Last Updated: 07/16/2024


Version: 2.5

The Versatile Electron Radiation Belt code (VERB) was developed by the Space Environment Modeling Group SEMG ( at the University of California, Los Angeles. The model has been described in Shprits et al., 2009, and Subbotin et al., 2010. It solves the Fokker-Planck equation for electron PSD [Schulz and Lanzerotti, 1974, Shprits et al., 2008b, Subbotin and Shprits, 2009]. The equation is solved using a finite differences approach and an implicit numerical scheme. The stability of such scheme is independent of the used time step. Following the approach used for the solution without mixed diffusion terms, described by Subbotin and Shprits[2009], the equation (1) is split into radial diffusion and local (energy, pitch angle, mixed) diffusion. The further separation of energy and pitch angle diffusion is impossible due to the existence of the mixed diffusion terms. Therefore, the implicit solution requires inversion of a model matrix of the 2-D operator on each time step. Inversion of such a big matrix is a quite time consuming computational operation, which is not required for the solution of the Fokker-Planck equation in the explicit formulation [Press et al., 1992]. However, the implicit scheme allows to use a longer model time step, while the time step in explicit scheme is limited by the Courant-Friedrichs-Lewy stability condition [Courant et al., 1928; Press et al., 1992], and the overall computational wall clock time with implicit scheme is lower.

The VERB code is written in C++, and was designed for use on a single-CPU computer and conforms to the C++ 2011 standard. The cross-platform code supports the compilation on various systems (Linux, Windows, Mac OS). Please see the link to the model description for more details


To improve the storm-based studies, the realistic field model will be included in the further model developments.


Inputs to VERB vary depending on the requested simulation. At a minimum, the user may just specify Kp and constant boundary conditions. GOES 13-15 measurements from the EPEAD (Energetic Proton, Electron and Alpha Detector) instruments may be used to scale the outer boundary in L-shell, which requires input of solar wind data in order to run the requested magnetic field model. These inputs are automatically generated for the requested model.


Outputs include the electron PSD (Phase Space Density) on the model grid, and optionally the invariant flux (electron flux computed from a dipole magnetic field model).

Model is time-dependent.

Change Log

Changed L grid size from 29 to 31. speed up in some routines

Updated diffusion Coefficients (main) Diffusion due to chorus waves: Wang et al. 2019, Wang and Shprits, 2019. Diffusion due to hiss waves: Orlova et al. 2016, Spasojevic et al. 2015


  • Geospace
  • Magnetosphere / Inner Magnetosphere / RadiationBelt

Space Weather Impacts

  • Near-earth radiation and plasma environment (aerospace assets functionality)



Code Languages: C++, Matlab


Publication Policy

In addition to any model-specific policy, please refer to the General Publication Policy.