Four-Dimensional Anisotropic Diffusion of Cosmic Rays in Realistic Galactic Magnetic Fields

The origin of the spectral break (or “knee”) in the cosmic-ray flux near 4 PeV remains debated, with uncertainty over whether it reflects a universal Galactic property or results from a combination of local factors. In this work, we demonstrate that the observed break can be naturally explained by anisotropic cosmic-ray diffusion in a realistic Galactic magnetic field, without requiring a high-energy cutoff at the source. We develop a four-dimensional propagation diffusion model based on a fully anisotropic diffusion tensor computed via the trajectory method in a two-component magnetic field. Our model accounts for all nine tensor components in Galactic coordinates, including off-diagonal terms from local field-aligned diffusion. This approach reproduces the knee feature as a consequence of energy-dependent diffusion and predicts its spatial variation across the Galaxy, governed by the structure and turbulence of the magnetic field. Additionally, the slope of the spectrum is shown to depend on the degree of anisotropy. Using this framework, we calculate cosmic-ray spectra in various Galactic regions and derive the corresponding diffuse gamma-ray flux. The resulting spectral shapes agree well with observations from LHAASO and Fermi-LAT.