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SR-NIEL – 7

Screened Relativistic (SR) Treatment for NIEL Dose

Nuclear and Electronic Stopping Power Calculator

(version 8.0)

Proton High AMS02 small

The current page is the update and the extension of the previous page, in which the comparison was limited to protons, helium-, lithium-, beryllium-, boron-, carbon-, nitrogen- and oxygen-nuclei. 

 

HelMod - the solar modulation model used within the SR-NIEL framework - is a well-known Monte Carlo code developed to describe the transport of GCRs through the heliosphere from interstellar space down to Earth (e.g., [HelMod (2022)], Chapter 8 of [Leroy and Rancoita (2016)]). 

In the current HelMod version 4 the modulation process, based on Parker’s equation, is applied to the propagation of GCRs in the inner and outer heliosphere, i.e., including the heliosheath. In fact, HelMod demonstrated to be capable of reproducing the fluxes observed by the Voyager probes in the inner and outer regions of the heliosphere up to its border. The HelMod model reproduced protons, antiprotons, nuclei, and electrons cosmic rays spectra observed - during solar cycles 23–24 and before - by several detectors, for instance, PAMELA, BESS, HEAO-3, ACE, and AMS-02 (e.g., see [HelMod (2022)] and Selected published HelMod spectra). In particular, the unprecedented accuracy of AMS-02 observations allowed one a better tuning of how solar modulation mechanisms are implemented inside the model. 

In addition, HelMod can be used to forecast the GCRs omnidirectional intensities that space missions may encounter after the lift-off (see discussion in [Boschini et al. (2022a)]).

Furthermore, the join GalProp-HelMod (2016) effort allowed one to determine local interstellar spectra (LIS) of protons, antiprotons, ions, and electrons, whose set is gradually extended. The already available LISs of cosmic rays species - from which the HelMod modulated spectra can be derived - are listed on the HelMod website. There, in fact, a user can require the HelMod spectra for specific past and future periods or refer to published datasets (e.g., those from AMS-02, Pamela, etc.), i.e.,

  • or single GCRs species and the future or past expected time interval can be chosen;
  • or, for each published experimental dataset (e.g., those from AMS-02, Pamela, etc.), HelMod modulated spectra can be obtained regarding the time of observation, the type of investigated GCR species (e.g., proton, helium-nuclei, etc.), and, finally, the set of published data

In the present webpage (e.g., see Comparison of solar modulation models with experimental data from AMS-02), a selection of observed spectra of GCRs species are reported (see also [Boschini et al. (2022b)]), together with the modulated spectra obtained from some currently used solar modulation models, in particular dealing with space radiation environment, i.e.,

 

Selected published HelMod spectra and heliosphere

It has to be remarked that modulated spectra cannot be likely approximated uniform through the heliosphere (e.g. see Section 9.2.3 of ECSS, 2020) and depend on time and position.

Fig4 Boschini2019
Fig5 Boschini2019

 Figure 1. Reproduced from Figures 4 and 5 of [Boschini et al. (2019)].

 

AsvSR2019 fig6

Figure 2. Reproduced from Figure 6 of [Boschini et al. (2019)].

 

BoschiniEtAl AdvSR Fig8 n

 Figure 3. Reproduced from Figure 8 of [Boschini et al. (2018c)].

  

AsvSR2019 fig7

Figure 4. Reproduced from Figure 7 of [Boschini et al. (2019)].

 


Figure 5. Reproduced from Figure 11 of [Boschini et al. (2017)]. AMS-02 proton data are from [Aguilar et al. (2015a)], AMS-02 helium data are from [Aguilar et al. (2015b)].

 

Figure 6. Reproduced from Figure 4 of [Boschini et al. (2018a)]. AMS-02 data (left panel) are from [Aguilar et al. (2014)], PAMELA data (right panel) are from [Adriani et al. (2011)].

 

Figure 7. Reproduced from Figure 5 of [Boschini et al. (2018b)]. ACE data (left panel) are from [George et al. (2009)], AMS-02 data (right panel) are from [Aguilar et al. (2017)].

 

Figure 8. Reproduced from Figure 6 of [Boschini et al. (2018b)]. ACE data (left panel) are from [George et al. (2009)], AMS-02 data (right panel) are from [Aguilar et al. (2017)].

 

Figure 9. Reproduced from Figure 4 of [Boschini et al. (2020a)].

 

Figure 10. Reproduced from Figure 10 of [Boschini et al. (2020a)].

 

For further information on the results, please visit the HelMod results webpage.

 

 

Comparison of solar modulation models with experimental data from AMS-02

To benchmark several models (see the complete discussion in Boschini et al., 2022c), we considered the ion spectra measured by AMS–02 onboard the International Space Station (Aguilar et al., 2021a). AMS is a state-of-the-art particle detector providing the most accurate measurements of the GCR ion spectra exploiting its large acceptance and its excellent control of systematics. For the present webpage, we adopted the latest fluxes published by the Collaboration which reported the update of previously published GCR fluxes (Aguilar et al., 2021a) and the fluxes for Ne, Mg, Si (Aguilar et al., 2020) for the period up to May 26, 2018, and Fe (Aguilar et al., 2021b), F (Aguilar et al., 2021c), Na, Al (Aguilar et al., 2021d) ion fluxes for the period up to October 30, 2019. Due to the long exposure time and, thus, the high collected statistics, these measurements provide an improved measurement of the GCR spectra behavior at high rigidities.

In the upper panels of Figures 9-23, the modulated spectra from CREME96, CREME2009, ISO-15390, and BON2020 are compared to both HelMod spectra and AMS02 data for protons, helium-, lithium-, beryllium-, boron-, carbon-, nitrogen-, oxygen-, neon-, magnesium-, silicon-, fluorine-, sodium-, aluminum-, iron-nuclei. As a function of rigidity R, relative differences of the solar model differential intensities, φ(R), with respect to that of AMS-02 data, φAMS-02(R), are calculated as

(1):

they are shown in the lower panels of the same figures. 

 

Fig. 11. Proton
Fig. 12. Helium
Fig. 13. Lithium
Fig. 14. Beryllium
Fig. 15. Boron
Fig. 16. Carbon
Fig. 17. Nitrogen
Fig. 18. Oxygen
Fig. 19. Fluorine
Fig. 20. Neon
Fig. 21. Sodium
Fig. 22. Magnesium
Fig. 23. Aluminum
Fig. 24. Silicon
Fig. 25. Iron

AllIons AMS02 20180526 1 Proton Rigidity

Figure 11. Upper panel: proton differential intensity in units of [m2 sr s GV]-1 measured by AMS-02 [Aguilar et al. (2021a)] (brown points) as a function of rigidity in GV from May 19, 2011, to November 26, 2018, and proton differential intensities - calculated at 1AU during the same period - for the presently investigated modulation models: CREME96 (blue curve), CREME2009 (orange curve), ISO-15390 (green curve), BON2020 (red curve) and HelMod (black curve). Lower panel: relative differences with respect to AMS-02 data calculated using Eq. (1). Adapted from Figure A5 and Figure 2 of Boschini et al. (2022c).

 AllIons AMS02 20180526 2 Helium Rigidity

Figure 12. Upper panel: helium differential intensity in units of [m2 sr s GV]-1 measured by AMS-02 [Aguilar et al. (2021a)] (brown points) as a function of rigidity in GV from May 19, 2011, to November 26, 2018, and helium differential intensities - calculated at 1AU during the same period - for the presently investigated modulation models: CREME96 (blue curve), CREME2009 (orange curve), ISO-15390 (green curve), BON2020 (red curve) and HelMod (black curve). Lower panel: relative differences with respect to AMS-02 data calculated using Eq. (1). Adapted from Figure A6 and Figure 2 of Boschini et al. (2022c).

AllIons AMS02 20180526 3 Lithium Rigidity

Figure 13. Upper panel: lithium differential intensity in units of [m2 sr s GV]-1 measured by AMS-02 [Aguilar et al. (2021a)] (brown points) as a function of rigidity in GV from May 19, 2011, to November 26, 2018, and lithium differential intensities - calculated at 1AU during the same period - for the presently investigated modulation models: CREME96 (blue curve), CREME2009 (orange curve), ISO-15390 (green curve), BON2020 (red curve) and HelMod (black curve). Lower panel: relative differences with respect to AMS-02 data calculated using Eq. (1). Adapted from Figure A7 and Figure 2 of Boschini et al. (2022c).

AllIons AMS02 20180526 4 Beryllium Rigidity

Figure 14. Upper panel: beryllium differential intensity in units of [m2 sr s GV]-1 measured by AMS-02 [Aguilar et al. (2021a)] (brown points) as a function of rigidity in GV from May 19, 2011, to November 26, 2018, and beryllium differential intensities - calculated at 1AU during the same period - for the presently investigated modulation models: CREME96 (blue curve), CREME2009 (orange curve), ISO-15390 (green curve), BON2020 (red curve) and HelMod (black curve). Lower panel: relative differences with respect to AMS-02 data calculated using Eq. (1). Adapted from Figure A8 and Figure 2 of Boschini et al. (2022c).

 

AllIons AMS02 20180526 5 Boron Rigidity

Figure 15. Upper panel: boron differential intensity in units of [m2 sr s GV]-1 measured by AMS-02 [Aguilar et al. (2021a)] (brown points) as a function of rigidity in GV from May 19, 2011, to November 26, 2018, and boron differential intensities - calculated at 1AU during the same period - for the presently investigated modulation models: CREME96 (blue curve), CREME2009 (orange curve), ISO-15390 (green curve), BON2020 (red curve) and HelMod (black curve). Lower panel: relative differences with respect to AMS-02 data calculated using Eq. (1). Adapted from Figure A9 and Figure 2 of Boschini et al. (2022c).

 

AllIons AMS02 20180526 6 Carbon Rigidity

Figure 16. Upper panel: carbon differential intensity in units of [m2 sr s GV]-1 measured by AMS-02 [Aguilar et al. (2021a)] (brown points) as a function of rigidity in GV from May 19, 2011, to November 26, 2018, and carbon differential intensities - calculated at 1AU during the same period - for the presently investigated modulation models: CREME96 (blue curve), CREME2009 (orange curve), ISO-15390 (green curve), BON2020 (red curve) and HelMod (black curve). Lower panel: relative differences with respect to AMS-02 data calculated using Eq. (1). Adapted from Figure A10 and Figure 2 of Boschini et al. (2022c).

AllIons AMS02 20180526 7 Nitrogen Rigidity

Figure 17. Upper panel: nitrogen differential intensity in units of [m2 sr s GV]-1 measured by AMS-02 [Aguilar et al. (2021a)] (brown points) as a function of rigidity in GV from May 19, 2011, to November 26, 2018, and nitrogen differential intensities - calculated at 1AU during the same period - for the presently investigated modulation models: CREME96 (blue curve), CREME2009 (orange curve), ISO-15390 (green curve), BON2020 (red curve) and HelMod (black curve). Lower panel: relative differences with respect to AMS-02 data calculated using Eq. (1). Adapted from Figure A11 and Figure 2 of Boschini et al. (2022c).

AllIons AMS02 20180526 8 Oxygen Rigidity

Figure 18. Upper panel: oxygen differential intensity in units of [m2 sr s GV]-1 measured by AMS-02 [Aguilar et al. (2021a)] (brown points) as a function of rigidity in GV from May 19, 2011, to November 26, 2018, and oxygen differential intensities - calculated at 1AU during the same period - for the presently investigated modulation models: CREME96 (blue curve), CREME2009 (orange curve), ISO-15390 (green curve), BON2020 (red curve) and HelMod (black curve). Lower panel: relative differences with respect to AMS-02 data calculated using Eq. (1). Adapted from Figure A12 and Figure 2 of Boschini et al. (2022c).

AllIons AMS02 20191030 9 Fluorine Rigidity

Figure 19. Upper panel: fluorine differential intensity in units of [m2 sr s GV]-1 measured by AMS-02 [Aguilar et al. (2021c)] (brown points) as a function of rigidity in GV from May 19, 2011, to October 30, 2019, and fluorine differential intensities - calculated at 1AU during the same period - for the presently investigated modulation models: CREME96 (blue curve), CREME2009 (orange curve), ISO-15390 (green curve), and HelMod (black curve). Lower panel: relative differences with respect to AMS-02 data calculated using Eq. (1). Adapted from Figure A13 and Figure 1 of Boschini et al. (2022c).

AllIons AMS02 20180526 10 Neon Rigidity

Figure 20. Upper panel: neon differential intensity in units of [m2 sr s GV]-1 measured by AMS-02 [Aguilar et al. (2020)] (brown points) as a function of rigidity in GV from May 19, 2011, to November 26, 2018, and neon differential intensities - calculated at 1AU during the same period - for the presently investigated modulation models: CREME96 (blue curve), CREME2009 (orange curve), ISO-15390 (green curve), BON2020 (red curve) and HelMod (black curve). Lower panel: relative differences with respect to AMS-02 data calculated using Eq. (1). Adapted from Figure A14 and Figure 2 of Boschini et al. (2022c).

AllIons AMS02 20191030 11 Sodium Rigidity

Figure 21. Upper panel: sodium differential intensity in units of [m2 sr s GV]-1 measured by AMS-02 [Aguilar et al. (2021d)] (brown points) as a function of rigidity in GV from May 19, 2011, to October 30, 2019, and sodium differential intensities - calculated at 1AU during the same period - for the presently investigated modulation models: CREME96 (blue curve), CREME2009 (orange curve), ISO-15390 (green curve), and HelMod (black curve). Lower panel: relative differences with respect to AMS-02 data calculated using Eq. (1). Adapted from Figure A15 and Figure 1 of Boschini et al. (2022c).

AllIons AMS02 20180526 12 Magnesium Rigidity

Figure 22. Upper panel: magnesium differential intensity in units of [m2 sr s GV]-1 measured by AMS-02 [Aguilar et al. (2020)] (brown points) as a function of rigidity in GV from May 19, 2011, to November 26, 2018, and magnesium differential intensities - calculated at 1AU during the same period - for the presently investigated modulation models: CREME96 (blue curve), CREME2009 (orange curve), ISO-15390 (green curve), BON2020 (red curve) and HelMod (black curve). Lower panel: relative differences with respect to AMS-02 data calculated using Eq. (1). Adapted from Figure A16 and Figure 2 of Boschini et al. (2022c).

AllIons AMS02 20191030 13 Aluminum Rigidity

Figure 23. Upper panel: aluminum differential intensity in units of [m2 sr s GV]-1 measured by AMS-02 [Aguilar et al. (2021d)] (brown points) as a function of rigidity in GV from May 19, 2011, to October 30, 2019, and aluminum differential intensities - calculated at 1AU during the same period - for the presently investigated modulation models: CREME96 (blue curve), CREME2009 (orange curve), ISO-15390 (green curve), and HelMod (black curve). Lower panel: relative differences with respect to AMS-02 data calculated using Eq. (1). Adapted from Figure A17 and Figure 1 of Boschini et al. (2022c).

AllIons AMS02 20180526 14 Silicon Rigidity

Figure 24. Upper panel: silicon differential intensity in units of [m2 sr s GV]-1 measured by AMS-02 [Aguilar et al. (2020)] (brown points) as a function of rigidity in GV from May 19, 2011, to November 26, 2018, and silicon differential intensities - calculated at 1AU during the same period - for the presently investigated modulation models: CREME96 (blue curve), CREME2009 (orange curve), ISO-15390 (green curve), BON2020 (red curve) and HelMod (black curve). Lower panel: relative differences with respect to AMS-02 data calculated using Eq. (1). Adapted from Figure A18 and Figure 2 of Boschini et al. (2022c).

AllIons AMS02 20191030 26 Iron Rigidity

Figure 25. Upper panel: iron differential intensity in units of [m2 sr s GV]-1 measured by AMS-02 [Aguilar et al. (2021b)] (brown points) as a function of rigidity in GV from May 19, 2011, to October 30, 2019, and iron differential intensities - calculated at 1AU during the same period - for the presently investigated modulation models: CREME96 (blue curve), CREME2009 (orange curve), ISO-15390 (green curve), and HelMod (black curve). Lower panel: relative differences with respect to AMS-02 data calculated using Eq. (1). Adapted from Figure A19 and Figure 1 of Boschini et al. (2022c).

By inspection of Figures 11-25, one can remark that the HelMod model exhibits an overall better agreement with AMS-02 data when compared to the other solar modulation models here presented.

 

Furthermore, the relative difference of fluences (i.e., the computed integrals of differential intensities over rigidity) evaluated from solar modulation models and that from AMS–02 data is computed by:

, (2)

where Φ(Rmin, Rmax) and ΦAMS-02(Rmin, Rmax) are the fluences of the solar model and that of AMS-02, respectively, in [m2 sr s]-1 in the rigidity interval between Rmin ---the minimum rigidity measured by AMS–02 (i.e., 1 GV for proton, ∼2 GV for other nuclei)--- and Rmax expressed in GV. Most of the considered models do not provide modulated spectra over the full rigidity range covered by AMS–02 experiment (i.e., up to TV). In particular, the BON2020 modulated spectra are provided up to 50 GeV/n, i.e., using Eq. (1) about 50 GV for proton and about 100 GV for the other nuclei. 

AllIons AMS02 Fig Fluence lin

Figure 23. ΔΦ values in percentage (see Eq. 2) for each model and each AMS–02 data set calculated up to Rmax. For the HelMod model, such a quantity was also calculated for the full rigidity range; the so-obtained value is almost overlapping that up to Rmax. The shaded area corresponds to |ΔΦ| < 2.5%. Reproduced from Figure 3 of Boschini et al. (2022c).

By inspection of Fig. 23, one can remark that the HelMod model achieves a good agreement over the full set of experimental data with, typically, ∆Φ within ±2.5%.

 

A further comparison among solar modulation models and observations was carried out by investigating how the expectations values differ from the experimental ones within the experimental errors, i.e., computing the quantity [Bobik et al. (2012)] (see Figure 24)

, (3)

where σAMS-02,i is the AMS-02 experimental relative error for the i-th data point, and Δφ(Ri) is obtained using Eq. (1).

AllIons AMS02 Fig eta lin

Figure 24. ηRMS values in percentage (see Eq. 3) for each model and each AMS–02 dataset for the incoming particle rigidity up to Rmax. For the HelMod model, such a quantity was also computed for the entire rigidity range available (open markers). The shaded area corresponds to ηRMS < 5%. Reproduced from Figure 4 of Boschini et al. (2022c). 

By inspection of Fig. 24, one can remark that the HelMod model again exhibits an overall better agreement with AMS-02 data when compared to the other solar modulation models here investigated with, typically, ηRMS within 5%.

Additional discussions can be found in the published paper by Boschini et al. (2022c).

In addition, the HelMod model is capable of providing the expected differential intensities for GCRs species in any heliospheric position (e.g., see Figure 1, discussions in [Boschini et al. (2019)] and references therein).

 

 

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[GalProp-HelMod (2016)] GalProp-HelMod (2016). As advertised on the GALPROP website, the HelMod website can be used as a service package to seamlessly calculate the effects of the heliospheric modulation for GALPROP output files. FROM GalProp homepage: "We are pleased to inform the community of the launch of a new service HelMod, which can be used to seamlessly calculate the effects of the heliospheric modulation for GALPROP output file".

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[HelMod (2022)] See [Boschini et al. (2022a)], [Boschini et al. (2022b)], [Boschini et al. (2022c)], [Boschini et al. (2021)], [Boschini et al. (2020a)], [Boschini et al. (2020b)], [Boschini et al. (2019)], [Boschini et al. (2018a)], [Boschini et al. (2018b)], [Boschini et al. (2017)], [Bobik et al. (2012)]; see also: Bobik et al. (2016), On the forward-backward-in-time approach for Monte Carlo solution of Parker's transport equation: One-dimensional case, Journal of Geophysical Research - Space Physics 121(5), 3920–3930, doi:10.1002/2015JA022237.

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