Three-dimensional direct numerical simulation of helicon discharge

Abstract

With the detailed consideration of electrochemical reactions and collision relations, a direct numerical simulation model of helicon plasma discharge with three-dimensional fluid-dynamic equations is proposed in the present work. It can improve the precision of results and widen the model applicability by discarding the small perturbation theory in previous helicon models which are partially analytical in essence. Under the assumption of weak ionization, the Maxwell equations coupled with the plasma parameters are directly solved in the whole computational domain. Thus the energy deposited from electromagnetic wave to plasma can be then easily calculated. The values of plasma parameters which include electron density, mean electron energy and heavy species density are obtained by solving a set of drift-diffusion equations. Meanwhile, seven kinds of chemical reactions in the plasma and two kinds of surface reactions on the wall are taken into account. All of the partial differential equations are solved by the finite element solver of COMSOL MultiphysicsTM with the full coupled method.#br#The results of numerical cases employing argon as the working medium show that there exists a sharp density jump from a low to high value as the radiofrequency power is raised. The density jump phenomenon is in accordance with the experimental results of Toki (Toki K, Shinohara S, Tanikawa T, Shamrai K P 2006 Thin Solid Films 506-507 597) and Chen (Chen F F 2007 Plasma Sources Sci. Technol. 16 593). The electron temperature decreases with an increase of the gas pressure, which is similar to Toki's (Toki K, Shinohara S, Tanikawa T, Shamrai K P 2006 Thin Solid Films 506-507 597) measurement by a RF compensation probe. In comparison with the classical sheath theory, the simulation result demonstrates that the distribution of parameters such as particle number density, the Deby length, electric potential and electron temperature can be solved exactly. In addition, the phenomenon of low-field density peak in helicon discharge was studied in the work. Previous research by Chen (Chen F F 2003 Phys. Plasmas 10 2586) suggests that this peak is caused by constructive interference from the reflected wave. The effect of length of the discharge chamber on the relation of electron density and background magnetic field is investigated numerically. The results validate the mechanism of wave interference reflected by endplates of the discharge chamber. Furthermore, the time-averaged magnetic energy density has more than one peak on the axial direction. Comparing the distribution of the magnetic energy density to that of the dimensionless amplitude of the helicon wave and the TG wave in the one-dimensional undamped condition, it found that the length of peak to peak of the helicon wave is just as twice as that of the magnetic energy density, which indicates that the substance of wave interference is involved in the standing wave generated by the helicon wave and its reflected wave from endplates.