Instabilities and Turbulence in Low-$\beta$ Guide Field Reconnection Exhausts with Kinetic Riemann Simulations

The role of turbulence in low-$\beta$, guide-field reconnection exhausts is explored in 2D reconnection and 2D and 3D Riemann simulations. The structure of the exhaust and associated turbulence is controlled by a pair of rotational discontinuities (RDs) at the exhaust boundary and a pair of slow shocks (SSs) that are generated by counterstreaming ions beams. In 2D the exhaust develops large-amplitude striations at the ion Larmor radius scale that are produced by electron-beam-driven ion cyclotron waves. The electron beams driving the instability are injected into the exhaust from one of the RDs. However, in 3D Riemann simulations, the additional dimension (in the out-of-plane direction) results in strong Buneman and electron-electron streaming instabilities at the RD which suppress electron beam formation and therefore the striations in the exhaust. The strength of the streaming instabilities at the RD are controlled by the ratio of the electron thermal speed to Alfv\'en speed, lower thermal speed being more unstable. In the 3D simulations an ion-ion streaming instability acts to partially thermalize the counterstreaming ion beams at the SSs. This instability is controlled by the ratio of the sound speed to Alfv\'en speed and is expected to be stable in the low $\beta$ solar corona. The results suggest that in a guide field reconnection exhaust with $1 \gg \beta > m_e/m_i$, the kinetic-scale turbulence that develops will be too weak to play a significant role in energy conversion and particle acceleration. Therefore, the energy conversion will be mostly controlled by laminar physics or multi-x-line reconnection.