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Reconciling cosmic-ray transport theory with phenomenological models motivated by Milky-Way data

Phenomenological models of cosmic-ray (CR) transport in the Milky Way (MW) can reproduce a wide range of observations assuming that CRs scatter off of magnetic-field fluctuations with spectrum $\propto k^{-δ}$ and $δ\sim [1.4,1.67]$. We study the extent to which such models can be reconciled with current microphysical theories of CR transport, specifically self-confinement due to the streaming instability and/or extrinsic turbulence due to a cascade of MHD fast modes. We first review why it is that on their own neither theory is compatible with observations. We then highlight that CR transport is a strong function of local plasma conditions in the multi-phase interstellar medium (ISM), and may be diffusive due to turbulence in some regions and streaming due to self-confinement in others. A multi-phase combination of scattering mechanisms can in principle reproduce the main trends in the proton spectrum and the boron-to-carbon ratio (B/C). However, models with a combination of scattering by self-excited waves and fast-mode turbulence require significant fine-tuning due to fast-mode damping, unlike phenomenological models that assume undamped Kolmogorov turbulence. The assumption that fast modes follow a weak cascade is also not well justified theoretically, as the weak cascade is suppressed by wave steepening and weak-shock dissipation even in subsonic turbulence. These issues suggest that there may be a significant theoretical gap in our understanding of MHD turbulence. We discuss a few topics at the frontier of MHD turbulence theory that bear on this (possible) gap and that may be relevant for CR scattering.