Evidence of Time-Dependent Diffusive Shock Acceleration in the 2022 September 5 Solar Energetic Particle Event

On 2022 September 5, a large solar energetic particle (SEP) event was detected by Parker Solar Probe (PSP) and Solar Orbiter (SolO), at heliocentric distances of 0.07 and 0.71 au, respectively. PSP observed an unusual velocity-dispersion signature: particles below $\sim$1 MeV exhibited a normal velocity dispersion, while higher-energy particles displayed an inverse velocity arrival feature, with the most energetic particles arriving later than those at lower energies. The maximum energy increased from about 20-30 MeV upstream to over 60 MeV downstream of the shock. The arrival of SEPs at PSP was significantly delayed relative to the expected onset of the eruption. In contrast, SolO detected a typical large SEP event characterized by a regular velocity dispersion at all energies up to 100 MeV. To understand these features, we simulate particle acceleration and transport from the shock to the observers with our newly developed SEP model - Particle ARizona and MIchigan Solver on Advected Nodes (PARMISAN). Our results reveal that the inverse velocity arrival and delayed particle onset detected by PSP originate from the time-dependent diffusive shock acceleration processes. After shock passage, PSP’s magnetic connectivity gradually shifted due to its high velocity near perihelion, detecting high-energy SEPs streaming sunward. Conversely, SolO maintained a stable magnetic connection to the strong shock region where efficient acceleration was achieved. These results underscore the importance of spatial and temporal dependence in SEP acceleration at interplanetary shocks, and provide new insights to understand SEP variations in the inner heliosphere.

💡 Research Summary

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The 2022 September 5 solar energetic particle (SEP) event was observed simultaneously by Parker Solar Probe (PSP) at 0.07 au and Solar Orbiter (SolO) at 0.71 au. PSP recorded a highly unusual onset: particles below ~1 MeV displayed the expected early‑arrival, velocity‑dispersion pattern, whereas particles above 1 MeV arrived later than the lower‑energy ones, producing an “inverse velocity arrival” (IVA) signature. Moreover, the inferred solar particle release (SPR) time at PSP was ~35 minutes later than the CME eruption time, and the maximum particle energy rose from ~20–30 MeV upstream of the shock to >60 MeV downstream. In contrast, SolO observed a classic SEP event with normal velocity dispersion across the full energy range up to >100 MeV.

To explain these disparate observations, the authors employed a newly developed, data‑driven SEP model called PARMISAN (Particle ARizona and MIchigan Solver on Advected Nodes). PARMISAN couples a three‑dimensional magnetohydrodynamic (MHD) simulation of the CME‑driven shock with a kinetic particle transport solver that includes spatially and momentum‑dependent diffusion, convection, and adiabatic energy changes. The model injects particles at the shock using a time‑dependent diffusive shock acceleration (DSA) formalism, where the acceleration time τ_A depends on the local diffusion coefficient κ, the shock geometry, and the shock’s evolution.

Simulation results reproduced the key PSP features: (1) early in the event, κ is small only for low‑energy particles, so they are accelerated and released quickly, yielding normal dispersion. High‑energy particles require a longer τ_A; because the shock is still forming and κ is larger, their release is delayed, creating the IVA signature. (2) As PSP crossed the shock and continued its rapid perihelion orbit, its magnetic footpoint drifted sunward, moving the magnetic connection from the upstream acceleration region to the downstream side. Consequently, PSP observed high‑energy particles streaming sunward after shock passage, consistent with the observed anti‑sunward anisotropy. (3) The downstream increase of turbulence reduces κ, shortening τ_A and allowing particles to reach >60 MeV, matching the observed rise in maximum energy.

For SolO, the model shows that its more distant, slower orbit kept the magnetic connection relatively stable and continuously linked to the strong, high‑efficiency acceleration region of the shock. Hence SolO recorded a conventional SEP time profile with normal velocity dispersion and high peak intensities across all energies.

The study demonstrates that (i) DSA at CME‑driven shocks is intrinsically time‑dependent; the acceleration efficiency evolves as the shock propagates and its turbulence level changes, and (ii) the observer’s orbital motion and resulting magnetic connectivity variations can dramatically reshape the observed SEP onset, energy spectrum, and anisotropy. The IVA and delayed SPR at PSP constitute the first direct observational evidence of time‑dependent DSA in the inner heliosphere.

These findings have important implications for SEP forecasting: models must incorporate the spatial‑temporal evolution of shock parameters and the dynamic magnetic connectivity of spacecraft, especially for missions operating close to the Sun. The authors suggest that extending PARMISAN to a broader set of events will test the generality of the results and help develop real‑time SEP warning tools that account for both shock evolution and observer motion.