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Abstract: Energetic particle generation is an important component of a variety of astrophysical systems, from seed particle generation in shocks to the heating of the solar wind. Starting with the kinetic equation, we have derived a magnetic pumping model, where particles are heated by the largest scale turbulent fluctuations. We show that for a spatially uniform flux tube this is an efficient heating mechanism up to the speed of the fluctuations, and naturally produces power-law distributions like those observed in the solar wind, as verified by particle-in-cell simulations. When this model is extended to a spatially varying flux tube, magnetic trapping renders magnetic pumping an effective Fermi heating mechanism for particles moving far faster than the speed of the fluctuations. To test this, we used satellite observations of the strong, compressional magnetic fluctuations near the Earth's bow shock from the Magnetospheric MultiScale (MMS) mission and found strong agreement with our model. Given the ubiquity of such fluctuations in different astrophysical systems this mechanism has the potential to be transformative to our understanding of how the most energetic particles in the universe are generated.