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 ex (x,y) and V ix (x,y). The current sheet solutions depend on the plasma density n in , merging magnetic field B 0 , ion velocity v i , and electron velocity ve in the upstream and the S evz =V ez /V dz parameter where V ez is the electron velocity accelerated by the reconnection electric field E z in the electron orbit meandering region, V dz ≃cE y /B x is the $\overrightarrow{E}$ × $\overrightarrow{B}$ drift velocity as electrons enter the orbit meandering region, B x is the merging magnetic field, and E y is the electrostatic electric field. With simplifying assumptions on the y-profiles of V ex and V ix , 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 E y amplitude E max 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 $∝B^2_0/n_{in}$. The electron energy gain is $∝(B^2_0 /8πn_{in})S_{evz}$. The $B^2_0/n_{in}$ scaling of the average ion and electron energy gains are consistent with laboratory experiments and space plasma observations.