iPATH

The iPATH model is a 2-D MHD SEP model that simulates Diffusive Shock Acceleration (DSA) at CME-driven shocks and follows the subsequent transport of energetic particles through the inner heliosphere. IPATH models the background solar wind and CME-driven shocks at the ecliptic plane starting at 0.05 AU and produces time profiles of SEP intensity spectra and pitch angle distributions as outputs at selected vantage points (e.g., at Earth or Mars). It considers both perpendicular and parallel diffusive factors of energetic particles, which come from Nonlinear Guiding Center Theory (NLGC) and Quasi-Linear Theory (QLT) respectively. The transport module is a Monte Carlo code which follows test particles through space described by the FTE and is set up for parallel computations. This model is improved over the original PATH model which was 1-D.

iPATH first creates the shock perturbation along the inner boundary, and propagates the CME outward with the forward shock region tracked with a 2-D onion-shell model. For each time step, a new outer shell is created based on the shock speed and all previous shells convect and adiabatically expand with the solar wind. Then accelerated particle distributions are calculated along the whole shock front, based on the diffusive shock acceleration. Accelerated particles are then allowed to diffuse back to the shock complex, and between each parcel behind the shock via parallel and perpendicular diffusion. This gives the distribution function in each shock parcel at each time step, which is important for the ESP phase when the shock arrives at the observer. Once a particle has moved a certain distance during a single time step, it escapes the shock and is transported through the unperturbed solar wind via a focused transport scheme, which includes terms for weak scattering and cross-field diffusion from the random walk of magnetic field lines. The FTE is solved using a backward stochastic differential equation approach until a steady state is found where ensemble averages of many test particle paths give the full particle distribution function.

Like other models using CME information as inputs, iPATH’s performance as a prediction model relies on how early we can acquire good quality CME parameters from observations. As the inner boundary is set at 0.05 AU (10 Rsun) and the shock is formed even further in, it cannot capture the SEP acceleration happening in the low corona and does not produce output for the first couple of hours of the events. iPATH is not able to fully capture the effects of previous CMEs without modifications on the model so the operational version is best suited for single CME events. The background solar wind used in iPATH is a simple homogeneous Parker spiral model, which cannot capture some complex solar wind geometries in a specific event. But this simplification is efficient for general prediction purposes.

• Background solar wind parameters based on 1 AU observations (solar wind density, speed, temperature, and magnetic field strength)

• CME parameters (CME speed, width, location, and perturbation duration)

• Turbulence parameters (turbulence level, turbulence spectral parameters, and radial dependencies of these parameters, for advanced users)

• Suprathermal seed particle input (suprathermal particle energy spectral parameters)

• Observer locations (radius, longitude)

• Time profiles for energetic proton/heavy ion intensities (differential fluxes) at a wide energy range (from hundreds of keVs to GeVs) at the chosen observer locations

• Event-integrated fluences (in MeV-1cm-2)

• Time profiles for integral flux above certain energies (in pfu)

• Figures for flux/fluence results and CME/shock configurations.