Determination of the characteristic magnetic pre-sheath length at divertor surfaces using micro-engineered targets on DiMES at DIII-D

The magnetic pre-sheath (MPS) length, LMPS, is a critical parameter to define the sheath potential, which controls the ion trajectory of low-Z species (D, T, He, and C), as well as the prompt re-deposition of high-Z species. To determine LMPS, we fabricated micro-trenches (30 × 30 × 4 μm) via focused ion beam milling on a silicon surface and exposed them to L-mode deuterium plasmas in DIII-D via the divertor material evaluation system (DiMES) removable sample exposure probe. The areal distribution of impurity depositions, mainly consisting of carbon, was measured by energy-dispersive x-ray spectroscopy (EDS) to reveal the deuterium ion shadowing effect on the trench floors. The carbon deposition profiles showed that the erosion was maximized for the azimuthal direction of φ = −40° (referenced to the toroidal magnetic field direction) as well as the polar angle of θ = 80°. A Monte Carlo equation-of-motion (EOM) model, based on a collisionless MPS, was used to calculate the azimuthal and polar deuterium ion angle distributions (IADs) at the surface for a range of LMPS = k × ρi, where ρi is the ion gyro radius and k = 0.5–4. Then, gross erosion profiles were calculated by a Monte Carlo micro-patterning and roughness (MPR) code for ion sputtering using as input the calculated azimuthal and polar IADs for each value of k. Good agreement with the experimental C deposition profiles was obtained for the case k = 2.5–3.5. This result is consistent with a previous kinetic modeling prediction of k ∼ 3, as well as previous analytical investigations that predicted the LMPS to be several ion gyro radii. A validation of theoretical sheath models supports its applicability to ITER and pilot plant divertors to successfully predict plasma–materials interactions.