Introduction to collisionless single-particle motion in plasmas

Plasmas are the fourth and most common of the four naturally occurring states of matter observed in the visible universe, existing over a wide parameter space, with densities and temperatures spanning several orders of magnitude. As a result, a hierarchy of models is used to understand this state of matter, with the choice of model used determined by the plasma parameters and the level of detail required. The simplest of these models is single particle motion, which neglects interactions with other particles that makeup the plasma and considers only how individual particles respond to the presence of external electric and magnetic fields. Despite its simplicity, this model offers a rich insight into how charged particles respond to electromagnetic fields and underpins our understanding of more complex plasma behavior. In this tutorial, we explore the ways particles move under the influence of these fields using the Lorentz force as the governing equation of motion. Depending on the configuration of the fields, this model reveals a wide variety of behaviors, such as drifts and magnetic mirroring. We begin by analyzing motion in uniform fields, then extend the discussion to include nonuniform and time-varying fields. To build intuition, we present simulations that visualize the resulting trajectories. We also derive analytical expressions for key phenomena to complement and explain the simulated results. Finally, we highlight how these drift motions are relevant to plasmas of current interest, including those found in laboratory settings and in plasma confinement devices.