Two-Temperature Model for the Simulation of Atmospheric-Pressure Helium ICPs MINGXIANG CAI, AKBAR MONTASER,* and JAVAD MOSTAGHIMI Department of Chemistry, George Washington University, Washington, D.C. 20052, U.S.A. (M.C., A.M.); and Department of Mechanical Engineering, University of Toronto, Toronto, Ontario M5S 1A4, Canada (J.M.) A two-temperature model (2-T model) was used to predict fundamental properties of pure helium inductively coupled plasmas (He ICPs). Plas- ma characteristics with the use of the 2-T model were compared to those obtained by the local thermodynamic equilibrum (LTE) model for the He ICP, to those of an Ar ICP, and to the existing experimental data. The distributions of electron and heavy-particle temperatures, electron number density, and electric and magnetic fields were obtained as a function of the internal diameters of the torch, the gas flow rates, the gap between the plasma tube and the MACOR insert, the generator frequency, and the active power. Overall, the He ICP was predicted to have a much higher electron temperature (>12,000 K) in the load coil region, but its axial heavy-particle and electron temperatures (~2000 K) at the analytical zone were lower than those of the Ar ICP (4000- 6000 K). The high-temperature region in the He ICP was constricted to a smaller region close to the wall of the plasma confinement tube as compared to that in the Ar ICP. Most of the input power in the He ICP was lost through the plasma quartz tube. The magnetic and electric fields inside the induction coil in the helium plasma were approximately one order of magnitude higher than those in the argon plasma. Index Headings: Computer simulation; Two-temperature model; Helium inductively coupled plasma. INTRODUCTION The exceptional excitation and ionization capabilities of the argon inductively coupled plasmas (At ICPs) are well documented ~ as sources for elemental and isotopic ratio analysis by atomic and mass spectrometries. Helium discharges are important in spectrochemical analysis be- cause of their unique potentials for providing a simpler background spectrum and achieving greater detection powers for the determination of halogens and other non- metals as compared to the Ar ICPs. However, experi- mental data on properties of most helium plasmas, par- ticularly He ICP discharges, currently are limited. The most important fundamental characteristics of ICP dis- charges are gas temperature (Tg), electron temperature (T~), and electron number density (no). 2 These and other parameters are measured experimentally or they can be estimated through computer simulation. Several experi- mental methods are available for the measurements of Te, Tg, and no.3 For example, Thomson and Rayleigh scattering 4-~ and the Langmuir-probe methods t2-15 are used for measurement of To, Tg, and n~, and the Stark broadening of the H a line is used to estimate ne. t6-~sThese experimental techniques are either very expensive (Thomson and Rayleigh scattering) or more applicable to diagnostic studies of extracted discharges or low-pressure Received 15 February 1995; accepted 1 June 1995. * Author to whom correspondence should be sent. glow discharges (Langmuir-probe method), or their ap- plication is restricted, particularly in the case of He ICP, because of the unavailability of accurate theoretical line broadening data (Stark broadening) at low densities. Clearly, the temperature fields, ne values, electric and magnetic fields, and other plasma properties can be cal- culated by computer modeling. Computer simulation can provide supplementary information for plasma discharg- es; ~9-3si.e., new data are obtained at low cost, operating conditions can be changed easily, and the entire spatial distributions in the plasma can be predicted for many parameters. Previous modeling studies of ICP discharges chiefly have focused on Ar ICP and molecular-gas ICP? °-37 Our recent work involved modeling a He ICP under local thermodynamic equilibrum (LTE) conditions. 38 Indeed, the majority of models used to simulate ICP discharges assume LTE to simplify the simulation process, but most analytical plasmas, especially He ICPs, are non-LTE plas- mas. The LTE assumption results in overestimation of the temperature in the plasmas. 36Two-temperature (2-T) models for Ar ICPs, using one-dimensional and two- dimensional electromagnetic fields, have been devel- oped? 6,36 The results obtained by these models are in close agreement with the available experimental results for the Ar ICPs. In this study, we simulated helium plasmas by modi- fying the computer code of a two-temperature model of an Ar ICP based on a two-dimensional electromagnetic field. 36 The distributions of T h (same as T,), T¢, no, and electric and magnetic fields in the He ICP were compared to those in an Ar ICP and to the results obtained from the LTE model. In addition, the distributions of To, Th, and n~ were predicted as a function of the internal di- ameters of the torch, the gap between the plasma tube and the MACOR insert, the plasma gas flow rates, the generator frequency, and the active power. The results obtained via simulation were compared to the existing experimental data to examine the validity of the math- ematical model. These theoretical predictions also were used to interpret analytical results achieved and to devise new directions for research in He ICP spectrometry. THEORETICAL CONSIDERATIONS AND PLASMA OPERATING CONDITIONS Basic Assumptions for the Model and Fundamental Properties of Electrons and Helium. For the model used in this work, the plasma (1) is assumed to be dry, optically thin, and axisymmetric; (2) possesses two-dimensional 1390 Volume 49, Number 10, 1995 0003-7028/95/4910.139052.00/0 APPLIED SPECTROSCOPY © 1995Society for AppliedSpectroscopy