The helioglow is a fluorescence of interstellar atoms inside the heliosphere, where they are excited by the solar EUV emission. So far, the helioglow of interstellar H and He have been detected. The helioglow features a characteristic distribution in the sky, which can be used to derive both the properties of interstellar neutral gas and those of the solar wind. This requires a simulation model capable of catching with a sufficient realism the essential coupling relations between the solar factors and interstellar. The solar factors include the solar wind flux and its variation with time and heliolatitude, as well as the heliolatitude and time variation of the solar EUV output. The ISN gas inside the heliosphere features a complex distribution function, which varies with time and location. The paper presents the first version of a WawHelioGlow simulation model for the helioglow flux using an optically thin, single scattering approximation. The helioglow computations are based on a sophisticated kinetic treatment of the distribution functions of interstellar H and He provided by the (n)WTPM model. The model takes into account heliolatitudinal and spectral variations of the solar EUV output from observations. We present a formulation of the model and the treatment of the solar spectral flux. The accompanying Paper II illustrates details of the line of sight evolution of the elements of the model and a brief comparison of results of the WawHelioGlow code with selected sky maps of the hydrogen helioglow, obtained by the SWAN instrument onboard the SOHO mission.
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