Electrodes in low pressure laboratory plasmas have a multitude of possible sheath structures when biased at a large positive potential. When the size of the electrode is small enough the electrode bias can be above the plasma potential. When this occurs an electron-rich sheath called an electron sheath is present at the electrode. Electron sheaths are most commonly found near Langmuir probes and other electrodes collecting the electron saturation current. Such electrodes have applications in the control of plasma parameters, dust confinement and circulation, control of scrape off layer plasmas, RF plasmas, and in plasma contactors and tethered space probes. The electron sheaths in these various systems most directly influence the plasma by determining how electron current is lost from the system. An understanding of how the electron sheath interfaces with the bulk plasma is necessary for understanding the behavior induced by positively biased electrodes in these plasmas.
This thesis provides a dedicated theory of electron sheaths. Motivated by electron velocity distribution functions (EVDFs) observed in particle-in-cell (PIC) simulations, a 1D model for the electron sheath and presheath is developed. In the presheath model, an electron pressure gradient accelerates electrons to near the electron thermal speed by the sheath edge. This pressure gradient generates large flow velocities compared to what would be generated by ballistic motion in response to the electric field. Using PIC simulations, the form of a sheath near a small electrode with bias near the plasma potential is also studied. When the electrode is biased near the plasma potential, the EVDFs exhibit a loss-cone type truncation due to fast electrons overcoming the small potential difference between the electrode and plasma. No sheath is present in this regime, instead the plasma remains quasineutral up to the electrode. Once the bias exceeds the plasma potential an electron sheath is present. In this case, 2D EVDFs indicate that the flow moment has comparable contributions from the flow shift and loss-cone truncation.
The case of an electrode at large positive bias relative to the plasma potential is also studied. Here, the rate of electron impact ionization of neutrals increases near the electrode. If this ionization rate is great enough a double layer forms. This double layer can move outward separating a high potential plasma at the electrode surface from the bulk plasma. This phenomenon is known as an anode spot. Informed by observations from the first PIC simulations of an anode spot, a model has been developed describing the onset in which ionization leads to the buildup of positive space charge and the formation of a potential well that traps electrons near the electrode surface. A model for steady-state properties based on current loss, power, and particle balance of the anode spot plasma is also presented.