Applications

The $\nabla B$ and curvature drifts mean that it is not possible to confine a plasma using curved magnetic fields or, more generally, in magnetic field configurations such that ${\bf B} \times \nabla B \ne 0$. One reason is that the charge-dependent drift ${\bf v}_{B}$ causes charge separations and the build up of an ambipolar electric field perpendicular to ${\bf B}$, which then leads to an $E\times B$ drift of the plasma across the magnetic field. These problems are of considerable interest in laboratory and fusion plasma physics.

These drifts are very important in understanding the motions of particles in the solar wind and Earth's magnetosphere. For instance, the $\nabla B$ and curvature drifts are important in understanding the injection of energetic particles close to Earth during magnetic substorms.

One specific illustration of how these drifts lead to particle acceleration involves shock waves, which have increases in magnetic field strength and direction across the shock (Figure 2.5). Consider the solar wind flow onto Earth's bow shock, in particular. The drift ${\bf v}_{B}$ is into the page for protons and out of the page for electrons. Notice now that the solar wind's convection electric field is into the page. Accordingly, the proton drift velocity ${\bf v}_{B}$ is parallel to ${\bf E}_{sw}$ while for electrons ${\bf V}_{B,e}$ is anti-parallel to ${\bf E}_{sw}$. In both cases, the drifting particles can gain energy, consistent with Eq. (2.4). This mechanism is called shock-drift acceleration. It is important in understanding energetic particles in the solar corona, interplanetary medium, and probably the outer heliosphere (as well as in Astrophysics).