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PLASMA DYNAMICS AT THE IONIZATION FRONT OF HIGH

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1 PLASMA DYNAMICS AT THE IONIZATION FRONT OF HIGH
PRESSURE DISCHARGES USING ELECTRON MONTE CARLO SIMULATIONS ON AN ADAPTIVE MESH* Ananth N. Bhoja) and Mark J. Kushnerb) a)Department of Chemical and Biomolecular Engineering University of Illinois, Urbana, IL, USA. b)Department of Electrical and Computer Engineering Iowa State University, Ames, IA, USA. Gaseous Electronics Conference, October 2006 * Work supported by the National Science Foundation.

2 Optical and Discharge Physics
OUTLINE  Introduction: High Pressure Discharges  Plasma Hydrodynamics Model  Kinetic Model – eMCS on Adaptive Mesh  Plasma Dynamics at the Ionization Front  100s Torr - Corona Discharges  10s Torr - Breakdown in cold HID lamps  Summary Iowa State University Optical and Discharge Physics GEC06_agenda

3 PLASMA DYNAMICS AT THE IONIZATION FRONT Optical and Discharge Physics
 The ionization front during breakdown at high pressure (10s Torr to 1 atm) is a region of high E/N (100s Td) having steep gradients.  Large “confined” E/N produces large Te and ionization rates.  Though high pressure discharges are collisional, these gradients may be so severe (few Td/mm) that electron transport can be non-local. Iowa State University Optical and Discharge Physics ANANTH_GEC06_01

4 MODELING OF PLASMA DYNAMICS AT THE IONIZATION FRONT
 Non-local transport in ionization fronts can be expected when  For these conditions both high spatial resolution and kinetic transport of electrons are required.  Two-dimensional (2D) plasma hydrodynamics models employing fluid techniques typically do not capture non-local effects.  To address these conditions, a 2D kinetic electron Monte-Carlo simulation (eMCS) module within a fluid model was developed to track and resolve electron dynamics at the ionization front. Iowa State University Optical and Discharge Physics ANANTH_GEC06_02

5 2-D PLASMA MODELING PLATFORM Optical and Discharge Physics
Iowa State University Optical and Discharge Physics ANANTH_GEC06_03

6 ELECTROSTATICS, CHARGED PARTICLE TRANSPORT
 Fully implicit solution of Poisson’s equation.  Continuity: Multi-fluid charged species equations using modified Scharfetter-Gummel fluxes.  Surface charge on dielectric surfaces.  2-d unstructured mesh, finite volume methods, Newton integration. Iowa State University Optical and Discharge Physics ANANTH_GEC06_04

7 Optical and Discharge Physics
ELECTRON, NEUTRAL TRANSPORT, REACTION KINETICS  Electron energy transport of bulk electrons:  Neutral species updated in a time-spliced manner between updates to charged species.  Reaction Kinetics include sources due to electron impact and heavy particle reactions, photoionization and contributions from secondary emission. Iowa State University Optical and Discharge Physics ANANTH_GEC06_05

8 Optical and Discharge Physics
POSITIVE CORONA DISCHARGE  Corona discharge as used for polymer surface treatment with a powered electrode (V0) 2 mm from a grounded plane.  Air at 760 Torr, V0 = 15 kV  Species: e, N2, N2*, N2+, N2**, N4+, N, N+, O2, O2+, O-, O2*, O2*(1S), O*, O(1S), H, OH. Iowa State University Optical and Discharge Physics ANANTH_GEC06_06

9 Optical and Discharge Physics
POSITIVE CORONA BREAKDOWN [e] cm E/N (Td) Te (eV) 5x x1015 0 - 10  E/N is enhanced at the ionization front to Td.  The enhanced E/N increases Te which rises at the front to eV.  In the ionized channel, E/N falls below 50 Td with Te = eV.  [e] of 1013 cm-3 in channel. 150 mm MIN MAX  15 kV, 760 Torr, N2/O2/H2O=79/20/1, 5 ns Iowa State University Optical and Discharge Physics Animation Slide-AVI ANANTH_GEC06_07

10 Optical and Discharge Physics
NON-LOCAL ELECTRON TRANSPORT - eMCS  Electron transport may become “non-local” due to large E/N ( Td) and severe gradients (1000s Td/mm).  Kinetic approaches are required to obtain the electron energy distribution (EED), f(r,,t) in position and time to compute electron transport and reaction rates.  Calculating f(r,,t) over the entire domain is computationally prohibitive.  Our kinetic approach uses an electron Monte-Carlo simulation on smaller “regions of non-equilibrium” identified during the avalanche using “sensors”.  Outside these regions, calculations proceed as before using the hydrodynamics equations. Iowa State University Optical and Discharge Physics ANANTH_GEC06_08

11 ADAPTIVE eMCS – SENSORS AND MESH Optical and Discharge Physics
 Sensors identify regions on the unstructured mesh. Te, ionization rates E/N (E/N) [e]  Combination of sensor outputs identify “non-equilibrium.” Boundary of non-equilibrium region with superimposed rectilinear mesh  For example, the non-equilibrium region in a positive corona can be tracked using [e]  1011 cm (E/N)  0.01 (E/N)max  A rectilinear mesh is superimposed over non-equilibrium region upon which eMCS is performed. Iowa State University Optical and Discharge Physics ANANTH_GEC06_09

12 ADAPTIVE eMCS – PARTICLE LAUNCHING Optical and Discharge Physics
 Pseudoparticles weighted by electron flux moving into the region are launched from edges to obtain f(r,,t) inside the region.  Velocity of launched particles is the vector sum VT of vthermal at a randomly selected angle and the drift velocity vd. Edges of MCS mesh VT r = random number Iowa State University Optical and Discharge Physics ANANTH_GEC06_10

13 ADAPTIVE eMCS COUPLED TO HYDRODYNAMICS Optical and Discharge Physics
 Trajectories of particles are integrated in time on the rectilinear mesh using interpolated electric fields to obtain f(r,,t).  Using f(r,,t), electron energy and electron impact sources are calculated on the rectilinear mesh and interpolated back to unstructured mesh nodes for use in the hydrodynamic model.  The Adaptive eMCS Module is called frequently enough to track the dynamics of the non-equilibrium region. Iowa State University Optical and Discharge Physics ANANTH_GEC06_11

14 Optical and Discharge Physics
POSITIVE CORONA: TRACKING THE FRONT (E/N) eMCS region 103 (Td/mm) Particle launch nodes  eMCS mesh tracks regions of high (E/N). [e] > 1011 cm-3 (E/N) > 1% of max.  Particles are launched from nodes on edges with a net influx of electrons to the region.  eMCS called every 100 ps. 150 mm  15 kV, 760 Torr, N2/O2/H2O=79/20/1, 5 ns (E/N) 103 Td/mm Iowa State University Optical and Discharge Physics Animation Slide-AVI ANANTH_GEC06_12

15 Optical and Discharge Physics
POSITIVE CORONA: Te eMCS  At the ionization front, eMCS produce peak values of Te of 6 – 7 eV as it traverses the gap, about 1 eV higher than fluid model. Te (eV) 150 mm  15 kV, 760 Torr, N2/O2/H2O=79/20/1 Iowa State University Optical and Discharge Physics ANANTH_GEC06_13 Animation Slide-AVI

16 POSITIVE CORONA: IONIZATION SOURCES
eMCS  Maxima in electron impact ionization sources with eMCS are smaller than with fluid model.  The higher Te and lower ionization sources indicate non-equilibrium in the EED at the front (cut-off tail). Ionization Sources (cm-3s-1) 150 mm  15 kV, 760 Torr, N2/O2/H2O=79/20/1 Iowa State University Optical and Discharge Physics Animation Slide-AVI ANANTH_GEC06_14

17 POSITIVE CORONA: ELECTRON DENSITY Optical and Discharge Physics
eMCS  [e] density in the ionized channel 2 – 3 times lower with eMCS due to lower ionization sources.  Width of channel is narrower and more in-tune with experimental observations. [e] (cm-3) 5x x1015 150 mm  15 kV, 760 Torr, N2/O2/H2O=79/20/1 Iowa State University Optical and Discharge Physics Animation Slide-AVI ANANTH_GEC06_15

18 Optical and Discharge Physics
BREAKDOWN IN COLD HID LAMPS : 10s Torr  Investigations into breakdown in a cylindrically symmetric lamp based on the experimental lamp geometry. 0.5cm Dielectric Powered electrode Plasma HEIGHT (cm) Quartz Air ELECTRODE GAP = 1.6 cm tube Dielectric Grounded Grounded housing electrode C L RADIUS (cm) Cylindrical center line  Ar, 10s Torr, V0= 2000 V  Species: e, Ar, Ar*, Ar**, Ar+, Ar2*, Ar2+. Iowa State University Optical and Discharge Physics ANANTH_GEC06_16

19 Optical and Discharge Physics
TRACKING THE IONIZATION FRONT  Te  [e]  [Sources]  MCS 10 eV 1013 cm-3 1020 cm-3s-1  Ionization front with steep gradients in [e] and ionization sources moves across the gap.  eMCS sensors are the ratios  A second fixed eMCS mesh tracks secondary electrons emitted from the cathode due to photons, ion bombardment.  Ar, 30 Torr, 2000 V, 400 ns MIN MAX Iowa State University Optical and Discharge Physics Animation Slide-AVI ANANTH_GEC06_17

20 Optical and Discharge Physics
EFFECT OF PRESSURE : Te 30 Torr 50 Torr 90 Torr 355 ns eMCS, 400 ns 540 ns eMCS, 700 ns 1245 ns eMCS, 1585 ns *6.2 7.7 5.5 6.4 5.0 6.1  Te at the front decreases with increasing pressure due to lower E/N.  Te from eMCS is 1.5 eV higher at 30 Torr, and 1 eV higher at 90 Torr. Te (eV) Animation Slide-AVI  Ar, 2000 V Iowa State University Optical and Discharge Physics * Typical values at locations midway across the gap as avalanche passes by. ANANTH_GEC06_18

21 EFFECT OF PRESSURE : IONIZATION SOURCES Optical and Discharge Physics
30 Torr 50 Torr 90 Torr eMCS eMCS eMCS *4.5 x 1019 1 x 1019 2.5 x 1019 1.1 x 1019 1.4 x 1019 1.1 x 1019  eMCS sources are also lower, indicating some non-equilibrium in the EED, but is comparable to fluid model values at higher pressures. [Sources] cm-3s-1 Animation Slide-AVI  Ar, 2000 V Iowa State University Optical and Discharge Physics * Typical values at locations midway across the gap as avalanche passes by. ANANTH_GEC06_19

22 EFFECT OF PRESSURE : ELECTRON DENSITY Optical and Discharge Physics
30 Torr 50 Torr 90 Torr eMCS eMCS eMCS *2.2 x 1011 1.0 x 1011 2.3 x 1011 1.0 x 1011 3.8 x 1011 2.5 x 1011  [e] density increases with pressure, but is lower with eMCS since ionization sources are lower. [e] cm-3 Animation Slide-AVI  Ar, 2000 V Iowa State University Optical and Discharge Physics * Typical values at locations midway across the gap as avalanche passes by. ANANTH_GEC06_20

23 Optical and Discharge Physics
SUMMARY  An eMCS was developed on adaptive meshes that track the ionization front of high pressure discharges using sensors.  In corona discharges at 100s Torr, the kinetic approach using eMCS yields Te 1 – 2 eV higher at the front.  eMCS calculated electron impact ionization sources have peak values lower by 3 – 5 times at the front, indicating non-equilibrium in the cut-off tail of the EED at these locations.  Electron density in the channel behind the ionization front is lower with eMCS, but the channel is also narrower in extent.  During breakdown in cold Ar-filled HID lamps at 10s Torr, Te at the front using eMCS are greater than fluid Te values but this difference diminishes as pressure increases.  At constant pressure, ionization sources and electron density are lower by 2 – 3 with eMCS than fluid values. Iowa State University Optical and Discharge Physics ANANTH_GEC06_21

24 Optical and Discharge Physics
ADAPTIVE eMCS ALGORITHM FLOWCHART  The Adaptive eMCS is called at time intervals frequent enough to track the dynamic ionization front. Iowa State University Optical and Discharge Physics ANANTH_GEC06_22

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