Simulations of electromagnetic effects in high frequency capacitively coupled discharges using the Darwin approximation

The Darwin approximation is investigated for its possible use in simulation of electromagnetic effects in large size, high frequency capacitively coupled discharges. The approximation is utilized within the framework of two different fluid models which are applied to typical cases showing pronounced standing wave and skin effects. With the first model it is demonstrated that Darwin approximation is valid for treatment of such effects in the range of parameters under consideration. The second approach, a reduced nonlinear Darwin approximation-based model, shows that the electromagnetic phenomena persist in a more realistic setting. The Darwin approximation offers a simple and efficient way of carrying out electromagnetic simulations as it removes the Courant condition plaguing explicit electromagnetic algorithms and can be implemented as a straightforward modification of electrostatic algorithms. The algorithm described here avoids iterative schemes needed for the divergence cleaning and represents a fast and efficient solver, which can be used in fluid and kinetic models for self-consistent description of technical plasmas exhibiting certain electromagnetic activity

Future studies on electron scattering; A renaissance

2014 is the centenary of the first announcement of the Franck-Hertz experiment [1], now regarded as one of the pivotal experiments of modern physics. The Franck-Hertz experiment is widely regarded as an experiment that provided validation of the Bohr theory of atomic structure, itself only published in 2013, however it should also be viewed as the first quantitative experiment in electron scattering and the birth of scientific study of atomic and molecular phenomena by collisions. Today we recognize that electron-atom and electron- molecule collisions are prevalent across nature, describing disparate phenomena whilst the exploitation of such collisions underpins many of the technologies upon which modern society relies. The centenary of the Franck-Hertz experiment is thus a suitable opportunity to review both our current knowledge of electron interactions and to consider the directions of future research. In this article I therefore aim to both review our current state of knowledge and look forward, proposing that recent advances are providing something of a renaissance to the field and are vital for emerging technologies as well as answering some of the greatest scientific challenges of the 21st century