University of California, Riverside
The Institute of Geophysics and Planetary Physics

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Particle Acceleration at Shocks

As we have seen, shock waves can be exceptionally efficient at converting their kinetic energy into heat. For example, the termination shock converts the extremely cold upstream solar wind plasma to a tremendously hot downstream plasma of one million degrees Kelvin over a very short distance. It is now generally thought that shock waves might therefore somehow also cause some part of the particle population to be accelerated to very high energies. We shall concentrate on just one of several possible acceleration mechanisms that have been suggested: diffusive shock acceleration, also known as first order Fermi acceleration, is of universal applicability and importance.

In the original model proposed by Enrico Fermi, "magnetic clouds" or "scattering centers," moving randomly, scattered particles. Because a fast-moving particle is likely to encounter more "head-on" collisions, in which the cloud and particle move toward each other, than "overtaking" collisions, where the cloud and particle are moving in the same direction, the particle slowly gains energy. The diffusive gain in energy is slow because the "disorganized" motion of the scattering centers ensures that particles can lose energy almost as often as they gain it.

a. Image
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Suppose now that some agency acts to organize the scatterers so that, whenever a particle collides with them, it is effectively a "head-on" collision. In this case, the energy gain would be much faster, that is a first-order process. Since a shock separates a high-speed and a low-speed flow, scattering centers that are convected with the flow, such as magnetic fluctuations, will look as though they are approaching one another from each side of the shock. The shock wave therefore organizes the scattering centers so that a particle scattering between them will see head-on collisions. The scattered particle will then gain energy much more rapidly and efficiently at a shock than in a medium of randomly moving scattering centers.

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Since all particles that are sufficiently energetic to scatter back and forth across a shock are equally likely to experience energization, the resulting particle distribution must be of a power law form, with the exponent determined by the flow speed upstream and downstream of the shock. For a strong shock, the exponent of the power law distribution is very close to the cosmic ray distribution that is observed from energies of several MeV to several TeV (c).

Power Law form:
On a log-log scale, a power law distribution resembles a straight line. The exponent of the power law distribution is the slope of the graph.

c. Image
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This log-log plot shows the flux of cosmic rays bombarding Earth as a function of their energy per particle. Researchers believe cosmic rays with energies less than ~3x1015 eV come from shock waves driven by supernova explosions. The origin of cosmic rays much more energetic than that (above the "knee" in the diagram) remains a mystery.

Voyager has played an important role in elucidating the physics of diffusive shock acceleration in the heliosphere. Researchers have observed diffusive shock acceleration of particles at planetary bow shocks and interplanetary shocks. Also, physicists expect the termination shock to accelerate pickup ions so that they become anomalous cosmic rays (d).

d. Image
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Schematic of the life cycle of a neutral atom. Interstellar neutral atoms stream into the supersonic solar wind, where some experience charge exchange to produce fast, outwardly streaming neutrals and pickup ions. The pickup ions are convected to the shock, where some are energized at the termination shock and become anomalous cosmic rays.

Within the orbit of the Earth, particle acceleration at interplanetary shocks may become a valuable tool in space weather forecasting, because accelerated particles escaping from the shock can run ahead, providing warning of an incipient disturbance.

The efficiency with which particles are accelerated at shocks has the interesting nonlinear effect of modifying the structure of the shock itself. Unlike an ordinary shock, where the upstream fluid does not "know" about the presence of a shock wave until it is "shocked," energetic particles, with their high mobility, can diffuse well ahead of the shock and communicate the existence of a shock to the incident flow. As it approaches the shock, the incident flow begins to slow, creating an extended precursor ahead of the new, weakened subshock.

We expect the termination shock, because it accelerates anomalous cosmic rays, to be a cosmic ray mediated shock. We therefore anticipate that Voyager will discover the first fully mediated cosmic ray shock, which will give us tremendous insight into the physics of particle acceleration at shocks, in far more exotic astrophysical environments, such as supernovae.

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