Xiaohang Chen

The propagation of solar energetic particles (SEPs) through the heliosphere is primarily guided by the interplanetary magnetic field (IMF), which is embedded in the solar wind plasma. Large-scale IMF structures can drive transient variations in SEP intensities. Using Solar Orbiter observations, we identify a distinct class of SEP variations: SEP flux deflections (SFDs), which are commonly detected in SEP events and frequently recur multiple times within a single event. SFDs are characterized by a sudden change in SEP flux directions where the intensities drop in one direction and increase in another direction, without a significant net change in total flux magnitude. These deflections occur dispersionlessly across a broad energy range—from tens of keV to over 100 MeV—and exhibit steep intensity gradients. SFDs appear to be associated with magnetic flux tubes whose boundaries exhibit features consistent with tangential discontinuities. We further show that the solar wind inside these structures exhibits distinct plasma properties, and that the SEP streaming direction within SFDs aligns closely to the flux-tube axis. These observations are consistent with magnetic flux tubes being a prevalent structure of the solar wind, and suggest that SEPs can serve as an effective diagnostic tool for probing the topology and dynamics of solar wind structures.

We present a detailed investigation of the shock properties associated with solar energetic particle (SEP) events that exhibit a concave (“nose-like”) shape in their energy spectrogram, characterized by inverse velocity arrival (IVA) of the particles, where high-energy particles arrive later than mid-energy ones. Using measurements from Solar Orbiter and Parker Solar Probe between 2018 and 2025, we identify 26 such SEP events and reconstruct the observed shock fronts in three dimensions. We derive shock parameters along the magnetic field lines connected to each spacecraft using kinematic modeling and coronal magnetohydrodynamic simulations. Our analysis indicates that IVA-SEP events arise due to the spatial and temporal evolution of the shock properties and magnetic connectivity. In most of the cases analyzed here, the magnetic connectivity starts on the flanks of coronal mass ejection-driven shocks, where shocks tend to be weak, and shifts toward the shock apex, sampling stronger portions of the shock front. This evolution of the shock properties at the connected field lines likely leads to the delayed arrival of high-energy particles and the progressive hardening of the SEP energy spectrum, observed in some of the events. We find a correlation between the transition energy at which the IVA begins and the shock speed along the connected field lines, consistent with expectations from time-dependent diffusive shock acceleration. Our results underscore the importance of the evolving shock properties, magnetic connectivity, and instrumental sensitivity in shaping SEP intensity profiles and the formation of IVA signatures.

The transport of solar energetic particles (SEPs) through the heliosphere is governed by the interplanetary magnetic field (IMF) embedded in the solar wind plasma. Large-scale fluctuations in the IMF give rise to the transient variation in SEP intensities. Here, we present Solar Orbiter (SolO) observations of a distinct class of SEP flux variations: short-timescale (~1 hr) directional flux reversals (DFRs). Data from the Energetic Particle Detector (EPD) reveal that these reversals are a common feature in SEP events, occurring simultaneously across a wide energy range (keV to tens of MeV) and exhibiting steep intensity gradients. Unlike classic 'dropout' events—where intensity decreases isotropically—DFRs display a asymmetric signature where a intensity drop in one direction coincides with a spike in another. These intermittent variations are associated with flux-rope magnetic structures and distinct solar wind properties, which serves as direct evidence that the spacecraft has encountered a new solar wind stream with a different magnetic field connectivity. These observations demonstrate that SEPs act as an effective probe of solar wind structures, providing new insights into their nature.

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 ∼1 MeV exhibited a normal velocity dispersion, while higher-energy particles displayed an inverse velocity arrival (IVA) 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. Our results reveal that the IVA 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.

We report on unusual magnetic wave activity seen in a region between the crossing of a current sheet and an interplanetary shock by the Parker Solar Probe (PSP). The PSP observed a shock driven by an interplanetary coronal mass ejection on 2021 June 30 at 14:58:19 at 0.76 au. Prior to the arrival of the shock, PSP encountered a current sheet on 2021 June 30 at 14:54:54. Through an analysis of the magnetic field and plasma measurements, we determine that the shock is a fast forward quasi-parallel shock. The magnetic field in the region between the current sheet and the shock was characterized by enhanced magnetic wave activity. To investigate the plasma waves in the region, a wavelet technique is applied to obtain the magnetic field fluctuation power spectral density, normalized reduced helicity, and magnetic field fluctuation hodogram. The results of the analysis reveal that the waves present in this region demonstrate right-hand polarization and have a relatively broad range of frequencies in the spacecraft frame. Our analyses reveal the simultaneous presence of low-frequency magnetohydrodynamic waves and whistler waves within this region and note that these waves become active precisely at the time of the current sheet crossing. The coexistence of different types of waves within this region presents a unique opportunity for further investigation and deepening our understanding of the underlying physical mechanisms governing these phenomena.

Solar energetic particles (SEPs) can pose hazardous radiation risks to both humans and spacecraft electronics in space. Numerical modeling based on first principles offers valuable insights into the underlying physics of SEPs and provides synthetic observables for SEPs at any time and location in the inner heliosphere. In this work, we present a numerical scheme, which conserves the number of particles based on integral relations for Poisson brackets, to solve the kinetic equation for particle acceleration and transport processes. We implement this scheme within the Space Weather Modeling Framework, developed at the University of Michigan. In addition, we develop a new shock-capturing tool to study the coronal mass ejection-driven shock originating from the low solar corona. These methodological advancements are applied to conduct a comprehensive study of a historical SEP event on 2013 April 11. Observations from multiple spacecraft, including the Solar and Heliospheric Observatory, Solar Dynamics Observatory, Geostationary Operational Environmental Satellite, Advanced Composition Explorer near Earth, and STEREO-A/B, are used for model–data comparison and validation. We show synthetic observables, including extreme ultraviolet and white-light images, proton time–intensity profiles, and energy spectra, and discuss their differences and probable explanations compared to observations. Our simulation results demonstrate the application of the Poisson bracket scheme with a particle solver to simulating a historical SEP event. We also show the capability of extracting the complex shock surface using our shock-capturing tool and understand how the complex shock surface affects the particle acceleration process.

On 2022 September 5, during Parker Solar Probe's (PSP) 13th encounter, a fast shock wave and a related solar energetic particle (SEP) event were observed as the spacecraft approached the perihelion of its orbit. Observations from the Integrated Science Investigation of the Sun (IS⊙IS) instrument suite show that SEPs arrived at the spacecraft with a significant delay from the onset of the parent solar eruption and that the first arriving SEPs exhibited an inverse velocity dispersion (IVD) for energetic protons above ~1 MeV. Utilizing data from multiple spacecraft, we investigate the eruption dynamics and shock wave propagation. Our analysis includes 3D shock modeling and SEP transport simulations to examine the origins of this SEP event and explore the causes of the delayed SEP onset and the observed IVD. The data-driven SEP simulation reproduces the SEP event onset observed at PSP, its evolving energy spectrum, and the IVD. This IVD is attributed to a relatively slow, ongoing particle acceleration process occurring at the flank of the expanding shock wave intercepted by PSP. This has significant implications for the role of shocks in the release of SEPs at widespread events and for methods used to infer the SEP release times. Furthermore, the match between the simulation and observations worsens when cross-field diffusion is considered, indicating that SEP diffusion had a minor effect on this event. These findings underscore the complexity of SEP events and emphasize the need for advanced modeling approaches to better understand the role of shock waves and other physical processes in SEP acceleration and release.

On September 5, 2022, during Parker Solar Probe's (PSP) 13th encounter, a fast shock wave and a related solar energetic particle (SEP) event were observed as the spacecraft approached the perihelion of its orbit. Observations from the Integrated Science Investigation of the Sun (ISOIS) instrument suite show that SEPs arrived at the spacecraft with a significant delay from the onset of the parent solar eruption and that the first arriving SEPs exhibited an Inverse Velocity Dispersion (IVD) for energetic protons above $\sim$1~MeV. Utilizing data from multiple spacecraft we investigate the eruption dynamics and shock wave propagation. Our analysis includes 3D shock modeling and SEP transport simulations to examine the origins of this SEP event and explore the causes of the delayed SEP onset and the observed IVD. The data-driven SEP simulation reproduces the SEP event onset observed at PSP, its evolving energy spectrum and the IVD. This IVD is attributed to a relatively slow, ongoing particle acceleration process occurring at the flank of the expanding shock wave intercepted by PSP. This has significant implications for the role of shocks in the release of SEPs at widespread events and for methods used to infer the SEP release times. Furthermore, the match between the simulation and observations worsens when cross-field diffusion is considered, indicating that SEP diffusion had a minor effect on this event. These findings underscore the complexity of SEP events and emphasize the need for advanced modelling approaches to better understand the role of shock waves and other physical processes in SEP acceleration and release.

Diffusion coefficients of energetic charged particles in turbulent magnetic fields are a fundamental aspect of diffusive transport theory but remain incompletely understood. In this work, we use quasi-linear theory to evaluate the spatial variation of the parallel diffusion coefficient κ _∥ from the measured magnetic turbulence power spectra in the inner heliosphere. We consider the magnetic field and plasma velocity measurements from Parker Solar Probe made during Orbits 5–13. The parallel diffusion coefficient is calculated as a function of radial distance from 0.062 to 0.8 au, and the particle energy from 100 keV to 1 GeV. We find that κ _∥ increases exponentially with both heliocentric distance and energy of particles. The fluctuations in κ _∥ are related to the episodes of large-scale magnetic structures in the solar wind. By fitting the results, we also provide an empirical formula of κ _∥ = (5.16 ± 1.22) × 10¹⁸ r ^1.17±0.08 E ^0.71±0.02 (cm² s⁻¹) in the inner heliosphere, which can be used as a reference in studying the transport and acceleration of solar energetic particles as well as the modulation of cosmic rays.