Authors: Weihao Liu (University of Michigan), Igor V. Sokolov (University of Michigan), Ofer Cohen (University of Massachusetts Lowell), Lulu Zhao (University of Michigan), Tamas Gombosi (University of Michigan)

Solar energetic particles (SEPs) and galactic cosmic rays (GCRs) are the primary sources of radiation hazards in space, thus requiring accurate predictions from models. In this study, we implement a high-resolution scheme using Poisson brackets to simulate the particle acceleration and transport processes. This scheme is efficient for numerical simulations as it conserves the number of particles and maintains the total-variation-diminishing (TVD) property, thus providing high-quality numerical results. It enables time-accurate SEP spectrum simulations and steady-state GCR spectrum modeling, within the Space Weather Modeling Framework (SWMF).

For SEP simulations, we use the magnetohydrodynamics (MHD) model, AWSoM-R, to simulate the background solar wind parameters, driven by the hourly-updated GONG magnetograms. A coronal mass ejection is launched by placing an imbalanced Gibson-Low flux rope on top of the active region. All the MHD data are coupled to run the SEP spectra, with the Poisson bracket scheme applied to the multiple magnetic field line tracker (M-FLAMPA). The spectra and integral intensity are compared with the SOHO/ERNE and GOES measurements, demonstrating the promising capability of the Poisson bracket scheme.

Besides, we apply the Poisson bracket scheme to simulate the steady-state GCR spectra. GCRs are generated in galactic sources and propagate until they approach the heliopause, where their Local Interstellar Spectrum (LIS) can be used as boundary condition in GCR models. We employ the modulation potential to quantify the average energy loss of GCRs inside the heliosphere and map the LIS to smaller heliocentric distances. This provides the boundary condition for GCRs at the outer boundary of the computational domain in our model (2-5 AU). Voyager-1 measurements are used to determine the LIS, with the modulation potential evaluated from Usoskin et al (2005). Finally, we show the modeled GCR proton spectrum in 2013 April and compare it with the PAMELA and AMS-02 measurements, demonstrating the strengths and potentials of using the Poisson bracket scheme in simulations.