Estimation of Radiation Exposure for Various Flights from Athens International Airport

: In recent decades, the exposure of aviation crews and passengers to cosmic radiation has been progressively increasing due to the growing need of flights. Therefore, there is a need for radiation assessment software tools to act as a complement to other radiation protection techniques and countermeasures. In this work, the exposure to cosmic radiation is estimated for flights from Athens International Airport to various international destinations, by performing Monte Carlo simulations with the validated tool DYASTIMA/DYASTIMA-R. The results of the estimated total ambient dose equivalent, as well as the ambient dose equivalent rate for different flights, applying a typical flying level and constant atmospheric conditions, are presented for the first time. This study is carried out for different phases of solar activity for the time period from 1996 to 2019, which includes the two recent Solar Cycles 23 and 24.


Introduction
During recent decades, the aviation industry has presented a trend of great growth, which has been driven by financial growth and development as well as the need for a more efficient global connectivity.While there have been a few short-term disruptions, mainly due to the COVID-19 pandemic, between 2020 and 2022, with many flights being either cancelled or operated at lower capacities, the aviation industry has demonstrated adaptability and resilience over time, flourishing and providing many opportunities not only for leisure, but also for work, creating many job positions.However, becoming a crew member (either pilot or flight attendant) is quite challenging and demanding, as there are many requirements and demands, such as education, training, skills, competencies, and physical and mental demands.
Therefore, due to the nature of their profession, aircrews are in general healthy compared to the general population, also known as the "healthy worker effect".This is both due to the selection process in order for someone to become a pilot or flight attendant, and due to the continuous and rigorous monitoring of crew health [1,2], along with the completely different lifestyle and high socio-economic status of this group.As a result, overall crew mortality is lower than that of the general population, while most medical factors, such as smoking and alcohol consumption, are less prevalent among aircrews.However, aircrews are occupationally exposed to factors that may have a negative impact on their health.Typical examples are various carcinogenic and mutagenic agents such as ionizing cosmic radiation, ultraviolet radiation, magnetic fields from cockpit instruments, ozone, various volatile substances such as aerosols, cabin air pollutants, emissions from aircraft fuel, irregular working hours, and continuous circadian rhythm disturbances [3].
Aircraft crews are constantly exposed to galactic cosmic radiation and, in exceptional cases, they may also be exposed to extreme solar energetic particle (SEP) events (energies higher than 200 MeV), which are more prevalent at high geographic latitudes and may result in ground-level enhancements in cosmic ray intensity (GLEs) [4][5][6][7][8].During some extreme events, GLEs may be recorded in lower-latitude regions as well (e.g., November 2003) [9].Thus, the exposure of pilots and cabin crews to cosmic radiation depends on various parameters such as altitude, flight path, duration of the flight, as well as solar activity [10].The study of the ambient dose equivalent rate as a function of geomagnetic shielding and solar activity is particularly significant for radiation protection purposes, as it may contribute to the assessment of radiation doses received by aircraft passengers and crew during different flights.It is highlighted that the radiation dose for passengers on aircrafts is less of a concern as they fly much less often compared to aircrew.Numerous studies have been conducted to calculate the radiation dose for various aviation routes during different solar activity phases [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] and a variety of analytical methods and models have been used so far.
However, besides the impact on health that crew face during flights due to cosmic radiation, electronic systems are also vulnerable to such radiation.More specifically, the radiation that penetrates the fuselage of the aircraft is responsible for additional thermal and shot noise on the complex electronic systems (called avionics) [26].Such noise increases the probability of error during signal transmission between devices or by depositing electric charges in the logical record, changing the information stored in cells.If these electric charges occur in multiple cells, a Multiple Bit Upset (MBU) is caused.Such effects may lead to the total failure of some electronic devices during flights, increasing the probability of accidents.In order to avoid radiation effects on electronic systems, various protection technologies and materials have been developed for absorbing and decreasing radiation on sensitive electronic components.Therefore, a study on radiation dose during flights will help in the estimation of electronic failure probability and choose suitable solutions for decreasing such a probability.
In this work, the radiation dose during different flight routes is estimated by performing Monte Carlo simulations with the validated software tool Dynamic Atmospheric Shower Tracking Interactive Model Application (DYASTIMA) [27,28], and its extension DYASTIMA-R, for the first time.DYASTIMA is a GEANT4 software application that can be used for the description and the calculation of different parameters regarding the secondary cosmic ray particles cascade, such as the energy of the particles and the energy deposition, generated by primary cosmic ray particles hitting the top of the Earth's atmosphere.The standalone tool was developed and validated by the Athens Cosmic Ray Group, and it is available alongside a Software User Manual at the Athens Neutron Monitor Station portal (http://cosray.phys.uoa.gr/index.php/dyastima)(accessed on 11 December 2023).The feature DYASTIMA-R was added in order to provide an estimation of several radiobiological parameters, which is crucial for the radiation assessment of the aircrews' occupational exposure to solar and galactic cosmic radiation (which consists of about 90% protons, 8% alpha particles, and small amounts of heavier nuclei, electrons, and positrons).Specifically, this new functionality allows radiation dose calculations on a human phantom to be performed, through a second simulation which is realized based on the results provided by DYASTIMA output for the different tracking layers (the atmospheric altitudes where the tracking of particles takes place).In order to conduct a radiation assessment analysis, international flights from Athens, Greece, to a range of destinations are selected.Results regarding the total ambient dose equivalent through a whole flight, as well as the ambient dose equivalent rate, are presented for the first time, while a comparison with other well-known and widely used software is performed.The results are thoroughly discussed, while, finally, conclusions and future steps are presented.The remainder of this paper is organized as follows: in Section 2, the method of calculating the ambient dose equivalent is presented.In Section 3, the results of this research are presented, and they are discussed in Section 4. The theoretically optimal path followed on each flight is illustrated in Figure 1.It is worth noting that the path for each flight, as well as the determination of its duration, is based on the theory of great circles, rather than on straight lines.As we move on a spherical surface, like Earth, the shortest path (geodesic) between two points corresponds, according to Riemannian geometry, to a great circle, and not to a straight line as in Euclidean geometry.The determination of the trajectory of each flight was carried out by using Python and applying the Geodesic routines of GeographicLib, as described at https://geographiclib.sourceforge.io/html/python/index.html(accessed on 10 November 2023).In this way, the distance between the beginning and final destination is divided into points whose distance is approximately 1 • .Through this procedure, the geographic coordinates of these points were defined, and then they were matched with the corresponding magnetic rigidity threshold values based on the magnetic rigidity maps that are available in the literature [36][37][38][39].These maps provide the magnetic rigidity value for each 5 • geographic latitude and 15 • geographic longitude at an altitude of 20 km, using the International Geomagnetic Reference Field (IGRF) model for the magnetic field for the respective time intervals.Finally, the magnetic rigidity values were matched with the corresponding values of the ambient equivalent dose rate dH*/dt, as calculated using simulations with DYASTIMA-R.

Results
In order to calculate the total ambient dose equivalent H*(10)total due to cosmic radiation, the duration of each flight was divided into ten-minute intervals.For each of the intervals, the dose was calculated, and subsequently, the cumulative exposure was computed.These calculations were conducted for an average flying altitude of 10.67 km or 35,000 ft (FL350), assuming constant atmospheric conditions, and without taking into account the altitude variation during take-off and landing.The results presented in Figure 2 provide an estimation of the H*(10) total of the flights listed in Table 2 for the years 2001 and 2009, corresponding to maximum and minimum solar activity conditions.The results are shown in the form of histograms in Figure 2, where the flights are arranged in ascending order of flight duration.It should be highlighted that, in all cases, these radiation doses remain within the permitted exposure limits; however, particular attention should be paid to the occupational exposure of pilots and flight attendants, as the doses are cumulative over the year.Greece adheres to EU directives on radiation protection, specifically the Basic Safety Standards Directive (2013/59/Euratom).This directive establishes fundamental standards, including a 20-millisieverts (mSv) annual dose limit for occupational exposure to ionizing radiation, with additional restrictions on equivalent doses to specific organs and tissues.The doses received by aircraft crews depend on the altitude, the duration, and the route of the flight, as well as on solar activity.As expected, a higher dose is observed during solar minimum conditions (2009), due to the negative correlation of cosmic ray intensity and solar activity.This is because during high solar activity, the intensified solar wind forms a protective shield that reduces cosmic ray intensity.In contrast, during low solar activity, the weakened solar wind allows more cosmic rays to penetrate, creating a negative correlation between cosmic ray intensity and solar activity.
It is also observed that the flights with the shortest duration (Athens-Larnaca and Athens-Rome) present the lowest dose values, while the flights with the longest duration (Athens-New York and Athens-Tokyo) have the highest dose values.However, we cannot draw a clear conclusion on radiation exposure based on flight duration alone.As shown, while the Athens-Madrid flight has the same duration as the Athens-London flight, the former has a lower overall dose.Similarly, the Athens-Dubai flight is longer than the Athens-Stockholm flight, and yet has a lower total dose.This shows the significant effect of the aircraft route of each flight, especially the geographic latitude, which is related to magnetic rigidity [21,22].

Results
In order to calculate the total ambient dose equivalent H*(10) total due to cosmic radiation, the duration of each flight was divided into ten-minute intervals.For each of the intervals, the dose was calculated, and subsequently, the cumulative exposure was computed.These calculations were conducted for an average flying altitude of 10.67 km or 35,000 ft (FL350), assuming constant atmospheric conditions, and without taking into account the altitude variation during take-off and landing.The results presented in Figure 2 provide an estimation of the H*(10) total of the flights listed in Table 2 for the years 2001 and 2009, corresponding to maximum and minimum solar activity conditions.The results are shown in the form of histograms in Figure 2, where the flights are arranged in ascending order of flight duration.It should be highlighted that, in all cases, these radiation doses remain within the permitted exposure limits; however, particular attention should be paid to the occupational exposure of pilots and flight attendants, as the doses are cumulative over the year.Greece adheres to EU directives on radiation protection, specifically the Basic Safety Standards Directive (2013/59/Euratom).This directive establishes fundamental standards, including a 20-millisieverts (mSv) annual dose limit for occupational exposure to ionizing radiation, with additional restrictions on equivalent doses to specific organs and tissues.The doses received by aircraft crews depend on the altitude, the duration, and the route of the flight, as well as on solar activity.As expected, a higher dose is observed during solar minimum conditions (2009), due to the negative correlation of cosmic ray intensity and solar activity.This is because during high solar activity, the intensified solar wind forms a protective shield that reduces cosmic ray intensity.In contrast, during low solar activity, the weakened solar wind allows more cosmic rays to penetrate, creating a negative correlation between cosmic ray intensity and solar activity.
It is also observed that the flights with the shortest duration (Athens-Larnaca and Athens-Rome) present the lowest dose values, while the flights with the longest duration (Athens-New York and Athens-Tokyo) have the highest dose values.However, we cannot draw a clear conclusion on radiation exposure based on flight duration alone.As shown, while the Athens-Madrid flight has the same duration as the Athens-London flight, the former has a lower overall dose.Similarly, the Athens-Dubai flight is longer than the Athens-Stockholm flight, and yet has a lower total dose.This shows the significant effect of the aircraft route of each flight, especially the geographic latitude, which is related to magnetic rigidity [21,22].Consequently, in addition to the total dose, it is instructive to also estimate the ambient dose equivalent rate dH*(10)/dt during a flight.In order to achieve that, the total dose is divided by the time duration of each flight.The results are shown in Figure 3, for the time period 1996-2019, also known as Solar Cycles 23 and 24.The lowest ambient dose equivalent rate is observed on the Athens-Dubai flight while the highest dose rate is observed on the Athens-Reykjavik flight.This is because Reykjavik as a destination is located at the highest geographic latitude, resulting in the aircraft passing through points of low magnetic rigidity during the flight.Low cut-off rigidities lead to increased dose rates, as the Earth s magnetic field lines are more "open" and, therefore, a larger number of particles with even lower energies can penetrate and, through their interactions with the atoms/nuclei of the atmosphere, give rise to products that reach the usual flying levels.On the contrary, Dubai is located at low latitude (also known as greater magnetic rigidity) and thus has a lower ambient dose equivalent rate, as the very perplexed geomagnetic field provides better shielding against low-energy incoming particles.Flights to central Europe (Amsterdam, Berlin, Brussels, and Paris) have almost the same dose rate, while flights to northern regions of Europe (London, Stockholm, and Moscow) present an increased dose rate.Similarly, the destinations in the greater Mediterranean region (Madrid, Rome, and Larnaca) show much lower dose rates.
It is worth noting that the ambient dose equivalent rate during the flights follows the 11-year and 22-year solar cycle to a greater or lesser degree [40], due to the negative correlation between solar activity and galactic cosmic ray intensity.Specifically, the highest dose rates due to galactic cosmic radiation occur during the time period 2007-2009, which corresponds to the extended solar minimum observed between Solar Cycles 23 and 24, while the lowest dose rates correspond to the solar maxima of Solar Cycles 23 and 24 (2001 and 2014, respectively).The dependence on solar activity is evident in flights with destinations of high geographic latitude and low magnetic rigidity (such as Reykjavik, Stockholm, New York, Central Europe, and Tokyo), while the dose rate in low-latitude flights is almost independent of the phase of the solar cycle (such as the Mediterranean region and Dubai).Consequently, in addition to the total dose, it is instructive to also estimate the ambient dose equivalent rate dH*(10)/dt during a flight.In order to achieve that, the total dose is divided by the time duration of each flight.The results are shown in Figure 3, for the time period 1996-2019, also known as Solar Cycles 23 and 24.The lowest ambient dose equivalent rate is observed on the Athens-Dubai flight while the highest dose rate is observed on the Athens-Reykjavik flight.This is because Reykjavik as a destination is located at the highest geographic latitude, resulting in the aircraft passing through points of low magnetic rigidity during the flight.Low cut-off rigidities lead to increased dose rates, as the Earth's magnetic field lines are more "open" and, therefore, a larger number of particles with even lower energies can penetrate and, through their interactions with the atoms/nuclei of the atmosphere, give rise to products that reach the usual flying levels.On the contrary, Dubai is located at low latitude (also known as greater magnetic rigidity) and thus has a lower ambient dose equivalent rate, as the very perplexed geomagnetic field provides better shielding against low-energy incoming particles.Flights to central Europe (Amsterdam, Berlin, Brussels, and Paris) have almost the same dose rate, while flights to northern regions of Europe (London, Stockholm, and Moscow) present an increased dose rate.Similarly, the destinations in the greater Mediterranean region (Madrid, Rome, and Larnaca) show much lower dose rates.
It is worth noting that the ambient dose equivalent rate during the flights follows the 11-year and 22-year solar cycle to a greater or lesser degree [40], due to the negative correlation between solar activity and galactic cosmic ray intensity.Specifically, the highest dose rates due to galactic cosmic radiation occur during the time period 2007-2009, which corresponds to the extended solar minimum observed between Solar Cycles 23 and 24, while the lowest dose rates correspond to the solar maxima of Solar Cycles 23 and 24 (2001 and 2014, respectively).The dependence on solar activity is evident in flights with destinations of high geographic latitude and low magnetic rigidity (such as Reykjavik, Stockholm, New York, Central Europe, and Tokyo), while the dose rate in low-latitude flights is almost independent of the phase of the solar cycle (such as the Mediterranean region and Dubai).

Discussion
The DYASTIMA/DYASTIMA-R software application has been successfully validated according to international standards set by the International Committee on Radiological Protection (ICRP) [41] and the International Commission on Radiation Units and Measurements (ICRU) [42] and has been used successfully for the calculation of the energy deposition as well as the ambient dose equivalent rate in the atmosphere of Earth for different scenarios (i.e., different atmospheric altitudes, different values of geomagnetic cutoff rigidity, different periods of solar activity), as well as other planets, such as Venus [29] and Mars [43].This is the first time that it has been used in order to estimate the ambient dose equivalent during a whole flight and not just for specific points.
For this reason, a comparison was made between the values obtained with DYAS-TIMA-R and those from the Federal Aviation Administration s (FAA) internationally recognized CARI-7 software, one of the oldest models available for radiation assessment [44].The comparison was performed for the years 2001 and 2009, taking FL350 as the flight altitude, and it is presented in Figure 4.It is observed that the values obtained with DY-ASTIMA-R are similar to those obtained with CARI-7.Small deviations are observed for flights of short and medium durations (approximately 20%), while the largest deviations (approximately 30%) are observed for the two long-duration flights (Athens-New York and Athens-Tokyo), both in 2001 and 2009, respectively.The difference is due to the systematic errors of the DYASTIMA input parameters, as they are mostly based on models, as well as the simplified flight profile which does not take into consideration changes in flying altitude during the flight (for example, lower or higher FLs), take-off and landing, as well as the actual route of the plane.Furthermore, each model requires different solar parameters.For example, DYASTIMA-R uses the differential primary cosmic ray spectrum (in this work provided by ISO15390 model, as retrieved by using the tool OMERE by TRAD), while CARI-7 takes into account the solar activity by using the sunspot number.But, regardless of the different parameters they use as input, they also use different numerical methods for extracting the results.More precisely, CARI-7 uses the MCNPX method while DYASTIMA-R uses the Geant4 method.So, it is obvious that the results will

Discussion
The DYASTIMA/DYASTIMA-R software application has been successfully validated according to international standards set by the International Committee on Radiological Protection (ICRP) [41] and the International Commission on Radiation Units and Measurements (ICRU) [42] and has been used successfully for the calculation of the energy deposition as well as the ambient dose equivalent rate in the atmosphere of Earth for different scenarios (i.e., different atmospheric altitudes, different values of geomagnetic cut-off rigidity, different periods of solar activity), as well as other planets, such as Venus [29] and Mars [43].This is the first time that it has been used in order to estimate the ambient dose equivalent during a whole flight and not just for specific points.
For this reason, a comparison was made between the values obtained with DYASTIMA-R and those from the Federal Aviation Administration's (FAA) internationally recognized CARI-7 software, one of the oldest models available for radiation assessment [44].The comparison was performed for the years 2001 and 2009, taking FL350 as the flight altitude, and it is presented in Figure 4.It is observed that the values obtained with DYASTIMA-R are similar to those obtained with CARI-7.Small deviations are observed for flights of short and medium durations (approximately 20%), while the largest deviations (approximately 30%) are observed for the two long-duration flights (Athens-New York and Athens-Tokyo), both in 2001 and 2009, respectively.The difference is due to the systematic errors of the DYASTIMA input parameters, as they are mostly based on models, as well as the simplified flight profile which does not take into consideration changes in flying altitude during the flight (for example, lower or higher FLs), take-off and landing, as well as the actual route of the plane.Furthermore, each model requires different solar parameters.For example, DYASTIMA-R uses the differential primary cosmic ray spectrum (in this work provided by ISO15390 model, as retrieved by using the tool OMERE by TRAD), while CARI-7 takes into account the solar activity by using the sunspot number.But, regardless of the different parameters they use as input, they also use different numerical methods for extracting the results.More precisely, CARI-7 uses the MCNPX method while DYASTIMA-R uses the Geant4 method.So, it is obvious that the results will be biased differently with different systematic errors.Many benchmark tests have been carried out for the performance of these two methods [45,46].be biased differently with different systematic errors.Many benchmark tests have been carried out for the performance of these two methods [45,46].It is worth noting that at this moment, the geometry and shielding of the aircraft are not taken into account by DYASTIMA/DYASTIMA-R software.Thus, the actual exposure inside the aircraft may be lower than the calculations made inside the atmosphere, depending on the type of the aircraft, the position of the person inside, the number of passengers, and the amount of fuel.For this reason, it is considered necessary to place detectors inside the cabin of the aircraft in order to include the effect of all the above [44].The actual data retrieved during these experiments could then be used for correcting the results obtained by DYASTIMA.Future plans for DYASTIMA include the possibility of optionally using aircraft geometry made of different materials, so that the shielding offered by each material can be studied.
As it seems, the calculation of the dose due to cosmic radiation (either the H*(10)total or the dH*(10)/dt)) during a flight is not an easy task, as it requires data from a very large number of simulations to be processed for different geographical coordinates, different values of magnetic rigidities, different atmospheric altitudes, and different phases of solar activity.In this context, a first attempt was made to estimate the dose during flights from Athens to different destinations using the software DYASTIMA/DYASTIMA-R. Future plans include the use of a more realistic flight path, i.e., more flight levels, altitude variation, take-off and landing time calculation, and more accurate trajectories, as well as performing dose calculations for more flights around the world.These results could then be compared to others found in the literature or provided by other software models, such as CARI-7 and AVIDOS [47].Another interesting plan is the estimation of the radiation dose during solar energetic particle events (SEPs) and ground-level enhancements (GLEs) of cosmic ray intensity, as well as a comparison of the results with those of other software and models [15,[48][49][50].During these events, depending on the flight path, the dose rate It is worth noting that at this moment, the geometry and shielding of the aircraft are not taken into account by DYASTIMA/DYASTIMA-R software.Thus, the actual exposure inside the aircraft may be lower than the calculations made inside the atmosphere, depending on the type of the aircraft, the position of the person inside, the number of passengers, and the amount of fuel.For this reason, it is considered necessary to place detectors inside the cabin of the aircraft in order to include the effect of all the above [44].The actual data retrieved during these experiments could then be used for correcting the results obtained by DYASTIMA.Future plans for DYASTIMA include the possibility of optionally using aircraft geometry made of different materials, so that the shielding offered by each material can be studied.
As it seems, the calculation of the dose due to cosmic radiation (either the H*(10) total or the dH*(10)/dt)) during a flight is not an easy task, as it requires data from a very large number of simulations to be processed for different geographical coordinates, different values of magnetic rigidities, different atmospheric altitudes, and different phases of solar activity.In this context, a first attempt was made to estimate the dose during flights from Athens to different destinations using the software DYASTIMA/DYASTIMA-R. Future plans include the use of a more realistic flight path, i.e., more flight levels, altitude variation, take-off and landing time calculation, and more accurate trajectories, as well as performing dose calculations for more flights around the world.These results could then be compared to others found in the literature or provided by other software models, such as CARI-7 and AVIDOS [47].Another interesting plan is the estimation of the radiation dose during solar energetic particle events (SEPs) and ground-level enhancements (GLEs) of cosmic ray intensity, as well as a comparison of the results with those of other software and models [15,[48][49][50].During these events, depending on the flight path, the dose rate may be significantly enhanced and affect the health of everyone on board, i.e., pilots, flight attendants, and passengers; thus, such a study would be of great importance.

Figure 1 .
Figure 1.Flights from Athens International Airport used in this study.

Figure 1 .
Figure 1.Flights from Athens International Airport used in this study.

Figure 2 .
Figure 2. The total ambient dose equivalent H*(10) for international flights from Athens for solar maximum and solar minimum conditions (2001 and 2009, respectively) as estimated by DYASTIMA-R.

Figure 2 .
Figure 2. The total ambient dose equivalent H*(10) for international flights from Athens for solar maximum and solar minimum conditions (2001 and 2009, respectively) as estimated by DYASTIMA-R.

Figure 3 .
Figure 3.The ambient dose equivalent rate dH*(10)/dt during international flights from Athens as calculated by DYASTIMA-R.

Figure 3 .
Figure 3.The ambient dose equivalent rate dH*(10)/dt during international flights from Athens as calculated by DYASTIMA-R.

Figure 4 .
Figure 4. Comparison of the total ambient dose equivalent H*(10) for international flights from Athens for 2001 (upper panel) and 2009 (lower panel), respectively, as calculated by DYASTIMA-R (blue) and CARI-7 (red).

Figure 4 .
Figure 4. Comparison of the total ambient dose equivalent H*(10) for international flights from Athens for 2001 (upper panel) and 2009 (lower panel), respectively, as calculated by DYASTIMA-R (blue) and CARI-7 (red).

Table 1 .
Airports used in this study including their geographical coordinates.

Table 2 .
Duration of flights used in this study.