Self-similar sheath expansion from a segmented planar electrode

The expansion of the pulsed plasma sheath away from a segmented planar electrode is studied using a collisionless particle-in-cell simulation. One segment of the electrode is biased negatively, while the other is fixed at ground potential. Cases where the grounded and biased segments are semi-infinite and where the width of the grounded segment is equal to the ion-matrix sheath width are considered. For the case of two half-planes, one grounded and one biased, it is found that the expanding sheath sweeps up ions from above the grounded segment and accelerates them to the biased segment, forming an arc of high ion density encircling a void region at the junction between the segments. Further, for this case sheath expansion is found to be self-similar as the problem lacks any length scale excepting the sheath width.