Plasma heating and current sheet structure in anti-parallel magnetic reconnection

Abstract

A theoretical model and an analytic theory of current sheet structure are presented for understanding anti-parallel driven magnetic reconnection in 2-1/2 dimension in collisionless plasmas. The theoretical model provides formulation to compute the current sheet y-profiles by specifying the profiles of electron and ion flow velocities V e x (x, y) and V i x (x, y). The current sheet solutions depend on the plasma density nin, merging magnetic field B0, ion velocity vi, and electron velocity ve in the upstream and the S evz = V e z / V d z parameter where Vez is the electron velocity accelerated by the reconnection electric field Ez in the electron orbit meandering region, V d z ≃ c E y / B x is the E → × B → drift velocity as electrons enter the orbit meandering region, Bx is the merging magnetic field, and Ey is the electrostatic electric field. With simplifying assumptions on the y-profiles of Vex and Vix, we have also developed an analytic theory of the current sheet structure. Analytic expressions for the anomalous resistivity, the electrostatic potential drop, and the maximum Ey amplitude Emax are obtained. The analytic results agree reasonably well with both the particle-in-cell simulation results and the numerical solutions of the theoretical model. The ions energy gain due to the potential drop is ∝ B 0 2 / n i n. The electron energy gain is ∝ (B 0 2 / 8 π n i n) S evz. The B 0 2 / n i n scaling of the average ion and electron energy gains are consistent with laboratory experiments and space plasma observations.