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The PI2FA project focused on creating and applying tools for multi-dimensional modeling of partially ionized chromospheric plasma based on the single-fluid and two-fluid multi-species formalism. Scientific questions include clarifying chromospheric heating mechanisms, creating multi-dimensional realistic models of the solar chromosphere incorporating ion-neutral effects, and understanding neutrals' role in prominence dynamics. The research focused on fundamental mechanisms of energy propagation and exchange in complex plasmas, such as waves, instabilities, and plasma-radiation interactions, seeking the transition from one-dimensional idealized models to multi-dimensional simulations, and observational support. Among the main conclusions, our research unveiled that multi-fluid effects become pronounced for waves with frequencies lower than typical inter-particle collisional frequencies, unlike suggested by theory of waves in homogeneous plasmas; we showed that ambipolar heating is most significant in the quietest regions, characterized by small-scale dynamo fields; we found that multi-fluid effects hold great importance within transition layers between cool and hot materials, such as the solar transition region and prominence-corona interface. Multi-fluid effects operate at scales beyond the resolution capabilities of even our most advanced instrumentation, necessitating specialized observational initiatives. Our initial steps in this direction allowed the detection of subtle differences in velocities between ions and neutrals, in line with theoretical predictions.
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