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.
