Current status and possible extension of the global neutron monitor network
aa r X i v : . [ phy s i c s . s p ace - ph ] M a y Current status and possible extension of the globalneutron monitor network
A.L. Mishev and I.G. Usoskin
Space Physics and Astronomy Research Unit, University of Oulu, Finland. Sodankyl¨a Geophysical Observatory, University of Oulu, Finland.May 27, 2020
Abstract
The global neutron monitor network has been successfully used over several decades tostudy cosmic ray variations and fluxes of energetic solar particles. Nowadays, it is used alsofor space weather purposes, e.g. alerts and assessment of the exposure to radiation. Here,we present the current status of the global neutron monitor network. We discuss the abilityof the global neutron monitor network to study solar energetic particles, specifically duringlarge ground level enhancements. We demonstrate as an example, the derived solar protoncharacteristics during ground level enhancements GLE ≈
12 200m) above sealevel. We present a plan for improvement of space weather services and applications of theglobal neutron monitor network, specifically for studies related to solar energetic particles,namely an extension of the existing network with several new monitors. We discuss theability of the optimized global neutron monitor network to study various populations of solarenergetic particles and to provide reliable space weather services.Keywords:Solar energetic particles, GLE events, neutron monitor network, radiation environmentFor contact: alexander.mishev@oulu.fi;alex [email protected]
Cosmic rays (CRs) represent flux of high-energy subatomic particles, mostly protons, α -particlesand traces of heavier nuclei. Their energy ranges from about 10 to 10 eV, following a power-law spectrum (Beatty et al., 2018). The bulk of CRs originate from the Galaxy, called galacticcosmic rays (GCRs), produced during and/or following supernova explosions, e.g., in supernovaremnants. GCRs are always present in the vicinity of the Earth and permanently impinge on theEarth’s atmosphere. While the low-energy CR particles are absorbed in the upper atmosphere,those with energies about GeV nucleon − produce secondary particles via interactions with the1tmospheric atoms. Those secondaries also collide with air nuclei, in turn producing other parti-cles, if their energy is sufficiently high. Each collision adds a certain amount of particles, leadingto the development of a complicated nuclear-electromagnetic-muon cascade known as an exten-sive air shower (for details see Grieder, 2001, 2011, and references therein).A sporadic source of high-energy particles penetrating the Earth’s atmosphere is related tosolar eruptive processes, viz. solar flares, and coronal mass ejection (CMEs), where solar ionscan be accelerated to high energies. Those particles are known as solar energetic particles (SEPs)(e.g. Cliver et al., 2004; Desai and Giacalone, 2016, and references therein). The energy of SEPsis usually of the order of tens of MeV nucleon − , rarely exceeding 100 MeV nucleon − , but insome cases, SEPs can be accelerated to about GeV nucleon − or even greater energy. In this case,similarly to the GCRs, SEPs produce a cascade of secondary particles in the Earth’s atmosphere,that reaches the ground and increases the count rates of ground-based detectors, such as neutronmonitors (NMs) (Hatton, 1971; Grieder, 2001). This special class of SEP events is called ground-level enhancements (GLEs) (e.g. Shea and Smart, 1982; Poluianov et al., 2017). The occurrencerate of GLEs is roughly ten per solar cycle, with a slight increase during the maximum and declinephase of the cycle (Shea and Smart, 1990; Stoker, 1995; Klein and Dalla, 2017).Accelerated to high energy solar ions lead to various space weather effects (e.g. Lilensten and Bornarel,2009; Koskinen et al., 2017). SEPs lead to solar array performance degradation, harm on elec-tronic components in space missions or single event effects leading to significant disruption ofspacecraft performance. SEPs also pose a threat to astronauts as well as aircrews over transpolarflights (e.g. Vainio et al., 2009, and references therein). Therefore, SEPs, including GLE parti-cles represent a specific and important space weather topic (e.g. Mishev and Jiggens, 2019, andreferences therein).SEP and GCR fluxes, can be conveniently measured by space-borne instruments (e.g. Aguilar et al.,2010; Adriani et al., 2016). However, most of the space-borne instruments are constrained inthe weight and size of the detector(s), which can affect their performance. Besides, space-borne probes are located most of the time in regions with high rigidity cut-off, which makesthem poorly suitable for the study of SEPs. GLEs can be studied using the worldwide NMnetwork (Simpson et al., 1953; Hatton, 1971; Stoker et al., 2000; Mavromichalaki et al., 2011;Moraal and McCracken, 2012; Papaioannou et al., 2014).Here, We propose an extension of the global neutron monitor network with several new de-tectors in order to optimize its performance, specifically for space weather purposes. We brieflydiscuss the ability of the current and optimized NM network for space weather services. A NM is a complex ground-based detector aiming for registration of secondary particles, mostlyneutrons, but also protons and a small amount of muons, produced by a primary CR particle in theEarth’s atmosphere (Simpson, 1957; Clem and Dorman, 2000). Standard NM consists of sensi-tive to thermal neutrons proportional counters based on He or boron-trifluoride enriched to B,surrounded by a moderator, usually paraffin wax or polyethylene, a reflector made of the samematerial as the moderator and a lead producer (for details see Clem and Dorman, 2000; Simpson,2000; B¨utikofer, 2018b, and references therein). The purpose of the moderator is to slow down,i.e., to reduce the energy of neutrons, leading to a considerable increase in their registration prob-2bility. The energy loss of a neutron during elastic collision increases with decreasing the atomicmass, therefore the moderator is selected to contain a significant amount of low mass nuclei e.g.Hydrogen. The lead producer, surrounds the moderator, aiming production of more neutrons byinelastic interactions in a thick target. Therefore, the producer is built by high atomic mass ma-terial. The outermost layer of the NM represents a moderator, namely the reflector, which has adouble purpose: first, it rejects the low energy neutrons result from interaction(s) of the very localsurroundings from penetrating in the NM, secondly, it allows to keep the produced in the leadneutrons inside the monitor.The introduction of a NM as a continuous recorder of CR intensity followed the design bySimpson et al. (1953). During the International Geophysical Year (IGY) 1957-1958 a 12 tubeneutron monitor was constructed, but other configurations have been also used (Simpson, 1957;Shea and Smart, 2000b; Simpson, 2000). The IGY neutron monitor was used world-wide asa detector to study CR variations. Lately, in the mid-sixties, the design of the IGY NM wasoptimized resulting in increased counting rate (Hatton and Carmichael, 1964; Carmichael, 1968;Hatton, 1971). This second generation of NM design is known as NM64 or supermonitor (fordetails see Simpson, 2000; Stoker et al., 2000, and references therein). Recently, mini-NMs havebeen installed at several stations, exhibiting good performance, specifically at low cut-off rigidityand high-altitude locations (Poluianov et al., 2015).The count rate of a NM provides reliable information about CR flux variations at the top ofthe Earth’s atmosphere, both long-term (e.g. the 11-year sunspot cycle and the 22-year solar mag-netic cycle), and short-term as Forbush decreases, diurnal CR variations and transient phenomenasuch as recently observed anisotropic cosmic ray enhancements (for details see Gil et al., 2018).NMs data are used to derive spectral and angular characteristics of GLEs and high-energy SEPs,specifically in the high-energy range and over the whole event timespan (e.g. Shea and Smart,1982; Cramp et al., 1997; Bombardieri et al., 2006; Vashenyuk et al., 2006b; Mishev et al., 2014,2017, 2018b). The information retrieved from NMs is essential to assess important topics re-lated to space weather, such as exposure to radiation of aircrew(s), henceforth exposure, and theinfluence of CRs on atmospheric chemistry (e.g. Bazilevskaya et al., 2008; Vainio et al., 2009;Usoskin et al., 2011; Mironova et al., 2015).In order to offer a useful tool, specifically for space weather purposes, the global NM networkshall provide coverage of the entire sky and real-time data access (e.g. Mavromichalaki et al.,2011). Here, we discuss the current status of the global NM network and present a plan for itsextension, aiming an optimization of its performance as a space weather tool.
Over the years, it was demonstrated that the global NM network is a powerful tool to studyprimary CR variations, transient phenomena, SEPs, and to provide data, which form an importantinput for space weather applications (e.g. B¨utikofer, 2018b). In reality, the NM network as awhole, together with the geomagnetic field, represents a giant spectrometer, which allows oneto observe the variations of the primary CRs, because NMs placed at various rigidity cut-offsare sensitive to different parts of CR spectrum. In addition, multi-vantage-point registration,specifically of SEPs, makes it possible to reveal the anisotropy of CRs in the vicinity of Earth,since the viewing cone of each station is a function on its location, particle rigidity, and angle of3ncidence of the arriving particle.The global NM network presently consists of about 50 stations spread over the world, for de-tails see Fig.1, where the NM stations with the corresponding rigidity cut-off are shown (Moraal et al.,2000; Mavromichalaki et al., 2011). Here the computation of the rigidity cut-off over the globewas performed with the MAGNETOCOSMICS code using the IGRF magnetospheric model cor-responding to the epoch 2015 (Desorgher et al., 2005; Th´ebault et al., 2015).The sensitivity of a NMs to primary CR is determined by the geomagnetic and atmosphericshielding. The rigidity cut-off is a function of the geomagnetic location of the monitor, while thethickness of the atmospheric layer above a given NM determines the atmospheric cut-off, sincethe primary CR must possess minimum energy ( ≈
430 MeV nucleon − for the sea level) to inducean atmospheric cascade, whose secondary particles reach the ground (e.g. Grieder, 2001). Theatmospheric cut-off plays an important role in polar NMs, specifically those at the sea level, sincethe geomagnetic rigidity cut-off is small in the polar regions. Several high-altitude polar NMs,e.g. SOPO/SOPB and DOMC/DOMB are more sensitive to primary CR, specifically SEPs, thanmid- and high rigidity cut-off NMs. Therefore, the rigidity range of the global NM network isdetermined by the atmospheric cut-off at polar regions, which posses the lower rigidity cut-offs,accordingly by the highest geomagnetic cut-off at about 17 GV in the magnetic Equator.Besides, polar NMs possess better angular resolution, which is important for the GLE analy-sis. With this in mind, a concept of the spaceship Earth, an optimized network consisting only ofpolar stations was proposed (Bieber and Evenson, 1995). However, one can see that the presentNM network provides good coverage of arrival directions, and almost symmetric response (seeFig.1), but several gaps exist, as discussed below.4
60 120 180 240 300 360-90-60-300306090 0 60 120 180 240 300 360-90-60-300306090 0 30 60 90 120 150 180 210 240 270 300 330 360-90-80-70-60-50-40-30-20-100102030405060708090 0 60 120 180 240 300 360-90-60-300306090 [GV] L a t i t ud e [ d e g ] Longitude [deg]
Figure 1: Present status of the global neutron monitor network and proposition for further exten-sion. The up triangles correspond to presently operational stations. The down triangles corre-spond to previously existed stations. Circles correspond to the new stations proposed here. Thecolor diagram depicts rigidity cut-off map computed in quiet magnetospheric conditions employ-ing the IGRF model corresponding to epoch 2015 (Th´ebault et al., 2015).
High-energy CRs are not deflected by the Earth’s magnetic field. Therefore, NMs can record high-energy CRs, propagating almost along a straight line, determined by the latitude and longitude ofthe geographic position of the station. The situation is more complicated for low-energy particles,which are more strongly deflected. Thus, a NM is characterized by his asymptotic direction,i.e., the direction from which particles impinge on a given point in the atmosphere of the Eartharriving at the border of the magnetosphere. It depends on the location, particle incidence angleand rigidity (for details see B¨utikofer, 2018a,b, and references therein). As a result, a NM issensitive to a certain segment of the sky. While for the continuous recording of the isotropic GCRintensity, the asymptotic direction of a NM is not important, it is crucial for registration of GLEs,because SEPs reveal essential anisotropy, specifically during the event onset. Therefore, gapsin asymptotic directions of the global NM network can compromise the registration of GLEs,accordingly the corresponding analysis and alert services.The present situation of operational polar NMs allows one to derive a comprehensive pictureof GLE characteristics and provide alert systems (see Figs.1, 2 and Table 1). However, a gapin the asymptotic directions of Arctic NMs is observed, precisely in the longitude range 130–250 ◦ in the northern polar region. While the South polar NMs provide good coverage of thesky, those at North exhibit gaps (Fig.2). One can see that the majority of NMs are lookingtowards the Equator, i.e., NMs in the North hemisphere are looking southward, while those in5ntarctica except DOMC, are looking northward. In addition, as was recently discussed, thehigh-altitude polar NMs such as DOMC and VSTK are more sensitive to SEPs (Poluianov et al.,2017). Therefore, there is a need for a NM, which is a counterpart of DOMC, i.e., high-altitude,low rigidity cut-off NM located in the North hemisphere close to the geomagnetic pole, as wellas several stations to cover the gap and/or to improve the sensitivity, specifically in a low energyrange.For example, if a GLE with narrow angular distribution of the particle flux occurs (see thepitch angle distribution in Fig.3) with anisotropy axis located in the polar region of the northernhemisphere, e.g. at 150 ◦ E, it would not be registered by the existing NMs, because the rapidlydiminishing from the apparent arrival direction particle flux (see the contours of equal pitch an-gle which also depict the particle flux intensity in the upper panel of Fig.2 and the pitch angledistribution (PAD) of GLE
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APTY 151.215 BRBG CALG5CAPS15DOMC 0.75 FSMT15INVK15 JBGO15KERG 1.25MWSN15 MRNY15 NAIN51 NRLK 15OULU 15 PWNK15SNAE 15 0.75SOPOTERA15 THUL1 5TXBY15 15 o o L a t i t ud e [ d e g ] Longitude [deg]
APTY 151.215 BRBG CALG5CAPS15DOMC 0.75 FSMT15INVK15 JBGO15KERG 1.25MWSN15 MRNY15 NAIN51 NRLK 15OULU 15 PWNK15SNAE 15 0.75SOPOTERA15 THUL1 5TXBY15 ALRT1 5 0,75SUMTVSTK5 HEIS15 0.75 1SEVZ 15 o o Figure 2: Asymptotic directions of polar NMs. The abbreviations are given in Table 1. The colorlines depict asymptotic directions plotted in the rigidity range 1–5 GV, for DOMC, SOPO, SUMTand VSTK from 0.7 to 5 GV respectively. The dashed lines correspond to new NMs proposedfor extension of the network or to be reopened. The lines of equal pitch angles relative to theanisotropy axis of example event are plotted for 15 ◦ and 30 ◦ for sunward direction. The upperpanel corresponds to the current global NM network, while the lower panel to the extended NMnetwork. The figure is adapted from (Mishev et al., 2018a). Here, We present several abilities of the global NM network, related to space weather servicesand solar physics research.
Registration of a GLE can provide an early alert for the onset of SEP event, which is specifi-cally important for various space weather services (for details see Kuwabara et al., 2006a,b). Ac-cordingly, alert systems, based on NM records have been developed (Souvatzoglou et al., 2014;Mavromichalaki et al., 2018; Dorman et al., 2019). Most of those alert systems are based on agood coverage of the arrival direction of GLE particles by the global NM network since a givennumber of stations shall exhibit a count rate increase. Therefore, an extended global NM network7able 1: Neutron monitors used in this study. Columns represent station name, location, geomag-netic cut-off rigidity and altitude above sea level. The table encompasses the current status oflow rigidity stations (the part above the dashed line), the closed but previously existing stationsto be reopened (the part between the dashed and dashed-dashed lines) and new stations proposedto extend the network (the bottom part).
Station latitude [deg] Longitude [deg] P c [GV] Altitude [m]Apatity (APTY) 67.55 33.33 0.57 177Barenstburg (BRBG) 78.03 14.13 0.01 51Calgary (CALG) 51.08 245.87 1.08 1128Cape Schmidt (CAPS) 68.92 180.53 0.45 0Dome C (DOMC) -75.06 123.20 0.01 3233Forth Smith (FSMT) 60.02 248.07 0.381 0Inuvik (INVK) 68.35 226.28 0.16 21Jang Bogo(JNBG) -74.37 164.13 0.1 29Kerguelen (KERG) -49.35 70.25 1.01 33Mawson (MWSN) -67.6 62.88 0.22 0Mirny (MRNY) -66.55 93.02 0.03 30Nain (NAIN) 56.55 298.32 0.28 0Neumayer (NEUM) -70.40 351.04 0.85 0Norilsk (NRLK) 69.26 88.05 0.52 0Oulu (OULU) 65.05 25.47 0.69 15Peawanuck (PWNK) 54.98 274.56 0.16 52Sanae (SNAE) -71.67 357.15 0.56 52South Pole (SOPO) -90.00 0.0 0.09 2820Terre Adelie (TERA) -66.67 140.02 0.02 45Thule (THUL) 76.60 291.2 0.1 260Tixie (TXBY) 71.60 128.90 0.53 0Alert (ALRT) 82.5 297.67 0.0 57Heiss island (HEIS) 80.62 58.05 0.1 20Haleakala (HLEA) 20.71 203.74 12.91 3052Vostok (VSTK) -78.47 106.87 0.0 3488Canary Islands (CANI) 28.45 342.47 11.76 2376New Zealand (NZLD) -43.59 170.27 3.28 1029Severnaya Zemlya (SEVZ) 79.29 96.5 0.11 10Summit (SUMT) 72.34 321.73 0.01 3126 ∼ − ,can be derived by modeling of the global NM network response.Methods for analysis of GLEs using NM data have been developed over the years, usuallybased on modeling of the global NM network response and optimization of a set of unknownmodel parameters n over the experimental data points corresponding to the number of NM sta-tions (e.g. Shea and Smart, 1982; Cramp et al., 1997; Bombardieri et al., 2006; Vashenyuk et al.,2006b). In general, the relative count rate increase of a given NM during GLE can be expressedas: ∆ N ( P cut ) N ( t ) = ∑ i ∑ k R P max P cut J sep i ( P , t ) S i , k ( P ) G i ( α ( P , t )) A i ( P ) dP ∑ i R ∞ P cut J GCR i ( P , t ) S i ( P ) dP (1)where N is the count rate due to GCR averaged over two hours before the event’s onset (e.g.Usoskin et al., 2015), which can be also variable in case of a long event occurred during a Forbushdecrease, ∆ N ( P cut ) is the count rate increase due to solar particles. J sep is the rigidity spectrum of i (proton or α -particle) component of SEPs, usually only protons are taken into account, accord-ingly J GCR i ( P , t ) is the rigidity spectrum of the i component (proton or α -particle, etc...) of GCRat given time t , G ( α ( P , t )) is the pitch angle distribution of SEPs, otherwise, for GCRs the angu-lar distribution is assumed to be isotropic, accordingly, A(P) is a discrete function with A ( P ) =1for allowed trajectories (proton with rigidity P can reach the station) and A ( P ) =0 for forbiddentrajectories (proton with rigidity P cannot reach the station). Function A is derived during theasymptotic cone computations. P cut is the minimum rigidity cut-off of the station, accordingly, P max is the maximum rigidity of SEPs considered in the model, whilst for GCR P max = ∞ . S k isthe NM yield function for vertical and for oblique incidence SEPs (Clem, 1997). The contribu-tion of oblique SEPs to NM response is particularly important for modeling strong and/or veryanisotropic events, while for weak and/or moderately strong events it is possible to consider onlyvertical ones and using S k for an isotropic case, which considerably simplifies the computations(Mishev and Usoskin, 2016a).The background due to GCRs can be computed using a convenient model, e.g., the force-fieldmodel with the corresponding local interstellar spectrum, considering explicitly the modulationpotential (Usoskin et al., 2005; Vos and Potgieter, 2015). The optimization can be performedover the set of model parameters n by minimizing the difference between the modeled and mea-sured NM responses using a convenient method (Tikhonov et al., 1995; Mavrodiev et al., 2004;Aster et al., 2005; Mishev et al., 2005). The modeling of the global network NM response canbe performed using the corresponding NM yield function, which establishes a connection be-tween the primary CR flux at the top of the Earth’s atmosphere and the count rate of the de-vice. Since the secondary CRs, resulting from the primary CR induced cascade in the Earth’satmosphere, can reach the ground level and eventually be registered by a NM, the yield func-tion incorporates the full complexity of the atmospheric cascade development including sec-ondary particle propagation in the atmosphere and the efficiency of the detector itself to regis-ter the secondaries (e.g. Clem and Dorman, 2000, and references therein). The NM yield func-tion can be determined by parameterization of experimental data, namely latitude survey(s) (e.g.Nagashima et al., 1989; Raubenheimer et al., 1981; Dorman et al., 2000) or can be assessed us-ing Monte Carlo simulations of CR propagation in the atmosphere (e.g. Debrunner and Brunberg,9968; Clem and Dorman, 2000). Recently, essential progress of Monte Carlo simulations of CRpropagation in the atmosphere was achieved, which resulted in several newly computed NMfunctions (Clem and Dorman, 2000; Fl¨ukiger et al., 2008; Mishev et al., 2013; Mangeard et al.,2016). A recently computed NM yield function by Mishev et al. (2013, 2020) is fully consistentwith the experimental latitude surveys and was validated by achieving good agreement betweenmodel results and measurements, including space-borne data (Gil et al., 2015; Nuntiyakul et al.,2018; Koldobskiy et al., 2019b).As an example, we present the derived spectra and PAD of GLE gle.oulu.fi . The derived SEPs spectra and PAD are shown in Fig.3. The relativisticsolar proton spectra were very hard, specifically during the event’s onset initial phase, whilst anarrow PAD was revealed. The SEP spectra remained hard (with nearly exponential shape) duringthe whole event, in contrast to other GLEs (e.g. Miroshnichenko, 2018, and references therein).The extended NM network allows to significantly improve the optimization procedure, namelyit results in reduction of the residual D , which is defined as: D = r ∑ mi = h(cid:16) ∆ N i N i (cid:17) mod . − (cid:16) ∆ N i N i (cid:17) meas . i ∑ mi = ( ∆ N i N i ) meas . (2)where m is the number of NM stations, ∆ N i N i is the relative NM count rate increase for the i NMstation.A robust optimization process and reliable solution are achieved when D ≤ D can be about8–12 %. We emphasize that a solution can be obtained even in the case of D ∼ n is the number of unknowns in the model, in order to be able to unfold the modelparameters (e.g. Himmelblau, 1972; Dennis and Schnabel, 1996; Mavrodiev et al., 2004). Thus,it is sufficient to retrieve information from 15–20 NMs, specifically those in a polar region, whilstthe mid-latitude stations provide the boundary conditions. However, this number of stations isreasonable in case of not complicated PAD and unidirectional SEP flux, such as GLE D compared to the actual number of NMs used for10he analysis, whilst a reduction of the number of NMs leads to a considerable reduction of theability of the global NM network to provide a reliable GLE analysis. The additional data usedfor the analysis with the extended NM network are based on forward modeling including realisticnoise similarly to Mavrodiev et al. (2004) employing the derived spectra and PAD during theactual analysis. We note, that the extended analysis is performed with all polar stations fromTable 1, which encompasses the extended network, who are added to the actual analysis (a partialoverlapping exists for some events, since several NMs from Table 1 are used also for the actualanalysis). For the analysis with the reduced NM network we removed about 5–10 NMs withmoderate response. F l u x [ P r o t on m - s r - s - G V - ] R [GV] GCR 0345 0350 0430 R e l a t i ve p r o t on f l u x Pitch Angle [deg]
Figure 3: Derived rigidity spectra and PAD during GLE
The increased intensity of CRs during SEP events, leads to an important space weather issue,namely exposure at flight altitudes (e.g. Mewaldt, 2006; Pulkkinen, 2007; Shea and Smart, 2012,and references therein). During intercontinental flights over the sub-polar and polar regions,aircrews are exposed to non-negligible radiation field due to secondary particles, which can besignificantly enhanced during major GLEs (Spurny et al., 1996, 2002; Shea and Smart, 2000a).Assessments of the exposure during GLEs requires detailed information of SEP spectra as aninput for a relevant model for computation of the exposure (e.g. Ferrari et al., 2001; Latocha et al.,2009; Copeland, 2017). 11able 2: The value of the merit function D obtained for the analysis of several GLEs (main phaseof the event) as a function of the number of the used NM stations. Columns 1–2 correspond tothe number and date of the GLE, while columns 3–5 correspond to D and number of the usedstations (in the brackets) for extended NM network, actual NM network used for the analysis andthe reduced NM network, respectively. N.A. depicts the case when the SEP spectra cannot beunfolded. The details for the analysis of the presented GLEs are given in (Mishev et al., 2014;Mishev and Usoskin, 2016a; Kocharov et al., 2017; Mishev et al., 2018b) as well as in this work. GLE
Here we present as an example the exposure to radiation at flight altitude during the strongestever observed GLE. The computation was performed using a numerical model (Mishev and Usoskin,2015; Mishev et al., 2018a). The effective dose rate at a given atmospheric depth h induced bya primary CR particle is computed by convolution of the exposure yield function with the corre-sponding primary CR particle spectrum: E ( h , T , θ , ϕ ) = ∑ i Z ∞ T ( P cut ) Z Ω J i ( T ) Y i ( T , h ) d Ω ( θ , ϕ ) dT , (3)where J i ( T ) is the differential energy spectrum of the primary CR arriving at the top of the atmo-sphere for i − th component (proton or α − particle) and Y i is the effective dose yield function forthis type of particles. The integration is over the kinetic energy T above T cut ( P c ) , which is definedby the local cut-off rigidity P c for a nucleus of type i , T cut , i = r(cid:16) Z i A i (cid:17) P c + E − E , where E =0.938 GeV/c is the proton’s rest mass.Accordingly, the effective dose yield function Y i is: Y i ( T , h ) = ∑ j Z T ∗ F i , j ( h , T , T ∗ , θ , ϕ ) C j ( T ∗ ) dT ∗ (4)where C j ( T ∗ ) is the coefficient converting the fluence of secondary particles of type j (neutron,proton, γ , e − , e + , µ − , µ + , π − , π + ) with energy T ∗ to the effective dose, F i , j ( h , T , T ∗ , θ , ϕ ) is the fluence of secondary particles of type j , produced by a primary particle of type i (pro-ton or α − particle) with given primary energy T arriving at the top of the atmosphere fromzenith angle θ and azimuth angle ϕ . The conversion coefficients C j ( T ∗ ) are considered ac-cording to Petoussi-Henss et al. (2010). We note, that employment of different conversion coef-ficients C j ( T ∗ ) (e.g. ICRP, 1996), would lead to increase of the exposure assessment of about 20%, which is considerably below the other model uncertainties (e.g. Copeland and Atwell, 2019;Yang and Sheu, 2020). 12sing the derived rigidity spectra for GLE L a t i t ud e [ d e g ] Longitude [deg]
Eff. dose [mSv]
Figure 4: Global map of the effective dose at altitude of 40 kft during GLE
The global NM network provides a good opportunity to study solar neutrons (e.g., Usoskin et al.,1997; Dorman, 2010; Artamonov et al., 2016). During solar eruptions, accelerated high-energy13ons can interact with matter in the solar atmosphere, resulting in in-situ production of differ-ent types of secondary particles, e.g. γ -rays and neutrons (for details see Hurford et al., 2003;Dorman, 2010, and references therein). Of specific interest are neutrons, the so-called solar neu-trons (e.g., Lingenfelter et al., 1965, and references therein). Since the solar neutrons are neutral,they propagate straight to the Earth, therefore bringing direct information of the acceleration site.If the energy of solar neutrons is greater than about 100 MeV, they can induce a nucleonic cascadein the Earth’s atmosphere and can be registered by NMs. The sensitivity of a NM to solar neutronsis greater when the atmospheric depth in the solar direction is smaller, because the atmosphere at-tenuates the flux of secondary nucleons in the cascade. An optimal location is high-altitude, closeto the Equator (Usoskin et al., 1997). In order to improve this capability, it is recommended toextend the current network with at least two high-altitude NMs, namely one located at the CanaryIslands and the other in New Zealand, and to re-open the Haleakala (HLEA) NM, details givenare in Table 1, (see also Artamonov et al., 2016). We note that the Canary Island NM is underconstruction (Private communication). We discussed the current status and application of the global neutron monitor network to study so-lar energetic particles, specifically for space weather purposes, namely alerts, assessment of SEPcharacteristics and the corresponding computation of the exposure to radiation at flight altitudes.As an example, we presented the ability of the global NM network data to be used for deriva-tion of the spectra and angular distribution of SEPs during the strongest GLE event of the ob-servational era: GLE
Acknowledgements
This work was supported by the Academy of Finland (project 321882 ESPERA) and (project304435 CRIPA-X). The work benefits from discussions in the framework of the InternationalSpace Science Institute International Team 441: High EneRgy sOlar partICle Events Analysis(HEROIC). The authors acknowledge all the researchers, NM station managers and colleagueswho collected the GLE records used for the analysis of GLE http://gle.oulu.fi/ / ). OuluNM data are also available at http://cosmicrays.oulu.fi .15 eferences Adriani, O., G. Barbarino, G. Bazilevskaya, R. Bellotti, M. Boezio, et al. Measurments ofCosmic-Ray Hydrogen and Helium Isotopes with the PAMELA Experiment.
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