First Order Fermi Acceleration
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 (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:
where the spectral index depends, for non-relativistic shocks, only on the compression ratio of the shock.
The term "First order" comes from the fact that the energy gain per shock crossing is proportional to, the velocity of the shock divided by the speed of light.
Read more about this topic: Fermi Acceleration
Famous quotes containing the word order:
“A self is, by its very essence, a being with a past. One must look lengthwise backwards in the stream of time in order to see the self, or its shadow, now moving with the stream, now eddying in the currents from bank to bank of its channel, and now strenuously straining onwards in the pursuit of its chosen good.”
—Josiah Royce (1855–1916)