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

Magnetic reconnection is a fundamental physical process which allows for the explosive release of magnetic energy into thermal and kinetic energy. It underlies many dynamics 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, $-(m_e/e)[(\bm{J}/en)\cdot \nabla](\bm{J}/en)$, which is one of the electron inertia terms of GOL, is referred to as the current tension electric field ($\bm{E}_{CT}$) by us due to its mathematical resemblance to magnetic tension. In many classic textbooks and review papers, $\bm{E}_{CT}$ 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 $\bm{E}_{CT}$ 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 $\bm{E}_{CT}$ has been ignored must be modified.