Electrohydrodynamic stability of a plasma-liquid interface

Abstract

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.

Numerical implementation of a cold-ion, Boltzmann-electron model for nonplanar plasma-surface interactions

“…11 The motivation of that work was not only to find the linear stability criterion of a conducting liquid surface due to the electric field in the sheath but it also provides a second reference case to compare with the results of CIBER. The simulation is set up in the same way as for the planar sheath in cartesian coordinates but the wall now has a sinusoidal height perturbation with an amplitude of 0:05k D Figure 6 displays the profiles of U along a line at z ¼ 0:2k D at the end of each simulation together with the predictions of the linear perturbation theory.…”

“…10 This work is motivated, in particular, by the latter topic which finds applications in nanoparticle synthesis, catalysis of chemical reactions, material processing, water treatment, sterilization, and plasma medicine. 10 Existing models of plasma-liquid interfaces have, until very recently, 11 neglected all effects involving charge separation and electric fields in the plasma.…”

Simulated dynamics of a plasma-sheath-liquid interface*

“…However all of these studies have neglected the fundamental role of the plasma sheath at the plasma-liquid interface. Langmuir's discovery of this sheath region, and the large electric fields contained within it, is one of the earliest discoveries in plasma science [16]; it is, therefore, surprising that sheath effects have only recently been theoretically investigated with a linear perturbation analysis [17]. This paper expands on this theoretical work by developing complementary numerical simulations.…”

“…This paper expands on this theoretical work by developing complementary numerical simulations. Comparisons are drawn between theory, simulation and relevant experimental observations.The linear perturbation theory in [17] took the simple Bohm model of a plasma sheath [18,19] which comprises a collisionless cold-ion fluid, with density n, velocity u and individual ion mass m i , and Boltzmanndistributed electrons, with temperature T e and sheath-edge density n 0 , which interact with each other and a conducting wall via the electrostatic field E as described by the potential f. The corresponding sheath equations are * Substantial portions of this paper are adapted from section 4.2 of the first author's recent PhD thesis.…”

“…( ) E e n n e k T exp . 3 B e 0 0 A linearisation procedure was performed in [17] in order to make these equations tractable. An alternative approach is to compute solutions directly with numerical simulations such as the C++ finite-difference code 'Cold Ions with Boltzmann Electron Relation' (CIBER) which is freely-available at http://github.com/ joshholgate/CIBER and is described in detail by [20].…”