The delayed arrival of faster solar energetic particles as a probe into the shock acceleration process

The particle acceleration and transport process during solar eruptions is a critical and long-standing problem in space plasma physics. Through decades of research, it is well accepted that particles with higher energies released during a solar eruption arrive at observers earlier than the particles with lower energies, forming a well-known structure in the dynamic energy spectrum called particle velocity dispersion, as frequently observed by space missions. However, this picture is challenged by new observations from NASA's Parker Solar Probe and ESA's Solar Orbiter that show an unexpected inverse velocity dispersion (IVD) phenomenon, where particles with higher energies arrive later at the observer. Facing this challenge, here we report the recent observations of such IVD structures with 10 solar energetic proton events observed by Solar Orbiter, and then analyze the mechanisms causing this unusual phenomenon. We suggest that shock diffusive acceleration, with respect to magnetic reconnection, is probably a dominant mechanism to accelerate protons to tens of mega-electron-volts in such events where particles need longer time to reach higher energies. Furthermore, we determine, innovatively, the physical conditions and time scales during the actual shock acceleration process that cannot be observed directly.