The Streaming Limit of Solar Energetic-Particle Intensities

As solar energetic particles (SEPs) stream outward along the interplanetary magnetic field after acceleration by shock waves near the Sun, their intensities are limited by scattering against self-generated Alfv\'en waves, trapping the particles near their source. This streaming limit varies with the magnetic rigidity of the particle and with distance from the source. Pitch-angle coupling can cause higher-energy protons to suppress the intensities of lower-energy ions causing flattened low-energy spectra on the early SEP intensity plateau. At sufficiently high energies, particle flow and wave trapping of particles weakens and the SEP spectra steepen, forming spectral "knees".