Hall MHD Simulations Of Collisionless Multiple X Line Reconnection

Magnetic reconnection is an effective mechanism for converting magnetic energy intokinetic and thermal energies of plasma, and plays an essential role in the energy couplingsystem between the Sun and the Earth. Recent research has ind_icated that the non-resistivity terms in the generalized Ohm's law have important effects on the reconnectiondynamics. Recently, the spacecraft observations provided the evidences of multiple Xline collisionless reconnection. In this thesis, the collisionless multiple X line reconnectionis investigated using a Hall magnetohydrodynamic (MHD) code which was derived frommulti-step implicit scheme.The behaviors of the plasmoid-like structures in multiple X line Hall MHD reconnec-tion are studied numerically in chapter 3. Driven by a waveform inflow, multiple X linereconnection is initiated in a long current layer, and the plasmoids are bound betweentwo neighboring reconnection sites. We investigate the behaviors of the plasmoid-likestructures in the absence and presence of an initial guide field B_y0 normalized by B₀ (B₀is the initial intensity of B_x field at the top and bottom boundaries of the simulation do-main) using a Hall MHD code. For the case with B_y0 = 0 the profiles of out-of-plane B_ycomponent are the bipolar signature or the bipolar wavelike signature which is caused byHall effect and independent of the external mechanism. Such B_y features are in line withthe observed signature of a closed-loop-like plasmoid in the magnetotail. The bipolarand fluctuation signatures of B_y have an asymmetric feature in the presence of a smallB_y0(= 0.1), and the B_y profile becomes a positive signature as B_y0 reaches or exceeds0.3. In the case of B_y0 = 0.5, a B_y bulge appears in the B_y signature when the enhancedB_y regions caused by Hall e?ect take place in the plasmoid. The B_y bulge evolves intoa peaking signature, whose maximum (B_y|max) is quickly raised and approaches to thelobe magnetic field strength. Such a significant enhancement of the B_y component in thecentral region of plasmoid might be representative of the observed strong core field inthe magnetic flux rope. The present results ind_icate the following implications: (1) Halleffect and a preexisting cross-tail component B_y are two important factors controllingthe occurrence of various plasmoid-like structures in the magnetotail. (2) In the laterphase the nonlinear interaction between Hall efect and the B_y flux added by the plasmainflow make a most important contribution to the growth of the core B_y field.A Hall MHD simulation of multiple X line reconnection, in which a di?usion regionaround the standing X line and the moving plasmoids are involved, is presented in chapter 4. The observed features of Hall magnetic and electric fields in the diffusionregion and the direction reversal of the electron ?ow in the vicinity of the magneticseparatrices are displayed in case 1 with the guide field B_y0 = 0. During the passageof a tailward moving plasmoid the bipolar B_y waveform signatures caused by the Hallcurrent and the Hall electric field signatures in case 1 are qualitatively in line with theobservations from Geotail and Cluster spacecrafts. Case 2 with B_y0 = 0.15 is carried outto investigate the reconnection configuration on the earthward side of the X line. Thepeaking signature of the positive B_y correlated with the bipolar (-/+) B_z is observedwhile an earthward moving plasmoid passes through the given point below the currentsheet and close to the midplane; but the negative B_y is recorded at the given point abovethe current sheet. Such positive and negative B_y signatures, which are comparable withthe observations from Cluster 3 and other Cluster spacecrafts, are attributed to the B_yasymmetric structures associated with Hall e?ect. The enhancement and variation ofthe electric field detected by Cluster 3 might be related to the -V'×B electric fieldassociated with the earthward movement of the X line.The effects of the initial guide field B_y0 on the reconnection dynamics are examinedin chapter 5. A uniform out-of-plane magnetic field component B_y0 is added to theequilibrium Harris sheet with plasmaβ= 0.5 and Lc = 0.5di (where Lc is the half-width of the equilibrium current layer and di is the ion inertial length). Driven by thecontinuous boundary inflows, the magnetic reconnections with the guide field B_y0/B₀ranging from 0 to 4.0 are investigated using a 2.5 dimensional Hall MHD code. Thefeatures of the reconnection field are substantially altered in the presence of the guidefield. The openness of the magnetic separatrix angle is slightly reduced and the anti-symmetric quadrupolar structure of B_y field and the symmetric distribution of plasmapressure P are replaced by an asymmetric B_y four-wing structure and an asymmetric Pplot as a non-zero B_y0 is added. The decoupling of electrons and ions also occurs nearthe X-line in the case with a finite B_y0, but the e?ect of initial B_y0 on the electron ?owis greater than that on the ion ?ow. The reconnection rates at the X-line drops from0.151 to 0.06, namely, (?)A/(?)t is reduced by a factor of 2.5 as B_y0/B₀ increases from 0to 4.0. The reduction of reconnection rate might be related to the reducing openness ofreconnection layer with the increasing B_y0.