MODELING OF MICRODISCHARGES FOR USE AS MICROTHRUSTERS Ramesh A. Arakoni a) , J. J. Ewing b) and Mark J. Kushner c) a) Dept. Aerospace Engineering University of Illinois b) Ewing Technology Associates c) Dept. Electrical Engineering Iowa State University mjk@iastate.edu, arakoni@uiuc.edu, jjewingta@comcast.net http://uigelz.ece.iastate.edu 52 nd AVS International Symposium, November 2, 2005. * Work supported by Ewing Technology Associates, NSF, and AFOSR.
AGENDA • Introduction to microdischarge (MD) devices • Description of model • Reactor geometry and parameters • Plasma characteristics • Effect of geometry, and power • Incremental thrust, and effect of power • Concluding Remarks Iowa State University Optical and Discharge Physics AVS2005_RAA_01
MICRODISCHARGE PLASMA SOURCES • Microdischarges are plasma devices which leverage pd scaling to operate dc atmospheric glows 10s –100s µ m in size. • Few 100s V, a few mA • Although similar to PDP cells, MDs are usually dc devices which largely rely on nonequilibrium beam components of the EED. • Electrostatic nonequilibrium results from their small size. Debye lengths and cathode falls are commensurate with size of devices. ( ( ) ) = ε ≈ − µ 1 / 2 L 2 V / qn 10 20 m cathode Fall c 0 I 1 / 2 ⎛ ⎞ T ⎜ ⎟ λ ≈ ≈ µ eV 750 cm 10 m , ⎜ ⎟ − D 3 ⎝ ⎠ n ( cm ) e • Ref: Kurt Becker, GEC 2003 Iowa State University Optical and Discharge Physics AVS2005_RAA_02
APPLICATIONS OF MICRODISCHARGES • MEMS fabrication techniques enable innovative structures for displays and detectors. • MDs can be used as microthrusters in small spacecraft for precise control which are requisites for array of satellites. FLOW THRU MICRO- DISCHARGE HOT GAS TO GAS IN NOZZLE Ewing Technology Associates Ref: http://www.design.caltech.edu/micropropulsion Iowa State University Optical and Discharge Physics AVS2005_RAA_03
DESCRIPTION OF MODEL • To investigate microdischarge sources, nonPDPSIM, a 2- dimensional plasma code was developed with added capabilities for pulsed operation. • Finite volume method in rectilinear or cylindrical unstructured meshes. • Implicit drift-diffusion-advection for charged species • Navier-Stokes for neutral species • Poisson’s equation (volume, surface charge, material conduction) • Secondary electrons by impact, thermionics, photo-emission • Electron energy equation coupled with Boltzmann solution • Monte Carlo simulation for beam electrons. • Circuit, radiation transport and photoionization, surface chemistry models. Iowa State University Optical and Discharge Physics AVS2005_RAA_04
DESCRIPTION OF MODEL: CHARGED PARTICLE, SOURCES • Continuity (sources from electron and heavy particle collisions, surface chemistry, photo-ionization, secondary emission), fluxes by modified Sharfetter-Gummel with advective flow field. � � ∂ N = − ∇ ⋅ φ + i S ∂ i t − ∇ ⋅ ε ∇ Φ = ρ + ρ • Poisson’s Equation for Electric Potential: V S • Photoionization, electric field and secondary emission: � � ′ ⎛ − − ⎞ � � � r r ′ ⎜ ⎟ ′ ⌠ σ 3 N ( r ) N ( r ) exp d r ⎜ ⎟ λ i ij j ⎮ � ⎝ ⎠ = S ( r ) � � ⎮ Pi ′ π − 2 ⎮ 4 r r ⌡ ( ) ( ) ⎛ ⎞ − Φ − ε 1/2 3 E/ q ∑ ⎜ ⎟ = −∇ ⋅ = = γ φ 2 W 0 S j , j AT exp , j ⎜ ⎟ Si E S ij j kT ⎝ ⎠ j S Iowa State University Optical and Discharge Physics AVS2005_RAA_05
ELECTRON ENERGY, TRANSPORT COEFFICIENTS • Bulk electrons: Electron energy equation with coefficients obtained from Boltzmann’s equation solution for EED. ( ) � � � � ∂ ε ⎛ ⎞ n 5 ∑ = ⋅ + σ − κ − ∇ ⋅ εϕ − λ ∇ = φ ⎜ ⎟ 2 e j E E n N T , j q ∂ EM e i i e e ⎝ ⎠ t 2 i • Beam Electrons: Monte Carlo Simulation • Cartesian MCS mesh superimposed on unstructured fluid mesh. Construct Greens functions for interpolation between meshes. Iowa State University Optical and Discharge Physics AVS2005_RAA_06
DESCRIPTION OF MODEL: NEUTRAL PARTICLE TRANSPORT • Fluid averaged values of mass density, mass momentum and thermal energy density obtained using unsteady, compressible algorithms. ∂ ρ � = −∇ ⋅ ρ + ( v ) ( inlets , pumps ) ∂ t � ( ) ( ) � ∂ ρ ⎛ ⎞ � � v ( ) ∑ ∑ = ∇ ⎜ ⎟ − ∇ ⋅ ρ − ∇ ⋅ τ + − µ N kT v v q N E S m q E ∂ i i i i i i i i i ⎝ ⎠ t i i ( ) ∂ ρ � � ( ) � c T ∑ ∑ = −∇ − κ ∇ + ρ + ∇ ⋅ − ∆ + ⋅ p T v c T P v R H j E ∂ p i f i i i t i i • Individual species are addressed with superimposed diffusive transport. ( ) ⎛ ⎞ ⎛ ⎞ + ∆ � ( ) ( ) N t t ⎜ ⎟ ⎜ ⎟ + ∆ = − ∇ ⋅ − ∇ + + i N t t N t v D N S S ⎜ ⎟ ⎜ ⎟ i i f i T V S ⎝ ⎠ N ⎝ ⎠ T Iowa State University Optical and Discharge Physics AVS2005_RAA_07
GEOMETRY AND MESH • Geometry A • Geometry B • Plasma dia: 150 µ m at inlet, 250 µ m at cathode. • Electrodes 130 µ m thick. • Dielectric gap 1.5 mm. • Geometry B: 1.5 mm dielectric above the cathode. • Fine meshing near electrodes, less refined near exit. • Anode grounded; cathode bias varied based on power deposition (0.25 - 1.0 W). • 10 sccm Ar, 30 Torr at inlet, 10 Torr at exit. Iowa State University Optical and Discharge Physics AVS2005_RAA_08
EXPERIMENT: GEOMETRY • Modeled geometry similar to experimental setup. • Plume characterized by densities of excited states. • Ref: John Slough, J.J. Ewing, AIAA 2005-4074 Iowa State University Optical and Discharge Physics AVS2005_RAA_09
CHARGED SPECIES: GEOMETRY A [Ar + ] (10 11 cm -3 ) [e] (10 11 cm -3 ) Potential (V) E-field (kV/cm) 1 200 0 -250 1 18 • Power deposition occurs in the cathode fall by • 10 sccm Ar, 0.5 W collisions with hot electrons. • Very high electric fields near cathode. Iowa State University Optical and Discharge Physics AVS2005_RAA_10
NEUTRAL FLUID PROPERTIES: GEOMETRY A Ar 4s (10 11 cm -3 ) Ar 4p (10 11 cm -3 ) Gas temp (°K) 100 200 700 1 1 300 • Plume extends downstream, can be used for diagnosis. • • 10 sccm Ar, 30 – 10 Torr Gas heating and consequent expansion is a source of thrust. • 0.5 W. • Ref: John Slough, J.J. Ewing, AIAA 2005-4074 Iowa State University Optical and Discharge Physics AVS2005_RAA_11
VELOCITY INCREASE WITH DISCHARGE Without With • Gas heating and discharge discharge subsequent expansion causes increase in velocity. • Steady state after one or two bursts of flow. • At high plasma density, momentum transfer between charged species and neutrals is also important. V max 130 m/s V max 170 m/s • 10 sccm Ar, 30 Torr at inlet, 10 Torr at exit. • 0.5 Watts. • Power turned on at 0.5 ms. 160 0 Animation Iowa State University Axial velocity (m/s) Optical and Discharge Physics 0 – 0.55 ms AVS2005_RAA_12
POWER DEPOSITION: IONIZATION SOURCES • 0.5 W • 1.0 W 0.5 W 1.0 W Max 5 x 10 20 Max 7.5 x 10 20 Max 1.5 x 10 20 Max 2 x 10 20 Bulk ionization (cm -3 sec -1 ) 100 Beam ionization (cm -3 sec -1 ) 1 • Ionization rates increase with power. • Beam electrons are equally as important as bulk electrons. • 10 sccm Ar, 30 Torr at inlet, 10 Torr at exit. Iowa State University Optical and Discharge Physics AVS2005_RAA_13
POWER DEPOSITION: PLASMA PROPERTIES • 0.75 W • 0.5 W • 1 W • 0.5 W • 0.75 W • 1 W Max 3.5 x 10 13 Max 2.25 x 10 13 Max 2 x 10 13 Max 700 Max 900 Max 980 [e] (cm -3 ) 5 x 10 11 Max Temperature (°K) 300 Max • Hotter gases lead to higher ∆ V and higher thrust production. • Increase in mean free path due to rarefaction may affect power deposited to neutrals. • With increasing [e], increase in production of electronically excited states. • 10 sccm Ar, 30 Torr at inlet, 10 Torr at exit. Iowa State University Optical and Discharge Physics AVS2005_RAA_14
POWER DEPOSITION: FLOW VELOCITY Power off 0.5 W 1.0 W Max 80 Max 160 Max 200 • 10 sccm Ar, 30 Torr at V y compared in the above plane. inlet, 10 Torr at exit. • Power turned on at 0.5 ms. MAX 5 Iowa State University Axial velocity (m/s) Optical and Discharge Physics AVS2005_RAA_15
BASE CASE RESULTS: GEOMETRY B [e] (cm -3 ) Potential (V) Bulk Ionization(cm -3 s -1 ) Gas temp (°K) Max 8 x 10 20 Max 1 x 10 14 1 901 100 100 301 1 0 -320 • Electrons are confined, discharge operates in an unsteady regime. • Ionization pulses travel towards anode. • Power densities are greater than that of Geometry A. • 10 sccm Ar, 30 – 10 Torr Iowa State University • 0.5 W, turned on at 0.5 ms Optical and Discharge Physics AVS2005_RAA_16
VELOCITY INCREASE: GEOMETRY B 0.5 W • Increase in velocity is due to expansion of hot gas. V y compared • Axial-velocity increase Max 140 Max 400 in the above not substantial at exit. plane. • 10 sccm Ar, 30 – 10 Torr • 0.5 W, turned on at 0.5 ms Animation MAX Axial velocity (m/s) Iowa State University 5 Optical and Discharge Physics 0 – 0.65 ms AVS2005_RAA_17
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