Kinetic Simulations of Magnetic Reconnection in Partially Ionized Plasmas

Fast magnetic reconnection occurs in nearly all natural and laboratory plasmas and rapidly releases stored magnetic energy. Although commonly studied in fully ionized plasmas, if and when fast reconnection can occur in partially ionized plasmas, such as the interstellar medium or solar chromosphere, is not well understood. This Letter presents the first fully kinetic particle-in-cell simulations of partially ionized reconnection and demonstrates that fast reconnection can occur in partially ionized systems. In the simulations, the transition to fast reconnection occurs when the current sheet width thins below the ion-inertial length in contrast to previous analytic predictions. The peak reconnection rate is $\ge 0.08$ when normalized to the bulk Alfvén speed (including both ion and neutral mass), consistent with previous experimental results. However, when the bulk Alfvén speed falls below the neutral sound speed, the rate becomes system size dependent. The normalized inflow velocity is ionization fraction dependent, which is shown to be a result of neutral momentum transport. A model for the inflow is developed which agrees well with the simulation results.

Figure 1

Example of a partially ionized reconnection simulation from series D with ${\chi }_0=0.1$ showing the central region at time $t{\mathrm{\Omega }}_{i0}=300$. (a) The out-of-plane current density is shown in color and solid lines are magnetic flux surfaces, (b) the out-of-plane magnetic field in color along with contours of the compressible neutral stream-function (dashed lines). For this case, simulation parameters map to the dimensional parameters $n_e=1.5\times {10}^{12}{\mathrm{cm}}^{-3}$, $B=28\mathrm{G}$ and $L_z=400d_{i0}=82\mathrm{m}$.

Figure 2

Transition between collisional and collisionless reconnection in series A. Panels show (a) the scaled reconnection rate, (b) and (c) the minimum current sheet width normalized to the local ion inertial length $d_i$ and the hybrid inertial length $d_i{\chi }^{-1/2}$, and (d) the electron temperature at the $X$ point.

Figure 3

Evaluation of the terms in Ohm’s law along the inflow of the ${\chi }_0=0.1$ case from series B at $t{\mathrm{\Omega }}_{i0}=175$. The ion diffusion region is defined by $\mathbf{J}\times \mathbf{B}<0$ corresponding to $|x|<6.5d_{i0}$. Equation (3) is tested by plotting the right-hand side as the dashed line. To reduce noise, ${\partial }^2{v}_{ny}/\partial x^2$ is averaged over $\pm 2.5d_{i0}$.

Figure 4

Ionization fraction and system size dependence of (a) the global reconnection rate, (b) the local inflow velocity, and (c) the ion diffusion region thickness for series B–D. Labeled lines in (a) show the scalings $R=0.08{\chi }^{1/2}$ (Alfvénic) and $R=0.075(\chi +{\beta }_i/2{)}^{1/2}$ (Magnetosonic). In (c), the solid line is $\mathrm{\Delta }/d_i=4{\chi }^{-1/2}$. In panel (d), Eq. (6) is tested using ${\mathrm{\Delta }}_0=4d_i$ and $\theta =1$ with the solid line showing equality.