Steady-State Properties of Driven Magnetic Reconnection in 2D Electron Magnetohydrodynamics

We formulate a rigorous nonlinear analytical model that describes the dynamics of the diffusion (reconnection) region in driven systems in the context of electron magnetohydrodynamics (EMHD). A steady-state analysis yields allowed geometric configurations and associated reconnection rates. In addition to the well-known open $X$-point geometry, elongated configurations are found possible. The model predictions have been validated numerically with two-dimensional EMHD nonlinear simulations, and are in excellent agreement with previously published work.

Figure 1

2D reconnection region geometry.

Figure 2

Linear eigenvalues $\gamma (\xi )$ for Eqs. (2, 3, 4) for the steady state in Eq. (7): $\gamma >0$ indicates instability.

Figure 3

Scaling of $\delta (B_x/w{)}^{1/3}$ vs ${\eta }_H$: numerical 2D EMHD (solid line), ${\eta }_H^{1/3}$ (dashed line).

Figure 4

Reconnection rates due to resistivity ($E_z^{\eta }$, dashed line) and hyper-resistivity ($E_z^H$, solid line).