This is thought to be the primary mechanism by which particles gain non-thermal energies in astrophysical shock waves.
It plays a very important role in many astrophysical models, mainly of shocks including solar flares and supernova remnants.
If it encounters a moving change in the magnetic field, this can reflect it back through the shock (downstream to upstream) at increased velocity.
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:
The term "First order" comes from the fact that the energy gain per shock crossing is proportional to
It is presently unclear what mechanism causes the particles to initially have energies sufficiently high to do so.
[5] 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".
This random process is now called second-order Fermi acceleration, because the mean energy gain per bounce depends on the mirror velocity squared,
The resulting energy spectrum anticipated from this physical setup, however, is not universal as in the case of diffusive shock acceleration.