The 3D numerical modeling of the solar modulation of galactic protons and helium nuclei related to observations by PAMELA between 2006 and 2009

A simulation study of galactic proton modulation from solar minimum to maximum conditions

“…The rigidity dependence of K , indicating the two power-law slopes, at Earth is illustrated in Figure 1 as the corresponding parallel mean free paths (MFP; λ ) for four selected times; with K = λ(v/3) where v is the particle speed and β = v/c, with c the speed of light. How K relates to K ⊥r and K ⊥θ has been described in detail by [6,8] and is not repeated here; see also [9]. The model requires the determination of 27-day averaged values for all modulation parameters that vary with time and as such with solar activity e.g.…”

“…These calculated averages establish realistic heliospheric conditions as they are propagated into the heliosphere with the solar wind, which latitudinal dependence is also changing from solar minimum to maximum. See [5,6,8] for an elaborate discussion of the details of this approach as applied to GCR data sets observed by PAMELA (e.g. [10,17]) and for AMS02 (e.g.…”

“…This stirred up a series of modulation modelling studies in order to establish what adjustment need to be made as required in mathematical and numerical models with respect to the elements of the diffusion and drift tensor in the relevant transport equation in order to reproduce GCR observations at Earth. In this context, [4,5] modelled proton, electron and positron spectral features observed by PAMELA, whereas [6] studied the modelling of GCR protons and helium nuclei as observed by PAMELA between 2006 and 2009 in a very quiet heliosphere, and [7] modelled also proton and anti-proton observations obtained after 2011. This work extends on this approach and studies the modulation of galactic protons from 2006 until 2017, a period coinciding with solar activity changing from minimum to maximum conditions, including a HMF polarity reversal.…”

Study Galactic Cosmic Ray Modulation with AMS-02 observation

“…[5] studied the P/He observed by AMS-02 from 2011 to 2017 and found that the decreases of P/He after solar polarity reversal is mainly caused by the dependence of modulation on / . [6] reproduced the proton and helium data observed by PAMELA from 2006 to 2009, and made a comprehensive study of the influence of different local interstellar spectrum (LIS) and / on the time variation of P/He in this time interval.…”

A Numerical Study of the effects of a Corotating Interaction Region on cosmic proton and helium transport

“…The mentioned TPE describes four modulation processes for GCRs which are: convection caused by the outward flowing solar wind; diffusion because of scattering by the turbulent solar magnetic field; adiabatic energy losses determined by the divergence of solar wind velocity; drift of particles caused by magnetic field curvatures, gradients and the current sheet [9,10,15]. In 3D modeling there are three diffusion coefficients (DCs) of importance, one parallel to the background magnetic field direction, and two perpendicular to the field, respectively in the radial and polar directions [3,9,14].…”