Stochastic Ion Heating by a Perpendicularly Propagating Electrostatic Wave

The motion of an ion in the presence of a constant magnetic field and a perpendicularly propagating electrostatic wave with frequency several times the ion cyclotron frequency is shown to become stochastic for fields satisfying $\frac{E}{B_0}>\frac{1}{4}{\left(\frac{\Omega }{\omega }\right)}^{\frac{1}{3}}\left(\frac{\omega }{k}\right)$. This stochasticity condition is independent of how close $\omega$ is to a cyclotron harmonic. Applications of current interest in supplementary heating of plasmas with rf power near the lower-hybrid frequency are suggested.