Shock Formation in Electron-Ion Plasmas: Mechanism and Timing

We analyze the formation of a collisionless shock in electron-ion plasmas in theory and simulations. In initially un-magnetized relativistic plasmas, such shocks are triggered by the Weibel instability. While in pair plasmas the shock starts forming right after the instability saturates [1,2], it is not so in electron-ion plasmas because the Weibel filaments at saturation are too small. An additional merging phase is therefore necessary for them to efficiently stop the flow. We derive a theoretical model for the shock formation time, taking into account filament merging in the nonlinear phase of the Weibel instability. This process is much slower than in electron-positron pair shocks, and so the shock formation is longer by a factor proportional to $\sqrt{m_i/m_e}\ln (m_i/m_e)$ [3]. \\ \\ (1) Bret et al, Physics of Plasmas 20, 042102 (2013). \\ (2) Bret et al, Physics of Plasmas 21, 072301 (2014). \\ (3) Stockem Novo et al, The Astrophysical Journal Letters, 803:L29 (2015).