Towards First-principle Characterization of Cosmic-ray Transport
  Coefficients from Multi-scale Kinetic Simulations
  A major uncertainty in understanding the transport and feedback of
cosmic-rays (CRs) within and beyond our Galaxy lies in the unknown CR
scattering rates, which are primarily determined by wave-particle interaction
at microscopic gyro-resonant scales. The source of the waves for the bulk CR
population is believed to be self-driven by the CR streaming instability
(CRSI), resulting from the streaming of CRs downward a CR pressure gradient.
While a balance between driving by the CRSI and wave damping is expected to
determine wave amplitudes and hence the CR scattering rates, the problem
involves significant scale separation with substantial ambiguities based on
quasi-linear theory (QLT). Here we propose a novel "streaming box" framework to
study the CRSI with an imposed CR pressure gradient, enabling first-principle
measurement of the CR scattering rates as a function of environmental
parameters. By employing the magnetohydrodynamic-particle-in-cell (MHD-PIC)
method with ion-neutral damping, we conduct a series of simulations with
different resolutions and CR pressure gradients and precisely measure the
resulting CR scattering rates in steady state. The measured rates show scalings
consistent with QLT, but with a normalization smaller by a factor of several
than typical estimates based on single-fluid treatment of CRs. A
momentum-by-momentum treatment provides better estimates when integrated over
momentum, but is also subject substantial deviations especially at small
momentum. Our framework thus opens up the path towards providing comprehensive
subgrid physics for macroscopic studies of CR transport and feedback in broad
astrophysical contexts.
