Ion cyclotron resonance heating is a plasma phenomenon where a time-varying electric field tuned to the cyclotron resonance frequency of one of the plasma species can selectively heat it. Simply, charged particles in a magnetic field rotate with a characteristic frequency. If an applied electric field rotates with that same frequency, particles with matching characteristic frequencies will be energized. This has many applications, although those applications require a fuller treatment of the topic which takes into account issues that arise from interactions between particles in a plasma. Nonetheless, the DSolve function can actually return a closed-form solution for non-resonant single ion trajectories!

In this post I'll show how to get that solution, as well as visualize what that solution looks like.