Fermi acceleration transfers bulk-flow energy to fast charged particles through encounters with moving magnetic scattering structures. Scattering is approximately elastic in each structure's rest frame; transformations between these frames produce a systematic energy change.
In first-order Fermi acceleration, converging scattering media produce a mean fractional energy gain linear in their relative speed divided by the particle speed. At a nonrelativistic shock wave, an almost isotropic ultrarelativistic population gains per crossing and per complete return cycle. The distinction between a crossing and a cycle must also be respected when assigning an escape probability.
Diffusive shock acceleration repeatedly returns particles to a shock wave by scattering them in the upstream and downstream plasma. For fluid speeds , particle speed , and shock compression ratio , the cycle gain is and the cycle escape probability is . Their ratio gives for the isotropic phase-space one-particle distribution function. For this is , corresponding to in the ultrarelativistic regime.
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Fermi acceleration refers to a process by which particles gain energy in a system where they are repeatedly scattered by moving obstacles. It is named after the physicist Enrico Fermi, who introduced this concept in the context of cosmic rays. In simple terms, the mechanism involves a particle (such as a proton) that moves through a medium filled with moving obstacles (like shock waves, magnetic fields, or other particles). When the moving particle interacts with these obstacles, it can gain kinetic energy.