1. 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 http://uigelz.ece.iastate.edu June 20, 2005. * Work supported by Ewing Technology Associates, NSF, and AFOSR. ICOPS2005_RAA_00

2. Iowa State University Optical and Discharge Physics AGENDA  Introduction to microdischarge (MD) devices  Description of model  Reactor geometry and parameters  Plasma characteristics for dc case  Incremental thrust, and motivation for pulsing  Effect of power on plasma characteristics  Effect of pulse width, power on incremental thrust  Concluding Remarks ICOPS2005_RAA_01

3. Iowa State University Optical and Discharge Physics  Microdischarges are plasma devices which leverage pd scaling to operate dc atmospheric glows 10s –100s  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.  Ref: Kurt Becker, GEC 2003 ICOPS2005_RAA_02 MICRODISCHARGE PLASMA SOURCES

4. Iowa State University Optical and Discharge Physics 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. ICOPS2005_RAA_03 Ewing Technology Associates Ref: http://www.design.caltech.edu/micropropulsion

5. Iowa State University Optical and Discharge Physics DESCRIPTION OF MODEL  To investigate microdischarge sources, nonPDPSIM, a 2- dimensional DC plasma code was developed with added capabilities for pulsed and rf discharges.  Finite volume method used 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. ICOPS2005_RAA_04

6. Iowa State University Optical and Discharge Physics  Continuity (sources from electron and heavy particle collisions, surface chemistry, photo-ionization, secondary emission), fluxes by modified Sharfetter-Gummel with advective flow field.  Poisson’s Equation for Electric Potential:  Photoionization, electric field and secondary emission: DESCRIPTION OF MODEL: CHARGED PARTICLE, SOURCES ICOPS2005_RAA_05

7. Iowa State University Optical and Discharge Physics ELECTRON ENERGY, TRANSPORT COEFFICIENTS  Bulk electrons: Electron energy equation with coefficients obtained from Boltzmann’s equation solution for EED.  Beam Electrons: Monte Carlo Simulation  Cartesian MCS mesh superimposed on unstructured fluid mesh. Construct Greens functions for interpolation between meshes. ICOPS2005_RAA_06

8. Iowa State University Optical and Discharge Physics  Fluid averaged values of mass density, mass momentum and thermal energy density obtained using unsteady, compressible algorithms.  Individual species are addressed with superimposed diffusive transport. DESCRIPTION OF MODEL: NEUTRAL PARTICLE TRANSPORT ICOPS2005_RAA_07

9. Iowa State University Optical and Discharge Physics GEOMETRY FOR MICROTHRUSTER  Fine meshing near the cathode to capture beam electrons accurately.  Anode grounded, cathode biased –300 to –500 V.  50 Torr Ar at inlet, expanded to 10 or 1 Torr at exit.  Flow rates 3 or 6 sccm.  Plasma dia. 150  m  Cathode 100  m  Anode 50  m  Dielectric gap 0.5 mm ICOPS2005_RAA_08

10.  Power deposition occurs in the cathode fall by collisions with energetic electrons.  Gas heating is the primary source of thrust. Iowa State University Optical and Discharge Physics PLASMA CHARACTERISTICS OF DC CASE Potential (V) -280 0 ICOPS2005_RAA_09 2 E-source (10 19 cm -3 s -1 ) 50  6 sccm Ar  -300 V  Power turned on at 1 ms 300 T gas (°K) 500 Animation Axial velocity 0 – 1.005 ms 0 Axial velocity (m/s) 250

11. Iowa State University Optical and Discharge Physics EFFECT OF PLASMA ON VELOCITY ICOPS2005_RAA_10  6 sccm Ar  -300 V  Power turned on at 1 ms 0 Axial velocity (m/s) 250 With discharge Without discharge

12. Iowa State University Optical and Discharge Physics PLASMA CHARACTERISTICS: CURRENT-VOLTAGE  Discharge operates on the near side of the Paschen curve.  Neutral density increases with higher flow rate leading to higher ionization rates. ICOPS2005_RAA_11 5100  (10 -6 g/cc) power off 3 sccm6 sccm

13.  Thrust calculated by:  Increase in thrust is the rate of momentum transfer to the neutrals when the discharge is switched on.  Meaningful incremental thrust occurs when plasma power to is greater than that of the flow Iowa State University Optical and Discharge Physics INCREMENTAL THRUST: MOTIVATION FOR PULSING ICOPS2005_RAA_12  6 sccm Ar  -300 V  Power turned on at 1 ms   F calculated close to cathode

14.  Fluid initialized by simulating for 1 ms.  Pulses of 300, 400, 500 V applied for 0.5, 1  s.  Pulse width has effect on incremental thrust. Optimize the duration of the pulse for maximum thrust per energy expended. Iowa State University Optical and Discharge Physics PULSING: VOLTAGE vs TIME ICOPS2005_RAA_13

15.  Plasma reaches steady state quickly whereas the fluid does not. Iowa State University Optical and Discharge Physics PLASMA CHARACTERISTICS : PULSED Potential (V) -280 0 ICOPS2005_RAA_14 2 Ionization (10 19 cm -3 sec -1 ) 50  6 sccm Ar  -300 V  1  s pulse 300 T gas (°K) 425 Beam electrons (10 19 cm -3 sec -1 )

16.  Absence of electrons near cathode fall due to high fields and gas rarefaction.  Beam electrons are important to sustain the plasma. Iowa State University Optical and Discharge Physics VARIATION OF [e] AND T GAS WITH BIAS VOLTAGE ICOPS2005_RAA_15 500 5 -300 V-400 V-500 V Logscale [e] (10 11 cm -3 ) -300 V-400 V-500 V  6 sccm Ar  Values shown at the end of a 1  s pulse 25 1 Logscale Beam electrons (10 20 cm -3 sec -1 )

17.  Power deposition varies non-linearly with applied voltage.  Gas heating leads to stagnation of flow upstream of the power deposition zone. Iowa State University Optical and Discharge Physics VARIATION OF V AXIAL AND T GAS WITH BIAS VOLTAGE ICOPS2005_RAA_16 -300 V-400 V-500 V 420 300 600 300 900 300 Gas temperature (°K) 250 0 -300 V-400 V-500 V Axial velocity (m/s)  6 sccm Ar  Values shown at the end of a 1  s pulse

18.  Incremental value is dependent on the duration of the pulse.  Pulse widths of 500 ns are too short for the flow to attain equilibrium with the plasma.  The effect of the discharge is felt even after the plasma is turned off due to gas heating. Iowa State University Optical and Discharge Physics EFFECT OF PULSE WIDTH ON THRUST ICOPS2005_RAA_17  6 sccm Ar  -400 V 500 ns 1  s

19.  Incremental thrust increases nearly linearly with power.  Higher power with small pulses may lead to higher efficiency.  Heat transfer to walls is small with if the pulse width is much less than conduction time scales. Iowa State University Optical and Discharge Physics EFFECT OF POWER ON THRUST ICOPS2005_RAA_18  6 sccm Ar  1  s pulse

20. Iowa State University Optical and Discharge Physics  An axially symmetric microdischarge was computationally investigated with potential application to microthrusters.  Higher flow rates resulted in higher power deposition for a fixed voltage due to increase in density of neutral species.  It was observed that pulsing of the discharge might be an efficient in terms of power consumed per thrust produced.  Studies were conducted to find the effect of parameters such as flow rate, power, and pulse width.  Small pulses with larger voltages might be more efficient at generating thrust. CONCLUDING REMARKS ICOPS2005_RAA_19