Computational investigation of incident ion angles and material erosion at rough graphite and silicon carbide divertor surfaces

We present a computational investigation of the dependence of material erosion on the incident ion angle at rough graphite and silicon carbide divertor surfaces. Ion angle distributions (IADs) for D plasmas at NSTX-U and DIII-D divertors were calculated by an equation-of-motion model that traces the ion trajectories in the sheath. Then, the effective sputtering yields and ion shadowed area fractions were calculated by a Monte Carlo micro-patterning and roughness code that applied the calculated IADs to surface topographic data that were obtained from optical confocal microscopy of rough graphite and SiC divertor surfaces from NSTX-U and DIII-D experiments. The calculations found that the effective sputtering yields, the sputtering pattern, and the shadowed area are determined by the detailed surface topology rather than the root mean square roughness RRMS, which represents deviations from a flat surface. The suppression of the effective sputtering yields for rough surfaces compared to the yield for a smooth surface was accounted for by the change of the mean local incident ion angle (LIIA) ⟨θ′⟩. The mean surface inclination angle distribution (SIAD) ⟨δ⟩ was found to be a useful parameter to estimate the LIIA from the calculated IADs. We report global empirical formulas for the mean LIIA and fraction of the area shadowed from the main ions for D plasmas for rough surfaces with B-field incident angles α = 85°–89° as a function of the mean SIAD ⟨δ⟩. We propose the use of the mean LIIA ⟨θ′⟩ to estimate the sputtering yield for rough surfaces from the angular dependence of the sputtering yield.