbol{J}/en)\cdot \nabla \right](\boldsymbol{J}/en)$, which is one of the electron inertia terms of GOL, is referred to as the current tension electric field (ECT) by us due to its mathematical resemblance to magnetic tension. In many classic textbooks and review papers, ECT is considered as a small quantity and thus is ignored. In this study, we present solid evidence from both theoretical studies and particle-in-cell (PIC) simulations to demonstrate that ECT dominates the electron inertia terms and plays important roles in providing reconnection electric field and energy dissipation in reconnection. Therefore, it should not be ignored. Based on our results, many classic textbooks in which ECT has been ignored must be modified. ECT dominates the electron inertia terms in the electron diffusion region (EDR) and thus cannot be ignored in the generalized Ohm's law ECT contribute significantly to the reconnection electric field and energy dissipation in the inner and outer EDRs Positive and negative J center dot ECT can be used to identify inner and outer EDRs, respectively