Does Diffusive Shock Acceleration Reach Steady State? Insights from a Near-Sun Shock Observed by Parker Solar Probe

Abstract: Collisionless shocks accelerate particles at a rate set by the diffusion coefficient of those particles in waves they themselves generate. Theory fixes that coefficient only in steady state, and no measurement has tested whether an evolving shock ever reaches that state. We report Parker Solar Probe observations of a fast, near-parallel interplanetary shock at 0.24 au, encountered four hours after eruption, with the upstream waves and the protons they scatter recorded on the same magnetic field line. From the wave spectra alone we derive the parallel mean free path of 0.05-30 MeV protons, resolved in energy and in distance from the shock. The mirror force of the measured compressive fluctuations supplies the scattering through the pitch angles that gyroresonance cannot reach. The mean free path grows with distance nearly as the steady self-generated solution requires, yet the steady balance holds at one energy only, near 1.3 MeV. The intensity profiles are a factor of two shallower than the measured coefficient predicts, because the waves are still growing. Confinement fails between 2.3 and 6 MeV, beginning a factor of two below what the age of the shock allows. The growth of the waves its own particles drive, rather than its age or its size, limits the energy an evolving shock confines.