Ion-matrix sheaths inside cylindrical bores with small radii and longitudinal grooves

In this paper, ion-matrix sheaths inside infinitely long cylindrical bores with longitudinal grooves are studied analytically to optimize ion implantation, concerning a broad range of industrial products. The radius of the cylindrical target is assumed to be less than the sheath length to simulate realistic targets, such as barrels and muzzles. The potential profiles inside and outside the grooves are derived and the ion velocity components inside the grooves are estimated. Finally, suggestions for improving the implantation uniformity on the surfaces of such targets are stated.