Instability, Collapse and Oscillation of Sheaths Caused by Secondary Electron Emission

The Debye sheath is shown to be unstable under general conditions. For surface materials with sufficient secondary electron emission (SEE) yields, the surface's current-voltage characteristic has an unstable branch when the bulk plasma temperature (Te ) exceeds a critical value, or when there are fast electron populations present. The plasma-surface interaction becomes dynamic where the sheath may undergo spontaneous transitions or oscillations. Using particle-in-cell simulations, we analyze sheath instabilities occurring in a high Te plasma slab bounded by walls with SEE. As the plasma evolves, whenever the sheath enters an unstable state, its amplitude rapidly collapses, allowing a large flux of previously trapped electrons to hit the wall. These hot electrons induce more than one secondary on average, causing a net loss of electrons from the wall. The sheath collapse quenches when the surface charge becomes positive because the attractive field inhibits further electrons from escaping. Sheath instabilities influence the current balance, energy loss, cross-B-field transport and even the bulk plasma properties. Implications for discharges including Hall thrusters are discussed. More generally, the results show that common theories that treat emission as a fixed (time-independent) "coefficient" do not capture the full extent of SEE effects

Instability, Collapse and Oscillation of Sheaths Caused by Secondary Electron Emission

The Debye sheath is shown to be unstable under general conditions. For surface materials with sufficient secondary electron emission (SEE) yields, the surface's current-voltage characteristic has an unstable branch when the bulk plasma temperature (Te ) exceeds a critical value, or when there are fast electron populations present. The plasma-surface interaction becomes dynamic where the sheath may undergo spontaneous transitions or oscillations. Using particle-in-cell simulations, we analyze sheath instabilities occurring in a high Te plasma slab bounded by walls with SEE. As the plasma evolves, whenever the sheath enters an unstable state, its amplitude rapidly collapses, allowing a large flux of previously trapped electrons to hit the wall. These hot electrons induce more than one secondary on average, causing a net loss of electrons from the wall. The sheath collapse quenches when the surface charge becomes positive because the attractive field inhibits further electrons from escaping. Sheath instabilities influence the current balance, energy loss, cross-B-field transport and even the bulk plasma properties. Implications for discharges including Hall thrusters are discussed. More generally, the results show that common theories that treat emission as a fixed (time-independent) "coefficient" do not capture the full extent of SEE effects

Controlling Charge and Current Neutralization of an Ion Beam Pulse in a Background Plasma by Application of a Small Solenoidal Magnetic Field

Propagation of an intense charged particle beam pulse through a background plasma is a common problem in astrophysics and plasma applications. The plasma can effectively neutralize the charge and current of the beam pulse, and thus provides a convenient medium for beam transport. The application of a small solenoidal magnetic field can drastically change the self-magnetic and self-electric fields of the beam pulse, thus allowing effective control of the beam transport through the background plasma. An analytical model is developed to describe the self-magnetic field of a finite-length ion beam pulse propagating in a cold background plasma in a solenoidal magnetic field. The analytical studies show that the solenoidal magnetic field starts to influence the self-electric and self-magnetic fields when ωce ≥ ωpeβb, where ωce = eΒ/mec is the electron gyrofrequency, ωpe is the electron plasma frequency, and βb = Vb/c is the ion beam velocity relative to the speed of light. This condition typically holds for relatively small magnetic fields (about 100G). Analytical formulas are derived for the effective radial force acting on the beam ions, which can be used to minimize beam pinching. The results of analytical theory have been verified by comparison with the simulation results obtained from two particle-in-cell codes, which show good agreement