The Effect of Thermal Pressure on Collisionless Magnetic Reconnection Rate

Modeling collisionless magnetic reconnection rate is an outstanding challenge in basic plasma physics research. While the seemingly universal rate of an order $\mathcal{O}(0.1)$ is often reported in the low-$\beta$ regime, it is not clear how reconnection rate scales with a higher plasma $\beta$. Due to the complexity of the pressure tensor, the available reconnection rate model is limited to the low plasma-$\beta$ regime, where the thermal pressure is arguably negligible. However, the thermal pressure effect becomes important when $\beta \gtrsim \mathcal{O}(1)$. Using first-principle kinetic simulations, we show that both the reconnection rate and outflow speed drop as $\beta$ gets larger. A simple analytical framework is derived to take account of the self-generated pressure anisotropy and pressure gradient in the force-balance around the diffusion region, explaining the varying trend of key quantities and reconnection rates in these simulations with different $\beta$. The predicted scaling of the normalized reconnection rate is $\simeq \mathcal{O}(0.1/\sqrt{\beta_{i0}})$ in the high $\beta$ limit, where $\beta_{i0}$ is the ion $\beta$ of the inflow plasma.