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Prompted by the relevant problem of temperature inversion (i.e. gradient ofdensity anti-correlated to the gradient of temperature) in solar physics, weintroduce a novel method to model a gravitationally confined multi-componentcollisionless plasma in contact with a fluctuating thermostat. The dynamics isdescribed via a set of effective partial differential equations for thecoarse-grained versions of the distribution functions of the plasma componentsand a temporally coarse-grained energy reservoir. We derive a stationarysolution of this system naturally predicting the inverted density-temperatureprofiles of the two-species as observed in systems of astrophysical interestsuch as the solar corona. We validate our method by comparing the analyticalresults with kinetic numerical simulations of the plasma dynamics in thecontext of the two-species Hamiltonian mean-field model (HMF). Finally, weapply our theoretical framework to the problem of the temperature inversion inthe solar corona obtaining density and temperature profiles in remarkably goodagreement with the observations.

Temperature inversion in a non-homogeneous collisionless plasma with a thermal boundary: the temporal coarse-graining method