A kinetic model enabling investigation of the penetration and degradation of a flux of electrons into high-latitude regions of the hydrogen-dominant upper atmosphere of an exoplanet by means of numerical solution of the Boltzmann equation has been developed. It is shown for the case of a dipolar magnetic field that a one-dimensional model makes it possible to obtain a correct solution to this problem. Computations of the precipitation of a flux of electrons from the magnetosphere into the atmosphere of a typical hot Jupiter and the atmosphere of the planet Jupiter in our Solar system have been carried out. The computations assume a Maxwellian velocity distribution for electrons with three characteristic energies, E (0) = 1, 10, and 100 keV. The efficiency of heating the atmosphere of a typical hot Jupiter and the planet Jupiter are considered. The heating efficiency displays only a weak dependence on the characteristic energy of the precipitating electrons. The heating efficiency for the upper atmosphere of Jupiter is also independent of the height, and lies in the range 7-9%. The heating efficiency for the atmosphere of a hot Jupiter depends appreciably on height, and varies from 7 to 18%. In the case of a hot Jupiter, the energy-absorption peaks for electrons with low kinetic energies lie in the region of higher heating efficiencies, substantially strengthening the contribution from precipitating electrons to the total heating of the atmosphere.
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