| Summary: | 28 February 2017 marked 75 years since the first confident registration of solar cosmic rays (SCRs), i.e., accelerated solar particles with energies from about 106 to ~1010 ÷ 1011 eV. Modern state of the problems related to the studies of Ground Level Enhancements (GLEs) of relativistic SCRs is critically analyzed based on available direct and proxy data. We are also taking into account extremely large fluxes of non-relativistic solar energetic particles (SEPs). Both kinds of SCR events are of great astrophysical and geo-scientific (geophysical) interests. A number of the GLE properties (total statistics, occurrence rate, longitude distribution, ranking of GLEs, a number of specific GLEs – so-called “rogue” SEP events etc.) are discussed in some detail. We note also the problems of GLE identification (definition) by ground-based observations, the difficulties in the studies of weak (“hidden”, or sub-) GLEs etc. One of serious challenges to the problem of radiation hazard in space is a lack of a clear, unambiguous relation between the fluxes (fluences) of relativistic SCR and non-relativistic SEPs. Special attention is paid to the recent debate on the validity, origin and properties of the “ancient” events AD775, AD994, AD1859 (Carrington event) and BC3372. We demonstrate that, in spite of existing uncertainties in proton fluences above 30 MeV, all of them are fitted well by a unique distribution function, at least, with the present level of solar activity. Extremely large SEP events are shown to obey a probabilistic distribution on their fluences with a sharp break in the range of large fluences (or low probabilities). The studies of this kind may be extended for periods with different levels of solar activity in the past and/or in the future. Dose rates at aircraft altitudes are also demonstrated during some GLEs. Several examples of using the SCR data and GLE properties in radiation prediction schemes are considered.
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