In the modern picture of galaxy formation, baryonic feedback is critical for shaping galaxies and regulating star formation. On small scales, feedback results from transporting momentum, radiation, thermal and relativistic particles but current-day magneto-hydrodynamic simulations of galaxies and galaxy clusters often neglect or over-simplify these transport processes. Electrons transport heat and cosmic rays exchange momentum and energy with the thermal plasma but both species are erroneously assumed to diffuse along magnetic field lines. However, this is in conflict with the latest plasma simulations and observations in the solar wind and of the galactic center, which imply efficient wave-particle scatterings so that the electrons and cosmic rays are advected with whistler and Alfvén waves, respectively. We propose a coordinated multi-scale approach that combines plasma kinetic and global fluid models of particle acceleration and transport in galaxies and galaxy clusters with unprecedented accuracy. In particular, we will run novel plasma simulations of shocks at supernovae and galaxy clusters, and study the plasma-wave mediated transport of electrons and cosmic rays. We will employ information field theory to coarse grain these models to derive effective transport coefficients, which will be implemented in macroscopic fluid models of cosmic ray transport and thermal conduction. Simulating feedback by cosmic rays, radiation and supernovae in cosmologically forming galaxies on scales from dwarfs to our Milky Way provides transformative changes of the physics accuracy of these models. This is complemented by cosmological galaxy cluster simulations with improved physics to understand the origin of the cluster-core bimodality, giant radio relics and halos. Comparing mock multi-frequency observables from radio to gamma-rays to data enables falsification or validation of the underlying plasma models and represents a major step towards predictive galaxy formation.
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