Website latest update on  Sept 10, 2018

Welcome to the HelMod Website. In these pages you can find information about the Solar Modulation Model for the propagation of Galactic Cosmic Rays through the Heliosphere from the Termination shock down to Earth.

As advertised on the GALPROP website, HelMod website can be used as a a service package to seamlessly calculate the effects of the heliospheric modulation for GALPROP output files.

HelMod is a 2D Monte Carlo model to simulate the solar modulation of galactic cosmic rays. The model is based on the Parker transport equation which contains diffusion, convection, particle drift and energy loss. Following the evolution of the solar activity in time, we are able to modulate the local interstellar spectra (LIS) of cosmic ray species, assuming their isotropy beyond the termination shock, down to the Earth's location inside the heliosphere.

The current HelMod Version is the result from a continous development since 1998 (Monte-Carlo approach to Galactic Cosmic Ray propagation in the Heliosphere, Nucl. Phys B-Proc Sup). The latest review on HelMod was published in 2017 (Propagation of Cosmic Rays in Heliosphere: the HelMod Model. Adv. Space Res. Available online 27 April 2017)

In the present website version, a solar modulation calculator is available for Cosmic Rays experiments carried out during solar Cycle 23 and 24.

In the 2D-HelMod code version 1.0 the standard Parker field without drifts was implemented;

From version 1.2 the dependence on the particle drift was added;

From version 1.4 the Parker magnetic field was modified in polar regions.

From version 1.5 the Solar Wind description was revisited for high and low activity periods, the Heliosphere was divided in regions related to spatial propagation of turbulence from Sun. Introduced the possiblity to evaluate solar modulation for electrons and positrons.

From version 2.0 the heliospheric magnetic field was modified in polar regions to accounts for different latitudinal gradients in opposite solar polarities.

From version 2.5 the spatial depenence of parallel diffusion coefficient was revisited according to Ulysses measurements of time variation cosmic rays counting rate.

From version 3.0 The numerical scheme was revisited and a backward-in-time approach adopted. The rigidity dependence of parallel diffusion coefficient revisited according to PAMELA and AMS-02 data. Introduced the possibility of evaluate solar modulation of ions. Developed an additional python module to link GALPROP LIS with HelMod results. From version 3.0.1, the online calculator and solar modulator accept the LIS file as a plain text.

From version 3.2 A systematic cross check between Solar Modulator and Online Calculator was performed for proton, antiproton and helium.

From version 3.4 Online version aligned with published model in Boschini et al 2017.

From version 3.4.2 the Online Calculator with advanced interface is available! This advanced interface allow to Users to modify selected HelMod Parameters.

From version 3.4.5 the Solar Modulator for Ions with advanced interface is available! 

From version 3.5.0 the Forecast Modulator  is available! 

Relevant result pictures from HelMod publications can be found in Results page.


This project is part of the activities on going at the AMS-02 Milano-Bicocca (Italy) group and IEP-SAS space physic (Kosice, Slovakia).

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Example of modulated spectrum for Proton for the period corresponding to AMS-02 Averaged data [Boschini et al. 2017]