Kang, 1996; Kang, 1997). The difficulty here is the long time required for particles to be accelerated to these energies. These shocks have characteristic inflow speeds of only $\lsim 0.01$c, and the magnetic fields are probably $\lsim 1~\mu$G. Those lead to acceleration timescales of at least a few times $10^8$ years near 100 EeV, and that will be recalled as the limiting propagation time through the CMB associated with the GZK feature.

These various constraints have significantly narrowed the field of candidate phenomena, but there are still several interesting possibilities. On the other hand we have so far only established constraints and said nothing about the physics of the acceleration process itself. In the next section I will remedy this, focusing especially on acceleration at shocks, since that mechanism is the one most commonly invoked to produce high energy charged particles.

Particle Acceleration Physics
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General Comments
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Cosmic Rays are usually discussed as a distinct population of particles in the universe, although that is largely a consequence of the distinct ways they reveal themselves to us. This approach to the physics is certainly appropriate if UHECRs, for example, are byproducts of the decay of relic massive particles or accelerated 