Sheath near a negatively biased electron-emitting wall in an ion-beam-plasma system and its implication to experimental measurement

In the previous experiment by Li et al., [Phys. Plasmas 19, 113511 (2012)], a deep virtual cathode was measured within an ion sheath near a negatively biased stainless steel plate immersed in an ion-beam-plasma system. The appearance of a virtual cathode was attributed to secondary electrons produced by the high speed ion beam instead of the plasma electrons since these electrons are depleted in the sheath. This paper presents a theoretical model of the sheath structure in the ion-beam-plasma system near an electron-emitting wall. The results show that the presence of the ion beam will compress the whole sheath and make it more difficult to form the virtual cathode, i.e., it causes the increase in the threshold density of the emitted electrons at the wall needed to form the virtual cathode. When comparing with the previous experimental results, it is found that the needed secondary electron yield is unrealistically high in order to obtain the experimentally measured depth of the virtual cathode. Possible experimental uncertainties are discussed concerning the use of an emissive probe when it is too close to the wall.