The potential structure, electric field, and sheath width for the ion‐matrix sheath in a cylindrical bore are calculated. The appropriate scaling length for this problem is found to be &sqrt;2 times larger than the planar ion matrix sheath width. If the radius of the bore is less than this scaling length, then the sheaths from ‘‘opposite’’ sides of the bore overlap, and the potential drop from the axis to the sidewalls decreases with the square of the bore radius. This limits the maximum energy of ions impacting the target. For bores larger than this scaling length, the asymptotic planar solutions are rapidly approached.