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Formation of the Cosmic-Ray Halo: The Role of Nonlinear Landau Damping
We present a nonlinear model of a self-consistent Galactic halo, where the processes of cosmic-ray (CR)
propagation and excitation/damping of MHD waves are included. The MHD turbulence that prevents CR escape
from the Galaxy is entirely generated by the resonant streaming instability. The key mechanism controlling the
halo size is the nonlinear Landau (NL) damping, which suppresses the amplitude of MHD fluctuations and, thus,
makes the halo larger. The equilibrium turbulence spectrum is determined by a balance of CR excitation and NL
damping, which sets the regions of diffusive and advective propagation of CRs. The boundary zcr(E) between the
two regions is the halo size, which slowly increases with the energy. For the vertical magnetic field of ∼1 μG, we
estimate zcr ∼ 1 kpc for GeV protons. The derived proton spectrum is in a good agreement with observational data.