We study peculiarities of Bose-Einstein condensation of photons that are in
thermodynamic equilibrium with atoms of noninteracting gases. General equations
of the thermodynamic equilibrium of the system under study are obtained. We
examine solutions of these equations in the case of high temperatures, when the
atomic components of the system can be considered as nondegenerated ideal gases
of atoms, and the photonic component can form a state with the Bose condensate.
Transcendental equation for transition temperature and expression for the
density of condensed photons in the considered system are derived. We also
obtain analytical solutions of the equation for the critical temperature in a
number of particular cases. The existence of two regimes of Bose condensation
of photons, which differ significantly in nature of transition temperature
dependence on the total density of photons pumped into the system, is revealed.
In one case, this dependence is a traditional fractional-power law, and in
another one it is the logarithmic law. Applying numerical methods, we determine
boundaries of existence and implementation conditions for different regimes of
condensation depending on the physical parameters of the system under study. We
also show that for a large range of physical systems that are in equilibrium
with photons (from ultracold gases of alkali metals to certain types of ideal
plasma), the condensation of photons should occur according to the logarithmic
regime.Comment: 12 pages, 3 figure