Particles in or near resonance with a plasma wave undergo perturbations of their equilibrium orbits due to stochastic fields. This contributes added diffusion damping to any wave in the plasma. In a steady‐state experiment this mechanism can cause the saturation of a wave. A theory of the current‐driven ion cyclotron instability modified by turbulent damping based on addition of a damping term to the linear dispersion relation is presented. The turbulent damping is interpreted as an upper bound on the linewidth of the wave. As current varies, the frequency and line width of the mode alter. Once the frequency of the ion cyclotron wave is lowered to nearly the ion cyclotron frequency, mode coupling to an ion‐acoustic wave seems to occur, damping the oscillations. Until this point, detailed predictions of theory agree well with experiment.