Enhancement of droplet ejection from molten and liquid plasma-facing surfaces by the electric field of the sheath

Maintaining the stability of a liquid surface in contact with a plasma is of crucial importance in a range of industrial and fusion applications. The most fundamental feature of a plasma-surface interaction, the formation of a highlycharged sheath region, has been neglected from the majority of previous studies of plasma-liquid interactions. This paper considers the effect of the electric field of the sheath on the ejection of micron-scale droplets from bubbles bursting at the liquid surface. A numerical simulation method, based on the ideal electrohydrodynamic model, is introduced and validated against the well-known Taylor cone theory. This model is then used to include the electrical effects of the sheath in simulations of bubble bursting events at a plasma-liquid interface. The results show a significant enhancement in droplet ejection at modest electric fields of between 10% and 20% of the critical field strength required for a solely electrohydrodynamic instability. This finding is in good qualitative agreement with experimental observations and its importance in a wide range of fusion and atmospheric-pressure plasma-liquid interactions is discussed. The inclusion of sheath physics in future studies of plasma-liquid interactions is strongly advocate

Mean Curvature Flow from Conical Singularities

We prove Ilmanen's resolution of point singularities conjecture by establishing short-time smoothness of the level set flow of a smooth hypersurface with isolated conical singularities. This shows how the mean curvature flow evolves through asymptotically conical singularities and resolves a particular case of Ilmanen's strict genus reduction conjecture. Precisely, we prove that the level set flow of a smooth hypersurface $M^n\subset \mathbb{R}^{n+1}$, $2\leq n\leq 6$, with an isolated conical singularity is modeled on the level set flow of the cone. In particular, the flow fattens (instantaneously) if and only if the level set flow of the cone fattens.Comment: 22 pages, 3 figures. Comments welcome

University Band Symphonic Band

Braden Auditorium Wednesday Evening April 22, 1998 8:00p.m

Approximation of mean curvature flow with generic singularities by smooth flows with surgery

We construct smooth mean curvature flows with surgery that approximate weak mean curvature flows with only spherical and neck-pinch singularities. This is achieved by combining the recent work of Choi-Haslhofer-Hershkovits, and Choi-Haslhofer-Hershkovits-White, establishing canonical neighbourhoods of such singularities, with suitable barriers to flows with surgery. A limiting argument is then used to control these approximating flows. We conclude by improving the entropy bound on the low-entropy Schoenflies conjecture

Symphonic Band University Band

Braden Auditorium Thursday Evening November 20, 1997 8:00 p.m

University Band Symphonic Band

Braden Auditorium Thursday Evening April 29, 1999 8:00p.m

Electrohydrodynamic stability of a plasma-liquid interface

Many plasma applications involve the plasma coming into contact with a liquid surface. Previous analyses of the stability of such liquid surfaces have neglected the presence of the sheath region between the bulk plasma and the liquid. Large electric fields, typically in excess of several MV m−1, and strong ion flows are present in this region. This paper considers a linear perturbation analysis of a liquid-sheath interface in order to find the marginal condition for instability. This condition shows that molten metal surfaces in tokamak edge plasmas are stable against the electric field, if a normal sheath is formed, due to the impact of ions on the surface. The stabilization of the liquid surface by ion bombardment is encouraging for the ongoing development of plasma-liquid technologies