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.
تحميل البحث