Introduction

All descriptions of plasma behavior are based, ultimately, on the motions of the constituent particles. For the case of an unmagnetized plasma, the motions are fairly trivial because the constituent particles move essentially in straight-lines between collisions. The motions are also trivial in a magnetized plasma in which the collision frequency, $\nu$, greatly exceeds the gyrofrequency, ${\mit\Omega}$. In this case, the particles are scattered after executing only a small fraction of a gyro-orbit, and, therefore, still move essentially in straight-lines between collisions. The situation of primary interest in this chapter is that of a magnetized, but collisionless (i.e., $\nu\ll {\mit\Omega}$), plasma, in which the gyroradius, $\rho$, is much smaller than the typical variation lengthscale, $L$, of the ${\bf E}$ and ${\bf B}$ fields, and the gyroperiod, ${\mit\Omega}^{-1}$, is much less than the typical timescale, $\tau$, on which these fields change. In such a plasma, we expect the motion of the constituent particles to consist of a rapid gyration perpendicular to magnetic field-lines, combined with free streaming parallel to the field-lines. We are particularly interested in calculating how this motion is affected by the spatial and temporal gradients in the ${\bf E}$ and ${\bf B}$ fields. In general, the motion of charged particles in spatially and temporally nonuniform electromagnetic fields is extremely complicated. However, we hope to considerably simplify this motion by exploiting the assumed smallness of the parameters $\rho/L$ and $({\mit\Omega}\,\tau)^{-1}$. What we are essentially trying to understand, in this chapter, is how the magnetic confinement of a collisionless plasma works at an individual particle level. The type of collisionless, magnetized plasma investigated here occurs primarily in magnetic fusion and space plasma physics contexts.