Cosmic-ray hydrodynamics: Alfv\'en-wave regulated transport of cosmic
  rays
  Star formation in galaxies appears to be self-regulated by energetic feedback
processes. Among the most promising agents of feedback are cosmic rays (CRs),
the relativistic ion population of interstellar and intergalactic plasmas. In
these environments, energetic CRs are virtually collisionless and interact via
collective phenomena mediated by kinetic-scale plasma waves and large-scale
magnetic fields. The enormous separation of kinetic and global astrophysical
scales requires a hydrodynamic description. Here, we develop a new macroscopic
theory for CR transport in the self-confinement picture, which includes CR
diffusion and streaming. The interaction between CRs and electromagnetic fields
of Alfv\'enic turbulence provides the main source of CR scattering, and causes
CRs to stream along the magnetic field with the Alfv\'en velocity if resonant
waves are sufficiently energetic. However, numerical simulations struggle to
capture this effect with current transport formalisms and adopt regularization
schemes to ensure numerical stability. We extent the theory by deriving an
equation for the CR momentum density along the mean magnetic field and include
a transport equation for the Alfv\'en-wave energy. We account for energy
exchange of CRs and Alfv\'en waves via the gyroresonant instability and include
other wave damping mechanisms. Using numerical simulations we demonstrate that
our new theory enables stable, self-regulated CR transport. The theory is
coupled to magneto-hydrodynamics, conserves the total energy and momentum, and
correctly recovers previous macroscopic CR transport formalisms in the
steady-state flux limit. Because it is free of tunable parameters, it holds the
promise to provide predictable simulations of CR feedback in galaxy formation.
