A variational sheath model for gyrokinetic Vlasov-Poisson equations

We construct a stationary gyrokinetic variational model for sheaths close to the metallic wall of a magnetized plasma, following a physical extremalization principle for the natural energy. By considering a reduced set of parameters we show that our model has a unique minimal solution, and that the resulting electric potential has an infinite number of oscillations as it propagates towards the core of the plasma. We prove this result for the non linear problem and also provide a simpler analysis for a linearized problem, based on the construction of exact solutions. Some numerical illustrations show the well-posedness of the model after numerical discretization. They also exhibit the oscillating behavior.

Microwave Differential Frequency Splitting Sensor Using Magnetic-LC Resonators

A differential microwave permittivity sensor and comparator is designed using a microstrip transmission line loaded with a magnetic-LC resonator. The microstrip transmission line is aligned with the electric wall of the resonator. The sensor shows a single transmission zero, when it is unloaded or loaded symmetrically on both halves. A second notch appears in the transmission response by asymmetrical dielectric loading on the two halves of the device. The frequency splitting is used to characterize the dielectric properties of the samples under test. The sensitivity of the sensor is enhanced by removing the mutual coupling between the two halves of the magnetic-LC resonator using a metallic wall. The sensors’ operation principle is explained through a circuit model analysis. A prototype of the designed sensor is fabricated and measurements are used for validation of the sensing concept. The sensor can be used for determination of the dielectric properties in solid materials or detecting defects and impurities in solid materials through a comparative measurement with a reference sample.

Analytic study on low- external ideal infernal modes in tokamaks with large edge pressure gradients

The problem of pressure driven infernal type perturbations near the plasma edge is addressed analytically for a circular limited tokamak configuration which presents an edge flattened safety factor. The plasma is separated from a metallic wall, either ideally conducting or resistive, by a vacuum region. The dispersion relation for such types of instabilities is derived and discussed for two classes of equilibrium profiles for pressure and mass density.

Numerical stability of a plasma sheath

We are interested in developing a numerical method for capturing stationary sheaths, that a plasma forms in contact with a metallic wall. This work is based on a bi-species (ion/electron) Vlasov-Ampère model proposed in [3]. The main question addressed in this work is to know how accurately classical time-dependent Vlasov-Ampère numerical schemes preserve in long time these non-homogeneous stationary solutions with emission/absorption boundary conditions. In the context of high-order semi-Lagrangian methods, due to their large stencil, interpolation near the boundary of the domain requires also a specific treatment.

Electrostatic interactions between ions near Thomas–Fermi substrates and the surface energy of ionic crystals at imperfect metals

The electrostatic interaction between two charged particles is strongly modified in the vicinity of a metal. This situation is usually accounted for by the celebrated image charges approach, which was further extended to account for the electronic screening properties of the metal at the level of the Thomas–Fermi description. In this paper we build upon a previous approach [M. A. Vorotyntsev and A. A. Kornyshev, Zh. Eksp. Teor. Fiz., 1980, 78(3), 1008–1019] and successive works to calculate the 1-body and 2-body electrostatic energy of ions near a metal in terms of the Thomas–Fermi screening length. We propose workable approximations suitable for molecular simulations of ionic systems close to metallic walls. Furthermore, we use this framework to calculate analytically the electrostatic contribution to the surface energy of a one dimensional crystal at a metallic wall and its dependence on the Thomas–Fermi screening length. These calculations provide a simple interpretation for the surface energy in terms of image charges, which allows for an estimation of the interfacial properties in more complex situations of a disordered ionic liquid close to a metal surface. The counter-intuitive outcome is that electronic screening, as characterized by a molecular Thomas–Fermi length lTF, profoundly affects the wetting of ionic systems close to a metal, in line with the recent experimental observation of capillary freezing of ionic liquids in metallic confinement.