An introduction to perpendicularly propagating Bernstein waves

Bernstein waves are electrostatic waves that propagate nearly perpendicular to the magnetic field in a magnetized plasma. Deriving their dispersion relation requires a kinetic treatment, and the full electromagnetic derivation is mathematically involved. Here, we present a simplified derivation of the dispersion relation for perpendicularly propagating Bernstein waves in a collisionless Maxwellian plasma. We also provide three practical methods for evaluating the dispersion relation and include compact Python scripts to facilitate the teaching and learning process.