The magnetic moment is independent of the particles charge and points in the direction opposite to the magnetic field. A plasma is diamagnetic.

5.2 Shock Acceleration

So how can a magnetic field accelerate a particle? If the magnetic field is frozen in to the plasma the electric conductivity must be extremely large and hence there can be no electric fields in the plasma. Now we all know that magnetic fields do not perform work on particles, so again, how can particles be accelerated in the interplanetary medium?

There are three different types of particle acceleration in the interplanetary medium,

• scatter-free acceleration in the electric field induced at the shock front, also called shock-drift acceleration,

• stochastic acceleration in turbulent media,

• acceleration by multiple reflections in the plasma parcels converging on the shock front, this is called diffusive acceleration.

Scatter-Free or Shock-Drift Acceleration

The simplest situation arises in quasi-perpendicular shocks, when the electric field E = -uu x Bu induced at the shock front is maximal. The electric field points along the shock front and the particles drift along the shock, see Fig. 26. The longer they drift along the shock, the more energy they gain. Their energy gain is proportional to the product of the particles charge, the induced electric field, and the length of the drift path in the shock. As the particle leaves the shock, it feels the magnetic field, and is bent back into the shock region. For low levels of turbulence this motion is more or less scatter free and the particle can cross the shock several times, always gaining energy. In fast magnetosonic and quasi-perpendicular shocks (a large fraction of the shocks outside 1 AU), the particles will also feel drifts in the shock frame. That motion can be divided into two components, the VB-drift and curvature drift due to the curvature of the shock. In fast quasi-perpendicular shocks VB-drift dominates and the particles gain energy. In slow shocks, the gradient points the other way and it is curvature drift that is parallel to the electric field. As the particles gain energy, their Larmor radii will gradually increase and at some point they will be scattered away from the shock, thus escaping from it. At this point, the particle has gained a substantial amount of energy. Particles with a small velocity component relative to the shock in the shock frame are the ones that remain stuck to the shock longest and hence gain the most energy. Thus, the initial velocity vector and pitch angle are important factors in determining whether particles gain remain in the shock for an appreciable amount of time and gain energy. The spectrum of accelerated particles is not easily derived, but must be determined by detailed

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