We present results of a new time-dependent kinetic model of the H atom penetration through the solar wind - interstellar medium interaction region. A kinetic 6D (time, two dimensions in space, and three dimensions in velocity-space) equation for interstellar H atoms was solved self-consistently with time-dependent Euler equations for the solar wind and interstellar charged components. We study the response of the interaction region to 11-year solar cycle variations of the solar wind dynamic pressure. It is shown that the termination shock location varies within ±7 AU, the heliopause variation is ~4 AU, and the bow shock variation is negligible. At large heliocentric distances, the solar cycle induces 10-12% fluctuations in the number density of both primary and secondary interstellar H atoms and atoms created in the inner heliosheath. We underline the kinetic behavior of the fluctuations of the H atom populations. Closer to the Sun the fluctuations increase up to 30-35% at 5 AU due to solar cycle variation of the charge exchange rate. Solar cycle variations of interstellar H atoms in the heliospheric interface and within the heliosphere may have major importance for the interpretation of H atom observations inside the heliosphere
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