Simulation of the Interaction Between Two Counterflowing Rarefied Jets Cyril Galitzine and Iain D. Boyd U.S. Department of Energy Office of Science Fusion Energy Sciences Program Grant # DE-SC0001939 Nonequilibrium Gas and Plasma Dynamics Laboratory Department of Aerospace Engineering University of Michigan Ann Arbor, Michigan 48109

Introduction Context This project is part of multi year collaborative research program at the University of Michigan focused on the control of the electron energy distribution function (EEDF) by the introduction of excited neutral states. Experiments will conducted by Prof. Gallimore’s lab and corresponding simulations run by Prof. Boyd and Kushner’s groups. This talk presents preliminary simulations conducted in support of the design of the experiment focused on the gasdynamics (not EEDF control)

EEDF Tailoring Why control the EEDF ? To improve the rate of reactions of practical interest in plasma processing that involve electrons: Activated species often has a complex structure with a threshold energy and resonances Shape of EEDF has a large impact on rate

EEDF Tailoring How to control the EEDF ? By introducing additional more/less energetic electrons By adding heavy species (neutrals, dust) How can the addition of Ar(4s) help control the EEDF in a low pressure, low density, weakly ionized Ar plasma ?

Flow Conditions Interaction region Helicon Neutral jet ΔL ~ 0.5 m D2 = 6.4 mm D1 = 45 mm ΔL ~ 0.5 m Helicon Neutral jet Interaction region

Experimental Setup Helicon plasma source Plasma jet in vacuum chamber

Motivations & Objectives Goals of preliminary study: Help design experimental setup Establish a baseline solution for gas dynamics EEDF Neutrals Questions to answer: Where does reaction take place ? Where to measure EEDF of ? Influence of flow parameters on shape & extent of interaction ? Formulate a local criterion (=measure) easily obtainable from DSMC results

Electrons via Boltzmann solver Roadmap Incrementally increase complexity/fidelity of simulations “Pure” DSMC PIC/DSMC/Fluid Preliminary study DSMC for neutrals PIC for ions Fluid (Maxwellian) electrons No electrical field Ambipolar assumption PIC/DSMC/EMC PIC/DSMC/EMC EEDF kinetics Electrons via Boltzmann solver Electrons via EMCS method (Weng & Kushner 1990)

Reduced Order Model Simplifying assumptions: -Ambipolar diffusion of e- and Ar+ -No electrical field -(Ar-Ar) VHS intermolecular potential between all species -Neglect chemical reactions (CEX & ionization) Study can be conducted with a “standard” DSMC code 9

Challenges of simulation Large disparity of scales between jets Adaptive procedure for DSMC parameters is required for efficient & accurate simulations (Kannenberg & Boyd J. Comput. Phys ‘97) Recirculation zone & low concentrations Computationally expensive simulations required to obtain good statistics for high mass flow rates (~1000 CPU hrs). Relative weighting of species required

Local Interaction Quantification To Identify zones suitable for EEDF measurements Where reaction is most prevalent Excited electron density is highest Measurements physically possible Formulate a local criterion (=measure) easily obtainable from DSMC results

Local Interaction Quantification To Identify zones suitable for EEDF measurements 1) Equilibrium reaction rate: assuming -Equilibrium rate constant: -T ~ 4eV ~ const Not a good indication of location of 1st reaction for incoming electrons. Need to account for electrons trajectories.

Local Interaction Quantification 2) Streamline integrated reaction rate: Number of reactions undergone by an electron as it travels on its streamline: Streamline Good description of where electron excitation reaction is likely to occur Reaches high values in area with low values (Not suitable for EEDF measurement)

Local Interaction Quantification 3) Combined Criterion Need to identify regions with both N1,SL ~ 1 and relative high

Global Criteria To compare relative merit of flow configurations and perform parametric studies Formulate global criteria (=measures) based on local criteria For a given region Ωexp where measurements are possible: Ωexp

Global Criteria Sensitivity of global rate to mass flow rate ratio

Summary & Future Work Review: Future work: A reduced order model was developed to rapidly conduct simulations to support the development of an experiment. Local criteria were developed to identify regions suitable for EEDF measures. Global criteria, useful to assess the relative merit of flow configurations were then formulated. Future work: Preliminary/sizing simulations: chemical reactions charged species electrical field Incorporate additional physics into reduced order model EEDF simulations: Implement hybrid approach to handle EEDF outside of DSMC

Questions ? Cyril Galitzine cyrilg@umich.edu Nonequilibrium Gas and Plasma Dynamics Laboratory University of Michigan