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. Email: bhoj@uiuc.edu b)Department of Electrical and Computer Engineering Iowa State University, Ames, IA, USA. Email: mjk@iastate.edu http://uigelz.ece.iastate.edu Gaseous Electronics Conference, October 2006 * Work supported by the National Science Foundation.

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

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

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

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

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

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

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

Optical and Discharge Physics POSITIVE CORONA BREAKDOWN [e] cm-3 E/N (Td) Te (eV) 5x1012 - 5x1015 30-3000 0 - 10  E/N is enhanced at the ionization front to 500-1000 Td.  The enhanced E/N increases Te which rises at the front to 6 - 7 eV.  In the ionized channel, E/N falls below 50 Td with Te = 0.5 -1 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

Optical and Discharge Physics NON-LOCAL ELECTRON TRANSPORT - eMCS  Electron transport may become “non-local” due to large E/N (500-1000 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

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-3 (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

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

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

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 1 30 Iowa State University Optical and Discharge Physics Animation Slide-AVI ANANTH_GEC06_12

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) 0 12 150 mm  15 kV, 760 Torr, N2/O2/H2O=79/20/1 Iowa State University Optical and Discharge Physics ANANTH_GEC06_13 Animation Slide-AVI

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) 1021 1025 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

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) 5x1012 5x1015 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

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

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

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 0 10  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

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 1017 1020  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

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 109 1013 Iowa State University Optical and Discharge Physics * Typical values at locations midway across the gap as avalanche passes by. ANANTH_GEC06_20

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

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