Left panel: Phase space densities of energetic protons measured with HSTOF at different distances upstream of the shock of the Bastille Day event. The spectra are plotted as a function of the wavenumber k in units of the wavenumber k1MeV of an Alfvén wave that resonates with a proton at 1 MeV and at zero pitch angle.
Right panel: The power spectral densities are plotted for the same distances. The scale of the wavenumber k = 2 π fA / VA of all panels refers to Alfvén waves propagating parallel within about 30° to the ambient magnetic field in anti-sunward direction.