Proton Acceleration in Low-beta Magnetic Reconnection with Energetic Particle Feedback

Magnetic reconnection regions in space and astrophysics are known as active particle acceleration sites. There is ample evidence showing that energetic particles can take a substantial amount of converted energy during magnetic reconnection. However, there has been a lack of studies understanding the backreaction of energetic particles at magnetohydrodynamical scales in magnetic reconnection. To address this, we have developed a new computational method to explore the feedback by non-thermal energetic particles. This approach considers the backreaction from these energetic particles by incorporating their pressure into Magnetohydrodynamics (MHD) equations. The pressure of the energetic particles is evaluated from their distribution evolved through Parker's transport equation, solved using stochastic differential equations (SDE), so we coin the name MHD-SDE. Applying this method to low-beta magnetic reconnection simulations, we find that reconnection is capable of accelerating a large fraction of energetic particles that contain a substantial amount of energy. When the feedback from these particles is included, their pressure suppresses the compression structures generated by magnetic reconnection, thereby mediating particle energization. Consequently, the feedback from energetic particles results in a steeper power-law energy spectrum. These findings suggest that feedback from non-thermal energetic particles plays a crucial role in magnetic reconnection and particle acceleration.