Determination of the equivalent circuit of inductively coupled plasma sources

Abstract

This article presents a new approach to investigate and model the electrical characteristics of inductive plasma sources. The technique is primarily based on the measurement of the total complex impedance of the plasma source. The measurements are subsequently numerically fitted to a generic and qualitative electrical model, predetermined by a classical Bode analysis of a circuit including a conductive dummy load of size comparable to the plasma itself. The match between the modeling and the experimental data using this new approach shows a drastic improvement compared to the usual inductively coupled plasma (ICP) electrical model, which is also detailed here as a comparison. We conclude the article on prospective benefits of an accurate electrical model for ICP plasma sources, showing in particular that the global electrical parameters of the discharge can be correlated with a good level of accuracy to the local electrical parameters of the plasma. Beyond the technological necessity to better understand the ICP plasma sources, these results also open many doors towards nonintrusive and accurate plasma monitoring technologies.

AETHER: A simulation platform for inductively coupled plasma

“…To our knowledge, the leading study that models the inductively coupled plasma as the secondary of an air core transformer is presented in [29]. This model is then improved with other works in literature [30,31]. The equations used in this model are explained elsewhere [5] and used in a previous study [32].…”

Design and Test of a Radio-Frequency Electrothermal Thruster

“…Colpo et al [18] did so by utilizing the concept of equivalent circuits. An equivalent circuit is an idealized, simple version of an electrically equivalent complex circuit.…”

“…Since the circuit had to be designed without experimental data for the (plasma) load impedance, sample impedance values were selected from published experimental data [18]. This data considered the resistance and reactance of a plasma discharge, using argon, over a range of RF power and discharge pressure representative of what was expected for the RFET.…”

“…This data considered the resistance and reactance of a plasma discharge, using argon, over a range of RF power and discharge pressure representative of what was expected for the RFET. Figure 21 shows the resistance of argon discharge versus RF power at three different pressure levels, while Figure 22 shows the reactance of argon versus power at the same three pressure levels (from Ref [1] and Ref [18]).…”

“…Classical Transformer Model.The classical transformer model shown inFigure 10is a simple equivalent circuit that treats the antenna coil as the primary winding of a transformer and the plasma as a resistive secondary winding. With these assumptions, an equation can be derived to estimate the impedance of the primary coil[18]. Z c represents the impedance of the coil, w represents the frequency of the power source, M represents the mutual inductance, R pl and L pl represent the resistance and inductance of the plasma, respectively, and L coil represents the inductance of the coil.…”