Experimental measurement of plasma sheath overlap

The plasma sheath is the boundary layer that separates a plasma from a surface such as an electrode or wall. The sheath adjacent to a large flat surface has a characteristic width $s_0$, which is the planar sheath width. If the surface has a step of height $d$, then some length scale $t_0$ describes the lateral transition at the sheath edge from one level to the other. Two parallel steps separated by a distance $W$ form a trench. When $W < t_0$, we expect that the sheaths from the two steps overlap and the sheath is pushed out of the trench. We have measured sheath overlap for a trench with variable width $W$ using a two dust particles. The dust particles float at the sheath edge, so their height above the electrode gives a quantitative measure of the sheath width. When $W\gg s_0$ the cluster height is independent of $W$. When $W < s_0$ the dust particles move upward, indicating that sheath overlap is occurring.