Evaluation of effective dose for gamma-rays of terrestrial gamma-ray flashes in aviation: spectral- and atmosphere-effects

Terrestrial Gamma-ray Flashes (TGFs) are intense and fast gamma-ray emissions, energy up to 100 MeV, generated within the Earth's atmosphere at altitudes below 20 km. Satellite observations indicate the TGFs are not a rare phenomenon, being produced on average at one per thunderstorm, yielding a global production rate of approximate to 35 TGFs/min within a latitude band of +/- 38 degrees. Furthermore, the TGFs may coincide with the flight altitudes for several commercial aircraft routes, typically within the 10-14 km range, and thus cause passengers/crews unexpected exposure to large fluxes of high-energy ionizing radiation, namely for distances of the order of km. Herein, we introduce a novel approach based on a simple analytic/numeric methodology to estimate the TGFs gamma-ray emissions effective doses based on the differential fluence of photons at aircraft altitude and tabulated effective dose conversion coefficients versus the photon energy. For the first time, we examine the effective dose dependence on TGF's gamma-ray energy spectrum models found in literature and the atmosphere mass thickness crossed by the gamma-rays. Additionally, since the real irradiation geometry of the whole body in aircraft might be a combination of the several idealized geometries used in radiation protection, we considered beyond the typical anteroposterior (AP), the posteroanterior (PA), and the rotational (ROT) geometries as representative irradiation geometries in exposure to TGF gamma-ray's emissions. We calculated the effective dose versus the distance between the TGF site and the aircraft altitude (12.5 km) within the 0.1-5.0 km range and atmosphere mass thickness within the 3.3-213 g cm(-2) range. Additionally, we calculated the average effective dose per fluence versus the atmosphere mass thickness crossed by the gammarays. At a distance of 1 km (34 g cm(-2)) and for the typical exponential cut-off power-law model (alpha = 1, E-C = 7.3 MeV), the effective dose was within the 0.18-0.19 mSv range, being the respective average effective dose per fluence within the 10.8-11.6 pSv cm(2) range. Moreover, for the variant of the exponential cut-off power-law model (alpha = 1, E-C = 7.3 MeV, E-min = 1 MeV), the effective dose was within the 0.42-0.46 mSv range, being the respective average effective dose per fluence at 34 g cm(-2) within the 12.7-13.6 pSv cm(2) range. Generally, the data obtained agree with the scarce data found in the literature for similar conditions, evidencing the effect of the parameterization of the TGFs gamma-rays energy models, which may result in a 2- to 10-fold effective dose escalation. For the typical exponential cut-off power-law model (alpha = 1, E-C = 7.3 MeV), the data obtained for an aircraft that passes through the vicinity of one TGF, with a distance of 1 km, points to an increase of the aircraft crew and passengers' doses of few tenths mSv over the cosmic radiation dose of few tens mu Sv along a typical flight of 6 h duration, representing approximate to 20% and approximate to 1% of the ICRP-2007 annual reference levels for passengers (1 mSv) and aircraft crew (20 mSv), respectively. More, with a distance of 0.5 km, the effective dose value is comparable with the annual dose for the aircraft crew due to the cosmic radiation for a typical yearly flight time of 500 h, representing approximate to 130% and approximate to 7% of the ICRP-2007 annual reference levels for passengers and aircraft crew, respectively.