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holds if the mirror is receding. This notion was used by Fermi (1949) to explain the mode of formation of cosmic rays. In this case the magnetic mirror is a moving interstellar magnetized cloud. In a random motion environment, Fermi argued, the probability of a head-on collision is greater than a head-tail collision, so particles would, on average, be accelerated. This random process is now called second-order Fermi acceleration, because the mean energy gain per bounce depends on the mirror velocity squared,
74:(downstream to upstream) at increased velocity. If a similar process occurs upstream, the particle will again gain energy. These multiple reflections greatly increase its energy. The resulting energy spectrum of many particles undergoing this process (assuming that they do not influence the structure of the shock) turns out to be a power law:
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Second order Fermi acceleration relates to the amount of energy gained during the motion of a charged particle in the presence of randomly moving "magnetic mirrors". So, if the magnetic mirror is moving towards the particle, the particle will end up with increased energy upon reflection. The opposite
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Shock waves typically have moving magnetic inhomogeneities both preceding and following them. Consider the case of a charged particle traveling through the shock wave (from upstream to downstream). If it encounters a moving change in the magnetic field, this can reflect it back through the shock
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There are two types of Fermi acceleration: first-order Fermi acceleration (in shocks) and second-order Fermi acceleration (in the environment of moving magnetized gas clouds). In both cases the environment has to be collisionless in order for the mechanism to be effective. This is because Fermi
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acceleration only applies to particles with energies exceeding the thermal energies, and frequent collisions with surrounding particles will cause severe energy loss and as a result no acceleration will occur.
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On the Origin of the Cosmic
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depends, for non-relativistic shocks, only on the compression ratio of the shock.
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Rieger, Bosch-Ramon and Duffy: Fermi acceleration in astrophysical jets.
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Acceleration phenomenon of oft-reflected charged particles
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undergo when being repeatedly reflected, usually by a
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Krymskii G.F. (1977) Dokl. Akad. Nauk SSSR 234, 1306
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