1. OPTIMIZING THE PERFORMANCE OF PLASMA BASED MICROTHRUSTERS* Ramesh A. Arakoni, a) J. J. Ewing b) and Mark J. Kushner c) a) Dept. Aerospace Engineering University of Illinois, Urbana, IL b) Ewing Technology Associates, Bellevue, WA c) Dept. Electrical and Computer Engineering Iowa State University, Ames, IA mjk@iastate.edu, arakoni@uiuc.edu, jjewingta@aol.com http://uigelz.ece.iastate.edu ICOPS 2006, June 4 - 8, 2006. * Work supported by Ewing Technology Associates, NSF and AFOSR. ICOPS06_MT_00

2. Iowa State University Optical and Discharge Physics AGENDA  Microdischarge (MD) devices as thrusters  Description of model  Scaling of thrust  Geometrical effects  Conclusions. ICOPS06_MT_01

3.  Microdischarges are plasmas that leverage pd scaling to operate at high pressures (10s-100s Torr) in small reactors (100s  m).  Typically operated as a dc discharge using wall stablization.  High E/N in the cathode fall generates energetic electrons producing high ionization.  High power densities (10s kW/cm 3 ) owing to small volume of discharge, producing high neutral gas temperatures.  Increase in gas temperature in flowing gas produces thrust. MICRODISCHARGE PLASMA SOURCES ICOPS06_MT_02 Iowa State University Optical and Discharge Physics

4. MICRODISCHARGES AS MICROTHRUSTERS  Micro-satellites weighing < few kg or require  Ns to mNs of thrust for station keeping.  Thrusters based on MD devices can deliver the required thrust using a only a few Watts of power.  The MD operates as an efficient heat source for the propellant. Expansion of the hot gas provides the required thrust. Iowa State University Optical and Discharge Physics ICOPS06_MT_03 300  m hole diameter Ref: J. Slough, J.J. Ewing, AIAA 2005-4074 Ref: Kimura, Horisawa, AIAA 2001-3791

5.  The force provided by the thruster is calculated by: where dm/dt is the mass flow rate, V e is the exit. Iowa State University Optical and Discharge Physics CALCULATION OF THRUST ICOPS06_MT_04 Ref: Robert G. Jahn, Phys. of Electric Propulsion, Mc-Graw Hill, 1989.

6.  The incremental thrust obtained due to the discharge is given by:  Common metric for efficiency is the thrust per unit power input to the system. In this case, we look at incremental thrust per unit power.  Typical values of the efficiency for electro-thermal and arc thrusters are about 0.1 – 0.2 N/kW.  Theoretical limit on efficiency is 2/V e, where V e is the exit velocity. Iowa State University Optical and Discharge Physics EFFICIENCY OF THRUSTER ICOPS06_MT_05

7. Iowa State University Optical and Discharge Physics DESCRIPTION OF MODEL ICOPS06_MT_06  To investigate microdischarge sources, nonPDPSIM, a 2- dimensional plasma-hydrodynamics code was used.  Finite volume method used on cylindrical unstructured meshes.  Implicit drift-diffusion-advection for charged species  Navier-Stokes for neutral species  Poisson’s equation (volume, surface charge)  Secondary electrons by ion impact.  Electron energy equation coupled with Boltzmann solution  Monte Carlo simulation for beam electrons.

8. 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:  Secondary electron emission: DESCRIPTION OF MODEL: CHARGED PARTICLE, SOURCES ICOPS06_MT_07

9. ELECTRON ENERGY, TRANSPORT COEFFICIENTS  Bulk electrons: Electron energy equation with coefficients obtained from Boltzmann’s equation solution for EED. Iowa State University Optical and Discharge Physics ICOPS06_MT_08  Beam Electrons: Monte Carlo Simulation  Cartesian MCS mesh superimposed on unstructured fluid mesh.  Greens functions for interpolation between meshes.

10. 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 ICOPS06_MT_09

11.  Plume characterizes densities of excited states. Iowa State University Optical and Discharge Physics EXPERIMENTAL GEOMETRY (BY OTHERS)  Ref: John Slough, J.J. Ewing, AIAA 2005-4074 ICOPS06_MT_10

12. Iowa State University Optical and Discharge Physics GEOMETRY OF THE MICROTHRUSTED  Plasma channel geometry:  300  m at inlet, 500  m at cathode.  130  m thick electrodes, 1.5 mm dielectric gap.  Anode grounded; cathode bias varied based on power deposition (a few W).  30 Torr (4 kPa) Argon at inlet, expanded to low pressures (5 - 10 Torr) downstream.  Gradation of meshing with a fine mesh near the discharge and coarse mesh near the outlet. ICOPS06_MT_11

13.  Power deposition occurs in the cathode fall by beam electrons and ion drift.  Electric fields of > 22 kV/cm in cathode fall.  15 sccm Ar, 30/10 Torr, 0.5 W Iowa State University Optical and Discharge Physics 15 SCCM: PLASMA CHARACTERISTICS -270 0 140 1.4 140 1.4 22.5 0 Potential (V) [Ar + ] 10 11 cm -3 Logscale [e] 10 11 cm -3 Logscale E field (kV/cm) ICOPS06_MT_12

14.  Gas heating and consequent expansion is a source of thrust.  More extended plume in experiment due to supersonic status.  15 sccm Ar, 30/10 Torr, 0.5 W Iowa State University Optical and Discharge Physics 15 SCCM: NEUTRAL FLUID 2 200 300 675 4 400  Ref: John Slough, J.J. Ewing, AIAA 2005-4074 [Ar(4p)] 10 11 cm -3 Logscale [Ar(4s)] 10 11 cm -3 Logscale Gas temp (K) ICOPS06_MT_13 Expt. plume

15. Iowa State University Optical and Discharge Physics VELOCITY INCREASE WITH DISCHARGE Animation 0 – 0.6 ms Power onCold flow  Gas heating and subsequent expansion produces increase in velocity.  When turning on discharge, pulsation initially occurs.  Incremental thrust: 0.05 mN,   thrust/power: 0.1 N/kW Total thrust: 0.12 mN. 0300 Axial velocity (m/s) ICOPS06_MT_14  15 sccm Ar, 30 – 10 Torr  0.5 W.

16. Iowa State University Optical and Discharge Physics 30 sccm, 1 W: AXIAL VELOCITY, THRUST  30 sccm Ar, 30 – 10 Torr  1.0 W 600 0  Increasing power produces increase Mach number near 1.  Incremental thrust: 0.2 mN  Total thrust of  0.5 mN.  Thrust per unit power: 0.17 N/kW. Axial velocity (m/s) ICOPS06_MT_15 Power onCold flow Animation 0 – 0.55 ms

17. Iowa State University Optical and Discharge Physics POWER DEPOSITION: PLASMA, GAS HEATING (°K)  Ionization efficiency increases with power due to larger excited state density  At higher temperatures and lower densities decouple power transfer from ions to neutrals. Max 675 K Max 875 K 300 Max [e] cm -3 (logscale) 1 100 0.5 W0.75 W 0.5 W0.75 W 2.6 x 10 13 1.4 x 10 13 ICOPS06_MT_16

18. Iowa State University Optical and Discharge Physics POWER DEPOSITION: FLOW VELOCITY  Increase in flow speed and thrust of 250% predicted with 0.75 W 0 MAX 0.5 WPower off0.75 W Max 160Max 300Max 400 ICOPS06_MT_17 V y in exit plane.

19. Iowa State University Optical and Discharge Physics EFFECT OF GEOMETRY: CATHODE THICKNESS  No significant effect of electrode thickness on velocity profile.  Thicker electrode could lead to longer service life.  30 sccm Ar, 30 / 10 Torr  1.0 W ICOPS06_MT_18

20. Iowa State University Optical and Discharge Physics EFFECT OF GEOMETRY: END CAP  Maximum increment in velocity for end cap thickness of 500  m.  Optimal thickness required to expand (and not cool) the hot gas.  1W, 30 sccm Ar, 30/10 Torr ICOPS06_MT_19

21. Iowa State University Optical and Discharge Physics OPTIMAL GEOMETRY: DOWNSTREAM PRESSURE 100 1 MAX 400 [e] cm -3 logscale Gas temp (°K)  5 Torr  10 Torr Max 1920 Max 1440 Max 6 x 10 14 Max 2.5 x 10 14  Lower downstream pressure produces a more confined plasma (a bit counter-intuitive)  Higher power density leads to hotter neutral gas. ICOPS06_MT_20  1W, 30 sccm Ar

22. Iowa State University Optical and Discharge Physics CONCLUDING REMARKS  A microdischarge was computationally investigated for potential use in microthrusters.  At flow rates of a few 10s sccm and up to 1 W power, 0.1 – 0.5 mN of thrust were achieved.  Thrust specific power consumption of 0.1-0.2 N/kW is predicted in-line with other arc discharge thrusters.  Placement of electrodes is important with respect to confinement of plasma and possible cooling of gas.  Slightly embedded electrodes resulted in maximum incremental thrust for a given flow rate and power. ICOPS06_MT_21