EPREM: Heliospheric Particle Acceleration Model

• EPREM is a physics-based numerical model that solves the focused transport equation on a co-moving Lagrangian grid to simulate particle acceleration and propagation.
• It couples with global MHD simulations to accurately capture CME-driven events by modeling shocks, compression fronts, and magnetic reconnection regions.
• The model produces time–intensity profiles, fluence spectra, and 3D spatial maps that are essential for validating observations and assessing space radiation risks.

Energetic Particle Radiation Environment Model (EPREM) is a physics-based numerical model for solar energetic particle acceleration and transport in the heliosphere. In current descriptions, EPREM solves the focused transport equation on a Lagrangian grid in a frame co-moving with the solar wind plasma, and it is used both in stand-alone configurations with idealized solar-wind and shock prescriptions and in coupled configurations driven by time-dependent magnetohydrodynamic simulations. Its standard products include time-intensity profiles, fluence spectra, and three-dimensional spatial distributions of energetic particles for event interpretation, model–data comparison, and radiation-environment assessment (Young et al., 19 Sep 2025, Linker et al., 2019, Guo et al., 2023).

1. Governing formulation and numerical representation

EPREM solves the focused transport equation for the particle distribution function on Lagrangian, co-moving simulation nodes that track plasma flow in the evolving solar-wind background. In the formulations described in the recent literature, the transport physics includes convection by the plasma flow, streaming along magnetic fields, adiabatic focusing, energy changes due to adiabatic processes, pitch-angle scattering, and source terms. In uncoupled implementations, perpendicular diffusion and drift can also be represented through an additional convection-diffusion equation, so the model can address both field-aligned transport and cross-field redistribution within a single simulation framework.

The numerical mesh is defined by nodes that move with the solar wind according to $\delta \vec{r} = \vec{V}\,\delta t$. Nodes are arranged on six logical surfaces forming a “cubed sphere,” and each stream follows a velocity path through the heliosphere. Stream observers report values at each node along a stream, whereas point observers are fixed locations in space that interpolate fields from surrounding nodes. This Lagrangian construction is intended to minimize numerical errors associated with strongly advected particle populations and to preserve the connection between the particle solution and the local plasma state (Young et al., 19 Sep 2025).

2. Coupling to coronal and heliospheric MHD frameworks

A major mode of EPREM operation is direct coupling to global MHD models of the corona and heliosphere. In the Solar Particle Event Threat Assessment Tool (STAT), CORHEL and MAS provide time-ordered three-dimensional MHD variables, including magnetic field $\mathbf{B}$, plasma velocity $\mathbf{V}$, and density $n$, and EPREM ingests these outputs to drive focused transport modeling. This coupling is used to investigate CME-driven solar particle events in the low corona, where the highest energy SEP events are generated. In the Bastille Day configuration, the coupled simulation models particle acceleration from 1 to 20 $R_\odot$, after which it models only particle transport. Region-growing interpolation and related diagnostics were introduced to convert EPREM’s scattered Lagrangian solution into continuous three-dimensional particle-flux maps, $r$–$\phi$ slices, and 1 AU longitude maps for comparison with observations (Linker et al., 2019, Young et al., 2020).

A second coupled configuration uses MAS as a thermodynamic MHD model of the solar corona and heliosphere, with the coronal domain spanning 1–30 $R_\odot$ and the heliospheric domain 28–230 $R_\odot$. In that setup, MAS solves for plasma density, temperature, and magnetic field while accounting for anisotropic thermal conduction, radiative losses, and wave-turbulence-driven coronal heating, and the dynamic outputs $\vec{B}$, $\mathbf{B}$0, and $\mathbf{B}$1 are ingested by EPREM. This suggests that EPREM is best understood not as a fixed-background transport code alone, but as a particle solver designed to operate inside event-specific, time-dependent plasma environments (Schwadron et al., 2024).

3. Acceleration regimes represented by EPREM

Within CME-driven applications, EPREM treats acceleration where plasma and magnetic-field compression is strong, such as at CME-driven shocks and compression fronts identified by large $\mathbf{B}$2 in the MHD solution. In the Bastille Day study, the model resolves the sites of most rapid acceleration close to the Sun and identifies maximum particle acceleration not just at the CME nose shock, but especially where field lines drape and bend around CME flanks. The resulting 1 AU fluence spectra exhibit broken-power-law behavior: over the low-energy range the fits agree with diffusive acceleration theory, while over the high-energy range they demonstrate variability in acceleration rate and mirror the inter-event variability observed in solar-cycle 23 ground level enhancement events (Young et al., 2020).

EPREM has also been used to represent energetic particles accelerated from quasi-separatrix layers and current sheets at the Sun. In that context, magnetic reconnection near the QSL drives reconnection exhausts and field-aligned flows, which in turn accelerate energetic particles, and the study describes the first global model of energetic particles accelerated from QSLs and above current sheets from the Sun. The acceleration is attributed to transient reductions and surges in $\mathbf{B}$3 with relatively little plasma compression, and the reconnection process also releases material previously contained within closed magnetic field structures, which are often rich in heavy ions and $\mathbf{B}$4He ions. A plausible implication is that EPREM’s domain of application extends beyond CME-front acceleration to the production of seed populations in magnetically complex coronal source regions (Schwadron et al., 2024).

4. Event-specific simulations and validation against observations

The best-documented EPREM event study in the supplied literature is the 14 July 2000 “Bastille Day” solar proton event. In that case, the coupled EPREM–CORHEL simulation roughly reproduces the peak event fluxes, and timing and spatial location of the energetic particle event, while the peak fluxes and overall variation within the first few hours agree well with GOES-08 observations. Plots of integral flux envelopes from multiple simulated observers near Earth further improve the comparison to observations, and preliminary STAT comparisons with NOAA GOES measurements show first-order agreement in timing and magnitude during the early coronal-driven phase.

The same study also isolates an important limitation. Because the modeled CME moves beyond the inner simulation boundary after several hours, the agreement degrades once acceleration is no longer represented outside the coronal domain. The published interpretation is therefore specific: EPREM accurately describes the acceleration processes in the low corona and resolves the sites of most rapid acceleration close to the Sun, but late-phase evolution depends on extending the coupled domain or incorporating heliospheric MHD backgrounds beyond 20 $\mathbf{B}$5 (Young et al., 2020, Linker et al., 2019).

5. Widespread SEP events, transport coefficients, and cross-field propagation

When not coupled to an external MHD model, EPREM functions in an uncoupled mode in which an ideal cone-shock is injected into a homogeneous background solar wind. In the 2025 parameter study of widespread SEP events, a baseline simulation was compared with seven variations in which a single parameter differed from its baseline value. All simulations exhibit complex profiles of SEP flux as a function of time and energy, with clear dependence on parameters related to diffusion, mean free path, and shock profile; all simulations also exhibit significant longitudinal spread in SEP flux, but for certain parameter values there exists a decrease or absence in SEP flux at observers located $\mathbf{B}$6 from the shock origin.

Within that formulation, the parallel mean free path can be prescribed as

$\mathbf{B}$7

or as

$\mathbf{B}$8

Suppressing perpendicular diffusion sharply constricts the angular extent of the SEP event, whereas with perpendicular diffusion widespread SEP events are produced. Increasing $\mathbf{B}$9 reduces acceleration to high energies, and a smoother, broader shock transition produces generally lower and less widespread SEP flux. This parameterization makes EPREM suitable for controlled numerical experiments on the morphology of observed SEP events and on the state of the solar wind through which the driving CME propagates (Young et al., 19 Sep 2025).

A related transport result bears directly on how EPREM-type models are interpreted. Work on turbulence strength and meandering field lines argued that modelling SEP cross-field transport as spatial diffusion has been shown to be insufficient without use of unrealistically large cross-field diffusion coefficients, because early-time propagation across the mean field direction is not diffusive as the particles propagating along meandering field lines. The same study reported the scaling $\mathbf{V}$0 for the Gaussian fitting of the longitudinal distribution of maximum intensities. This suggests that EPREM parameterizations of perpendicular transport are decisive for reproducing rapid access across longitude and the wide event extents inferred from multi-spacecraft SEP observations (Laitinen et al., 2018).

6. Seed populations, extreme-event scenarios, and position in the modeling landscape

EPREM–MAS simulations of QSLs and current sheets connect the model to the problem of SEP seed-population formation. In those simulations, common sources of energetic particles were discovered over broad longitudinal distributions in the background solar wind, far from the sites of particle acceleration driven by compressions and shocks in front of CMEs, and these were identified as accelerated energetic particles from the QSLs and current sheets. Even in the absence of a CME, persistent sources of suprathermal and energetic particles were simulated at QSLs and the heliospheric current sheet, leading to the conclusion that QSL-driven acceleration provides a persistent, dynamic seed population for CME/shock-driven events. The predicted seed populations are expected to be rich in $\mathbf{V}$1He and heavy ions (Schwadron et al., 2024).

For radiation-environment applications, models such as EPREM require input fluence spectra for boundary or initial conditions. A recent methodology relates the soft X-ray flux $\mathbf{V}$2 of the driving solar flare to a “worst-case” event-integrated proton fluence spectrum, with the scaling

$\mathbf{V}$3

and uses both a single inverse power law and a Band function to represent integral spectra across energy or rigidity. The stated implication for EPREM is practical: this provides a direct, physically-motivated method to specify upper-bound input spectra for hypothetical or extrapolated flare scenarios, including spacecraft mission design, lunar or Mars radiation risk, and exoplanet studies (Herbst et al., 9 Feb 2025).

Within the broader heliospheric radiation-environment literature, EPREM is not discussed by name in a recent community review, but the type of model represented by EPREM—a fully physics-based numerical transport model of energetic particle acceleration and propagation in the heliosphere, frequently coupled to MHD simulations of solar eruptions—is described as central to the next generation of predictive SEP and GLE modeling. The same review emphasizes several limitations that apply directly to EPREM-class tools: physics-based models are computationally expensive, magnetic connectivity and transport mechanisms are poorly constrained near the Sun, high-energy and multi-point observations remain limited, and standardized validation and model intercomparison are still needed. In that sense, EPREM occupies a well-defined position in the current model taxonomy: it is a research-grade, physics-based framework whose value depends on realistic plasma backgrounds, transport parameterization, and rigorous validation against multi-spacecraft data (Guo et al., 2023).