Efficiency of proton-driven Weibel instability at thermalizing initially two-temperature astrophysical plasmas

Whether a faster-than-Coulomb collisionless mechanism equilibrates ion-electron plasmas with ions initially much hotter than electrons is a fundamental plasma physics question and important for understanding low-luminosity astrophysical accretion flows. Here we study whether Weibel instabilities driven by proton temperature anisotropy produce such a mechanism. From theory and particle-in-cell simulations, we find that although the Weibel instability amplifies magnetic fields much faster than the ionelectron collision rate, the ratio of the saturated magnetic energy to the initial ion energy scales as the fourth power of the electron to ion mass ratio for an initially unmagnetized plasma. The energy transferred to electrons is of order the saturated magnetic energy, and so the instability cannot induce a faster-than-Coulomb electron-ion equilibration. However, we suggest why the same instability for an initially modestly magnetized plasma would provide more efficient equilibration.