[1] In this paper we use the fluence distributions observed by two different instruments, RHESSI and Fermi GBM, corrected for the effects of their different orbits, combined with their different daily TGF detection rates and their relative sensitivities to make an estimate of the true fluence distribution of TGFs as measured at satellite altitudes. The estimate is then used to calculate the dead-time loss for an average TGF measured by RHESSI. An independent estimate of RHESSI dead-time loss and true fluence distribution is obtained from a Monte Carlo (MC) simulation in order to evaluate the consistency of our results. The two methods give RHESSI dead-time losses of 24-26% for average fluence of 33-35 counts. Assuming a sharp cut-off the true TGF fluence distribution is found to follow a power law with l = 2.3 AE 0.2 down to $5/600 of the detection threshold of RHESSI. This corresponds to a lowest number of electrons produced in a TGF of $10 14 and a global production rate within AE38 latitude of 50000 TGFs/day or about 35 TGFs every minute, which is 2% of all IC lightning. If a more realistic distribution with a roll-off below 1/3 (or higher) of the RHESSI lower detection threshold with a true distribution with l ≤ 1.7 that corresponds to a source distribution with l ≤ 1.3 is considered, we can not rule out that all discharges produce TGFs. In that case the lowest number of total electrons produced in a TGF is $10 12 .

[1] Up to a few years ago, terrestrial gamma ray flashes (TGFs) were only observed by spaceborne instruments. The aircraft campaign ADELE was able to observe one TGF, and more attempts on aircraft observations are planned. There is also a planned campaign with stratospheric balloons, COBRAT. In this context an important question that arises is what count rates we can expect and how these estimates are affected by the initial properties of the TGFs. Based on simulations of photon propagation in air we find the photon fluence at different observation points at aircraft and balloon altitudes. The observed fluence is highly affected by the initial parameters of the simulated TGFs. One of the most important parameters is the number of initial photons in a TGF. In this paper, we give a semi-analytical approach to find the initial number of photons with an order of magnitude accuracy. The resulting number varies over several orders of magnitude, depending mostly on the production altitude of the TGF. The initial production altitude is also one of the main parameters in the simulations. Given the same number of initial photons, the fluence at aircraft and balloon altitude from a TGF produced at 10 km altitude is 2-3 orders of magnitude smaller then a TGF originating from 20 km altitude. Other important parameters are altitude distribution, angular distribution and amount of feedback. The differences in altitude, altitude distribution and amount of feedback are especially important for the fluence of photons observed at altitudes less than 20 km, and for instruments with a low-energy threshold larger than 100 keV. We find that the maximum radius of observation in 14 km for a TGF with the intensity of an average RHESSI TGF is smaller than the results reported by Smith et al. (2011), and our results support the conclusion in Gjesteland et al. (2012) and Østgaard et al. (2012) that TGFs probably are a more common phenomenon than previously reported.Citation: Hansen, R. S., N. Østgaard, T. Gjesteland, and B. Carlson (2013), How simulated fluence of photons from terrestrial gamma ray flashes at aircraft and balloon altitudes depends on initial parameters,

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