Simulations of the radiation environment at ISS altitudes

Simulations of the radiation environment at ISS altitudes

Acta Astronautica 65 (2009) 279 – 288 www.elsevier.com/locate/actaastro Simulations of the radiation environment at ISS altitudes Katarina Gustafsson...

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Acta Astronautica 65 (2009) 279 – 288 www.elsevier.com/locate/actaastro

Simulations of the radiation environment at ISS altitudes Katarina Gustafssona,∗ , Lembit Sihvera, b , Davide Mancusia , Tatsuhiko Satoc , Koji Niitad a Nuclear Engineering, Chalmers University of Technology, SE-41296 Gothenburg, Sweden b Roanoke College, 221 College Lane, Salem, VA 24153, USA c JAEA, Tokai-mura, Naka-gun, Ibaraki 319-1184, Japan d RIST, Tokai-mura, Ibaraki-ken 319-1106, Japan

Received 6 July 2007; received in revised form 17 January 2009; accepted 22 January 2009 Available online 4 March 2009

Abstract In order to evaluate and simulate the response of detectors, for measurements of radiation environment inside and outside the International Space Station (ISS), a model for the outside space radiation environment at the altitudes of ISS is required. This estimation can be performed by using e.g. one of the two web-based model packages: CREME96 (Cosmic Ray Effects on Micro Electronics) and SPENVIS (the SPace ENVironment Information System). The main goal of this work is to compare and evaluate these web interfaces and the results given in order to understand how these will influence the simulations of experiments on the ISS. © 2009 Elsevier Ltd. All rights reserved. Keywords: Space radiation; Radiation environment models; CREME96; SPENVIS

1. Introduction During their time spent in space, the personnel on spacecraft are exposed to radiation with various charges and energies. The space radiation environment depends on several objects such as space weather, mission destination and mission duration. To estimate the radiation exposure, a particle and heavy ion transport simulation tool is required. The tool chosen by our collaboration is PHITS (Particle and Heavy-Ion Transport code System) [1], which is a 3-D Monte Carlo transport code under development by RIST, JAEA, KEK (Japan) and Chalmers (Sweden). PHITS is able to simulate both transport and collision processes in all materials present in space vehicles and human bodies, but needs the space radiation environment as an input. This input can be given by two ∗ Corresponding author. Fax: +46 31 772 3079.

E-mail address: [email protected] (K. Gustafsson). 0094-5765/$ - see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.actaastro.2009.01.040

web-based model packages; CREME96 (Cosmic Ray Effects on Micro Electronics) [2] and SPENVIS (the SPace ENVironment Information System) [3]. Both packages can give an estimation of the outside space radiation environment, which can be used as an input in PHITS. The focus of this paper is on evaluation of CREME96 and SPENVIS, which are built from different blocks of models, but our comparison will be limited to their ability describing the space radiation flux: (1) before interacting with any space vehicle material or space personnel and (2) at altitude interesting for ISS (International Space Station) applications.1

1 The ISS altitude varies, but maximum allowed is 460 km and minimum allowed is 280 km.

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2. Model packages A comparison between the two space radiation environment model packages CREME96 and SPENVIS has been performed. Both packages are available through web interface, but include somewhat different models, which will be described in more details below. When this comparison started, there was also a third model package available on the internet; SIREST (Space Ionizing Radiation Effects and Shielding Tools), developed by Singleterry et al. [4] at NASA. However, this package is not available any longer. SIREST was based on the AP8 and AE8 models including NOAAPRO [5], which made it possible to estimate the trapped particle flux during the intermediate solar cycle. SIREST was also based on the Badhwar & O’Neill [6] for the GCR environment. SIREST was the only web-based package which included a model for the albedo neutron flux. According to the developer of SIREST, another model package is planned and although the focus for this new package will not be identical to the old one it should anyway be possible to be used for our ISS applications. 2.1. CREME96 CREME96 [2], which is an update of the Cosmic Ray Effect on Micro-Electronics code, developed by Tylka et al. at the US Naval Research Laboratory, has a user friendly web interface and generate a package consisting of AP8 trapped proton models [7], the semiempirical model by Nymmik et al. [8] for GCRs, solar particle events based on data from GOES proton data and measurements from the Chicago’s IMP-8/CRT for HZE (high charge and high energy) particles. 2.1.1. Geomagnetic transmission An important part of the comparison includes an evaluation of a model for the geomagnetic transmission, included in CREME96. When charged particles from interplanetary space reach the Earth’s magnetic field it has a certain ability to reach a specific position inside Earth’s magnetosphere and this occurrence is referred to as geomagnetic transmission. World-wide grids are created and as a function of latitude, longitude, altitude and arrival direction one can get the minimum magnetic rigidity required to reach a specific position. The model in CREME96 is based on a combination of International Geomagnetic Reference Field [9] and the extended Tsyganenko model [10]. Benefits from this model are for example improved ability to consider geomagnetic disturbances and magnetospheric current systems and

averaging over arrival directions. So far only two orbits implement these geomagnetic transmission calculations: 51.6◦ at 450 km (Mir and International Space Station) and 28.5◦ at 450 km (general orbit for Shuttle missions). Other orbits do not include the same benefits. For further reading see [2]. 2.2. SPENVIS SPENVIS [3] is an ESA funded project developed by the Belgian Institute for Space Aeronomy. The web interface present several models for the radiation sources and is the only public available web-based package which includes a trapped proton anisotropy model. In SPENVIS there exist different models for each radiation source, which can be chosen depending on the application. SPENVIS also make use of geomagnetic transmission [11]. In SPENVIS it is possible to choose three different models for trapped protons; AP8 [12], CRRESPRO [13] or SAMPEX/PET PSB97 [14], but since CRRESPRO is designed for higher altitudes than ISS altitudes it is not included in this comparison. For trapped electrons, SPENVIS includes several optional models: AE8 [12], CRRESELE [15] or the AE8MIN-update ESA-SEE1 [16], but these are not considered in this paper. The galactic cosmic rays are evaluated based on the same model as in CREME [17]; notice this is the old CREME version. In SPENVIS three possible models can be used to estimate the solar proton fluences: JPL-91 [18], King [19] and the ESP models [20,21]. Regarding the contribution of the solar energetic ions, SPENVIS is based on the old CREME model for predicting the fluences. 3. Orbit data When using SPENVIS, the orbit parameters must always be defined by the user, but the case for CREME96 provides other possibility. One can always define the orbit by hand, but CREME96 involves (1) a pre-defined orbit for estimating trapped protons; this orbit is at 500 km altitude and includes no advantages and, therefore, it is excluded from this comparison, and (2) a pre-calculated orbit, at 450 km altitude, for estimating galactic cosmic rays; as explained in Section 2.2.1, this pre-calculated orbit includes several advantages and is, therefore, of high importance for this evaluation. The orbit data is based on the ISS orbit data during solar maximum from the 29th of April 2002, which has an altitude of approximately 400 km. In order to

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investigate altitude dependency and geomagnetic transmission these orbit parameters has been used along with an altitude of 450 km. Since both trapped protons and galactic cosmic rays are depending on the solar cycle, above mentioned ISS orbit data is also used with a solar minimum condition. The aim was to compare whole orbits and, therefore, following the recommendations by CREME96 and SPENVIS the number of orbits chosen was 200 and 61.6, respectively. When using SPENVIS one define dates for mission start and end; at solar maximum and solar minimum the dates are around 29th of April 2002 and 17th of July 1996 respective. For CREME96 it was chosen the default solar minimum and solar maximum for solar-quiet conditions. See Appendix for further input parameters details.

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4. Results and discussion In Fig. 1 the estimated flux for protons (Z = 1), simulated by CREME96, is shown at solar maximum and at solar minimum for a 400 km altitude. The solar maximum condition, as expected, gives rise to a lower proton flux than at solar minimum. For trapped protons, this is due to the higher amount escaping the van Allen belts due to increased amount of interactions with, during solar maximum, the more expanded atmosphere of the Earth. The results, when using different trapped proton models in SPENVIS, for estimating the proton flux at 400 km altitude can be seen in Fig. 2. Please, note the energy span for the SAMPEX/PET PSB97 trapped proton models, 18.5–500 MeV. When using SAMPEX/PET PSB97

CREME96 (Protons) Flux (particles/m2-s-sr-MeV/n)

1.E+05 Solar maximum 1.E+03 Solar minimum 1.E+01 1.E-01 1.E-03 1.E-05 1.E+00

1.E+01

1.E+02 1.E+03 Energy (MeV/n)

1.E+04

1.E+05

Fig. 1. Estimated proton flux by CREME96.

SPENVIS (Protons) Flux (particles/ (m2-sr-s-MeV/n)

1.E+05 AP8 Max AP8 Min 1.E+03

SAMPEX/PET PSB97 Min

1.E+01

1.E-01

1.E-03 1.E+00

1.E+01

1.E+02

1.E+03

Energy (MeV/n) Fig. 2. Estimated proton flux by SPENVIS.

1.E+04

1.E+05

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K. Gustafsson et al. / Acta Astronautica 65 (2009) 279 – 288 Different proton contributions solar maximum

Flux (particles/m2-s-sr-MeV/n)

1.E+07

CREME96 - Trapped protons

1.E+05

CREME96 - Other proton contribution SPENVIS - Trapped protons

1.E+03

SPENVIS - Other proton contribution

1.E+01 1.E-01 1.E-03 1.E-05 1.E-07 1.E-01

1.E+00

1.E+01

1.E+02 1.E+03 Energy (MeV/n)

1.E+04

1.E+05

Fig. 3. Different proton contributions at solar maximum by CREME96 and SPENVIS.

CREME96 and SPENVIS (Protons) solar maximum Flux (particles/m2-s-sr-MeV/n)

1.E+05 CREME96 SPENVIS

1.E+03 1.E+01 1.E-01 1.E-03 1.E-05 1.E+00

1.E+01

1.E+02 1.E+03 Energy (MeV/n)

1.E+04

1.E+05

Fig. 4. Estimated proton flux at solar maximum by CREME96 and SPENVIS.

one looses trapped protons for the lower energy less than 18.5 MeV, but on the other hand it gains contribution from the trapped protons up to 500 MeV instead of 400 MeV which is the case for AP8 Min in SPENVIS. As can be seen in Fig. 3, the largest contribution of protons up to 400 (SPENVIS) and 600 MeV (CREME96) origins from trapped protons, and above no trapped protons are included. In Fig. 3, an estimation of the proton flux by using SPENVIS is also included; although the differences between CREME96 and SPENVIS can more clearly be seen from the results shown in Fig. 4. Fig. 4 shows an evaluation of the estimated flux from CREME96 and SPENVIS at solar maximum. Comparing the flux at 400 km altitude the conclusion is that SPENVIS estimates higher flux than CREME96 for the cases simulated. Since both CREME96 and SPENVIS

use the AP8 models, the difference between the results from CREME96 and SPENVIS must be caused by some other parameter(s). One should also be aware of the different energy limits for trapped protons. One important remark is the altitude dependence of the proton flux. The altitude of interest is in the lower part of the van Allen belts and therefore an increase in altitude will raise the flux as can be seen in Fig. 5 for CREME96 at solar maximum conditions for two altitudes, 400 and 450 km. Equal behaviour can be noticed when using SPENVIS. Another important is the established fact that the AP8 model needs to be used with care, with respect to the geomagnetic field model and epoch. The flux of heavier ions was also simulated at different altitudes. In Fig. 6, the flux of oxygen (Z = 8) during solar maximum, simulated with CREME96, is

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283

CREME96 (Protons) solar maximum Flux (particles/m2-s-sr-MeV/n)

1.E+05 CREME96 (altitude 400 km) CREME96 (altitude 450 km)

1.E+03 1.E+01 1.E-01 1.E-03 1.E-05 1.E+00

1.E+01

1.E+02 1.E+03 Energy (MeV/n)

1.E+04

1.E+05

Fig. 5. Estimated proton flux at different altitudes at solar maximum by CREME96.

CREME96 (Oxygen) solar maximum

Flux (particles/m2-s-sr-MeV/n)

1.E-03 1.E-04 1.E-05 1.E-06 Pre-calculated orbit, alt 450km By hand defined orbit, alt 400km

1.E-07

By hand defined orbit, alt 450km 1.E-08 1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

Energy (MeV/n)

Fig. 6. Estimated flux (oxygen) at solar maximum by CREME96.

shown at 400 and 450 km altitude. As can be seen, the altitude has a minor impact and instead, for explicitly CREME96, the progress of a pre-calculated orbit, using the geomagnetic transmission functions described in Section 2.2.1, and its advantages gives an important contribution to a more accurate flux estimation. In Fig. 7, the flux of oxygen (Z = 8) at 450 km altitude simulated with both CREME96 and SPENVIS is shown. For energies above 200 MeV/n, the trend is similar to each other for both model packages. The largest difference between the results from CREME96 and SPENVIS is in the lower energy region where a peak around 5–10 MeV/n can be seen in the results from CREME96, whereas for SPENVIS the flux is not changing for energies up to 10 MeV/n. The peak seen in the results from CREME96 origin from the anomalous cosmic rays (ACR). When using SPENVIS one can choose to

include fully or singly ionized ACR, and as can be seen in Fig. 7 the contribution from the fully ionized ACR will increase the flux at lower energies. During solar maximum the solar wind is more intense and this provides a greater attenuation of the GCR. Therefore it is of interest to investigate the oxygen flux during a solar minimum condition. As can be seen in Fig. 8 the flux increases and at energies around 1000 MeV/n one can see a factor of two higher flux than at solar maximum condition. The simulated iron (Z = 26) flux at 450 km altitude using CREME96 and SPENVIS is shown in Fig. 9. As can be seen there is a difference between the simulated results up to high energies around 1000 MeV/n. Fig. 10 shows the worst case (worst week) scenario with 99% confidence level estimated by CREME96 and as can be seen, the use of pre-calculated or by hand

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K. Gustafsson et al. / Acta Astronautica 65 (2009) 279 – 288 CREME96 and SPENVIS (Oxygen) solar maximum

Flux (particles/m2-s-sr-MeV/n)

1.E-03 1.E-04 1.E-05 1.E-06

CREME96 SPENVIS (no ACR)

1.E-07

SPENVIS (fully ionized anomalous) 1.E-08 1.E+00

1.E+01

1.E+02 1.E+03 Energy (MeV/n)

1.E+04

1.E+05

Fig. 7. Estimated flux (oxygen) at solar maximum by CREME96 and SPENVIS.

CREME96 and SPENVIS (Oxygen) solar minimum

Flux (particles/m2-s-sr-MeV/n)

1.E-02 1.E-03 1.E-04 1.E-05 CREME96

1.E-06

SPENVIS 1.E-07 1.E-08 1.E+00

1.E+01

1.E+02 1.E+03 Energy (MeV/n)

1.E+04

1.E+05

Fig. 8. Estimated flux (oxygen) at solar minimum by CREME96 and SPENVIS.

CREME96 and SPENVIS (Iron) Flux (particles/m2-s-sr-MeV/n)

1.E-04 1.E-05 1.E-06 CREME96 (solar maximum)

1.E-07

SPENVIS (solar maximum) CREME96 (solar minimum)

1.E-08

SPENVIS (solar minimum) 1.E-09 1.E+00

1.E+01

1.E+02 1.E+03 Energy (MeV/n)

1.E+04

Fig. 9. Estimated flux (iron) by CREME96 and SPENVIS.

1.E+05

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285

CREME96 (Worst case, Solar protons) Flux (particles/m2-s-sr-MeV/n)

1.E+08 Precalculated orbit User defined orbit

1.E+06 1.E+04 1.E+02 1.E+00 1.E-02 1.E-04 1.E-06 1.E-08 1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

Energy (MeV/n) Fig. 10. Worst case estimations for protons by CREME96.

SPENVIS (Solar protons)

Fluence (particles/m2-sr-MeV/n)

1.E+13

King JPL-91

1.E+11

1.E+09

1.E+07

1.E+05 1.E-01

1.E+00

1.E+01 Energy (MeV/n)

1.E+02

1.E+03

Fig. 11. Worst case estimations for protons by SPENVIS.

defined orbit at 450 km altitude has a large impact on the flux. This is related to the earlier mentioned advantages with the pre-calculated orbit. The worst week scenario is based on fluence averaged over 180 h of the 19–27 October 1987 event. In Fig. 11 the estimation includes SPENVIS solar proton scenario at 450 km altitude during one year using the King (with Burrell statistics) and JPL-91 model for a 95% confidence level under stormy magnetosphere. Notice that King is an older model and is based on data between 1966 and 1972; the JPL-91 uses data collected between 1963 and 1991 and therefore is expected to have higher statistical validity. In Fig. 12 the CREME96 worst case (worst week) scenario with 99% confidence level is presented; the fluence for CREME96 is based on the flux estimated in Fig. 10 for a pre-calculated orbit and then

multiplied by 180 h. The figure also presents the ESP worst case event model with a 99% confidence level over a one year period at 450 km altitude. One should compare these two with care and be aware of the focus on the October 1989 event fluence by CREME96 and the focus on fluence as a function of confidence level and mission duration by ESP. 5. Conclusions When estimating the trapped proton flux, the altitude is an important parameter. The altitudes of the ISS are in the lower part of the inner van Allen belt and with increasing altitude there will be an increased contribution of trapped protons to the particle flux. SPENVIS was shown to estimate a slightly higher proton flux than CREME96.

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CREME96 and SPENVIS (Worst case, Solar protons)

Fluence (particles/m2-sr-MeV/n)

1.E+13 1.E+11 1.E+09 1.E+07

CREME96 ESP worst case

1.E+05 1.E+03 1.E-01

1.E+00

1.E+01 Energy (MeV/n)

1.E+02

1.E+03

Fig. 12. Worst case estimations for protons by CREME96 and SPENVIS.

For the heavier ions the altitude has a minor impact on the estimated flux. Instead the geomagnetic transmission functions give a large difference between the simulated results from CREME96, using pre-calculated geomagnetic transmission functions or by hand defined orbit. The largest difference between CREME96 and SPENVIS is in the lower energy region where the estimation of the ACRs is an important factor; for applications such as dose and dose equivalent estimations inside the ISS, these lower energies are not of importance since they will not have sufficient energy to go through the walls of the ISS. Since both the quality of the models for the external radiation environment and the geomagnetic transmission functions used in the calculations are affecting the results, more systematic comparisons of the different models with available measurements should be performed before any conclusions about the quality of the CREME96 and SPENVIS models can be made. The impact of the different estimated flux both for trapped protons and heavier ions on radiation exposure such as dose will be published elsewhere. Acknowledgments The authors want to acknowledge the use of CREME96, SPENVIS and SIREST and their administrators for help regarding questions about the web interface and the models. We also would like to thank Jonathan K. Weaver at the Johnson Space Centre for providing the orbit data for the International Space Station. This work was supported at Chalmers by the Swedish National Space Board. Part of the expenses associated with K. Gustafsson’s participation at the 16th IAA Humans in Space Symposium, Beijing, China,

where this paper was presented, was supported by “Wilhelm och Martina Lundgrens Vetenskapsfond 1”. Appendix Input parameters used during runs with CREME96 can be seen in Table 1. Table 2 shows the input parameters for runs with SPENVIS.

Table 1 Input parameters used during runs with CREME96. Trapped protons and GCRs (a) Pre-calculated orbit Altitude (GCRs) Inclination (b) By hand defined orbit Apogee Perigee Inclination Initial longitude of the ascending node Initial displacement of the ascending node Displacement of perigee from the ascending node Number of orbits Trapped proton spectra Calculated transmission functions Magnetic weather conditions Flux Atomic number Solar quiet Solar-energetic particle Spacecraft location

450 km 51.6◦ 401.63 km/460 km 382.89 km/440 km 51.378◦ 297.09◦ 340.12◦ 67.675◦ 200 Whole orbit Whole orbit Quiet (stormy at worst case scenario) 1–26 Solar minimum/solar maximum Worst week Inside Earth’s magnetosphere

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Table 2 Input parameters used during runs with SPENVIS. Orbit definitions Orbit type Start date End date Trajectory duration Apogee Perigee Inclination Right ascension of the ascending node Argument of perigee True anomaly

Solar max General 27 April 2002 2 May 4 days 401.63 km/460 km 382.89 km/440 km 51.38◦ 297.09◦ 67.68◦ 340.12◦

Trapped radiation AP-8 SAMPEX/PET PSB97

Solar maximum/solar minimum

Ion energy Thickness Ion range Interplanetary weather conditions Geomagnetic shielding Solar proton fluences King JPL-91 ESA worst case event

Solar min General 15 July 1996 19 July 1996 4 days 401.63 km/460 km 382.89 km/440 km 51.38◦ 297.09◦ 67.68◦ 340.12◦

0 cm H–Ni M = 1 or 2 Quiet

Burrell statistics

References [1] H. Iwase, K. Niita, T. Nakamura, Development of generalpurpose particle and heavy ion transport Monte Carlo code, Journal of Nuclear Science and Technology 39 (11) (2002) 1142–1151. [2] A.J. Tylka, et al., CREME96: a revision of the cosmic ray effect on micro-electronics code, IEEE Transactions on Nuclear Science 44 (6) (1997) 2150–2160 (see also http://creme96.nrl. navy.mil/). [3] D. Heynderickx et al., New radiation environment and effect models in ESA’s SPace ENvironment Information System (SPENVIS), Proceedings of RADECS 2003, pp. 643–646 (see also http://www.spenvis.oma.be/intro.html). [4] R.C. Singleterry, et al., Creation and utilization of a World Wide Web based space radiation effects code: SIREST, Physica Medica 17 (suppl. 1) (2001) 90–93 (see also http://sirest.larc. nasa.gov/). [5] S.L. Huston, K.A. Pfitzer, A new model for the low altitude trapped proton environment, IEEE Transactions on Nuclear Science 45 (6) (1998) 2972–2978. [6] G.D. Badhwar, P.M. O’Neill, Galactic cosmic radiation model and its applications, Advances in Space Research 17 (2) (1996) 7–17. [7] S.F. Fung, Recent development in the NASA trapped radiation models, Geophysical monograph 97 (1996) 79–91.

95% confidence level 95% confidence level 95% confidence level

Stormy magnetosphere Stormy magnetosphere Stormy magnetosphere

[8] R.A. Nymmik, et al., A model of galactic cosmic rays fluxes, Nuclear Tracks and Radiation Measurements 20 (3) (1992) 427–429. [9] R. Langel, et al., International geomagnetic reference field 1991 revision, Journal of Geomagnetism and Geoelectricity 43 (12) (1991) 1007–1012. [10] P.R. Boberg, et al., Geomagnetic transmission of solar energetic protons during the geomagnetic disturbances of October 1989, Geophysical Research Letters 22 (9) (1995) 1133–1136. [11] C. Störmer, Periodische Elektronenbahnen im Field eines Elementarmagnetron und ihre Anwendung auf Bruches Modellversuche und auf Eschenhaagens Elementatwellen des Erdmagnetismus, Zeitschrift für Astrophysik 1 (1930) 237–274. [12] J.I. Vette, The NASA/National Space Science Data Center Trapped Radiation Environment Model Program (1964–1991), NSSDC/WDC-A-R&S 91-29, 1991 [13] J.D. Meffert, M.S. Gussenhoven, CRRESPRO documentation, PL-TR-94-22118, Environmental Research Papers, 1994, p. 1158. [14] D. Heynderickx, et al., A low altitude trapped proton model for solar minimum conditions based on SAMPEX/PET data, IEEE Transactions on Nuclear Science 46 (6) (1999) 1475–1480. [15] D.H. Brautigam, J.T. Bell, CRRESELE Documentation, PLTR-95-2128, Environmental Research Papers, 1995, p. 1178. [16] A.L. Vampola, Outer zone energetic electron environment update, Conference on the High Energy Radiation Background

288

K. Gustafsson et al. / Acta Astronautica 65 (2009) 279 – 288

in Space, Workshop Record, Held in conjunction with IEEE Nuclear and Space Radiation Effects Conference (Cat. No. 97TH8346), 1998, pp. 128–136. [17] J.H. Adams Jr., Cosmic ray effects on microelectronics, Part IV, Naval Research Laboratory Memorandum Report 5901, 1986. [18] J. Feynman, et al., Interplanetary proton fluence model: JPL 1991, Journal of Geophysical Research 98 (A8) (1993) 13281–13294.

[19] J.H. King, Solar proton fluences for 1977-1983 space missions, Journal of Spacecraft and Rockets 11 (6) (1974) 401–408. [20] M.A. Xapsos, et al., Probability model for worst case solar proton event fluences, IEEE Transactions on Nuclear Science 46 (6) (1999) 1481–1485. [21] M.A. Xapsos, et al., Probability model for cumulative solar proton event fluences, IEEE Transactions on Nuclear Science 47 (3) (2000) 486–490.