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)
2

EEDF Tailoring
Why control the EEDF ?
•To improve the rate of reactions of practical interest in plasma processing that involve electrons:
1
A  e  

A*  e 
k
etching
A* 
 ...
Activated species
k1   dv Adv e f A v A  f e v e  v r v r

•  v r  often has a complex structure with a threshold energy and resonances

Shape of EEDF has a large impact on rate

3
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 ?
1
Ar *  e  

Ar  e 
k

4
Flow Conditions
D2 = 6.4 mm
D1 = 45 mm
Helicon
ΔL ~ 0.5 m
Neutral jet
Interaction region
5
Experimental Setup
Helicon plasma source
Plasma jet in vacuum chamber
6
Motivations & Objectives
Goals of preliminary study:
• Help design experimental setup
• Establish a baseline solution for gas dynamics
EEDF
Neutrals
Questions to answer:
k
Ar  e  reaction take place ?
• Where does Ar *  e  
• Where to measure EEDF of
?
1

Formulate
a local criterion (=measure) easily obtainable from DSMC results
• Influence of flow parameters on shape & extent of interaction ?
7
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
-3
n[m ]

Ar 

•
Ar *
•
Computationally expensive simulations required to
obtain good statistics for high mass flow rates
(~1000 CPU hrs).
Relative weighting of species required
10
Local Interaction Quantification
To Identify zones suitable for EEDF measurements
1) Equilibrium reaction rate:
r1 
#reactions
 k1nAr * ne
m3  s
1
Ar *  e  

Ar  e 
k
assuming
-Equilibrium rate constant:
-T ~ 4eV ~ const
k1  4.3 1016  Te0.74

k
•Not a good indication of location of 1st Ar *  e  

Ar  e  reaction for incoming
electrons.
•Need to account for electrons trajectories.
1

Ý2  m
Ý1
m
Ý2  m
Ý1
m


Ý2  8 m
Ý1
m
Ý2  8 m
Ý1
m
12
Local Interaction Quantification
2) Streamline integrated reaction rate:
Number of reactions undergone by an electron as it travels on its
streamline:
r
v  (uz ,ur )
Streamline

z(t),r(t)
•Good description of where electron excitation reaction is likely to occur

•Reaches high values in area with low n e values (Not suitable for EEDF measurement)


13
Local Interaction Quantification
3) Combined Criterion
Need to identify regions with both N1,SL ~ 1 and relative high n e


14
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
15
Global Criteria
Sensitivity of global rate to mass flow rate ratio
16
Summary & Future Work
Review:
•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
•Incorporate additional physics into reduced order model • charged species
• electrical field
EEDF simulations:
•Implement hybrid approach to handle EEDF outside of DSMC
17
Questions ?
Cyril Galitzine
cyrilg@umich.edu
Nonequilibrium Gas and Plasma Dynamics Laboratory
University of Michigan
18