1. 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-SC
Nonequilibrium Gas and Plasma Dynamics Laboratory
Department of Aerospace Engineering University of Michigan Ann Arbor, Michigan 48109

2. 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)

3. 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

4. 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 ?

5. 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

6. Experimental Setup
Helicon plasma source
Plasma jet in vacuum chamber

7. 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

8. 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)

9. 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

10. 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

11. 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

12. 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.

13. 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)

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

15. 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

16. Global Criteria
Sensitivity of global rate to mass flow rate ratio

17. 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

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