MODELING OF MICRODISCHARGES FOR USE AS
MICROTHRUSTERS
Ramesh A. Arakonia) , J. J. Ewingb) and Mark J. Kushnerc)
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
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
Iowa State University
Optical and Discharge Physics
MICRODISCHARGE PLASMA SOURCES
 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.
LcathodeFall  2Vc 0 / qnI 
1/ 2
 10  20m
1/ 2
 TeV


D  750
3 
 ne ( cm ) 
cm  10 m ,
 Ref: Kurt Becker, GEC 2003
ICOPS2005_RAA_02
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.
FLOW THRU MICRODISCHARGE
GAS IN
HOT GAS TO
NOZZLE
Ewing Technology
Associates
Ref: http://www.design.caltech.edu/micropropulsion
ICOPS2005_RAA_03
Iowa State University
Optical and Discharge Physics
DESCRIPTION OF MODEL
 To investigate microdischarge sources, nonPDPSIM, a 2dimensional 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
Iowa State University
Optical and Discharge Physics
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 i
     Si
t
 Poisson’s Equation for Electric Potential:
     V   S
 Photoionization, electric field and secondary emission:
 
  r  r  3


d r 
 N i (r ) ij N j (r ) exp 
 
 

S Pi (r )  
 2
r
4

r


S Si    j ,
ICOPS2005_RAA_05

1/2
3

 W  q E/  0 
jE  AT 2 exp 

kTS

,


jS    ij j
j
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.

ne    
5
 
2
 j  E  EEM  ne  Ni i       Te , j  qe
t
2

i
 Beam Electrons: Monte Carlo
Simulation
 Cartesian MCS mesh
superimposed on unstructured
fluid mesh. Construct Greens
functions for interpolation
between meshes.
ICOPS2005_RAA_06
Iowa State University
Optical and Discharge Physics
DESCRIPTION OF MODEL:
NEUTRAL PARTICLE TRANSPORT
 Fluid averaged values of mass density, mass momentum and
thermal energy density obtained using unsteady, compressible
algorithms.


   ( v )  ( inlets , pumps )
t


 v 



   N i kTi     v v        qi N i Ei  S i mi  i qi E
t
i
 i



 
 c pT 

  T  v c pT   Pi   v f   Ri H i   ji  E
t
i
i
 Individual species are addressed with superimposed diffusive
transport.

 N i t  t   
   SV  S S
N i t  t   N i t      v f  Di NT 

N
T



ICOPS2005_RAA_07
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
Iowa State University
Optical and Discharge Physics
PLASMA CHARACTERISTICS OF DC CASE
Animation
Axial velocity
0 – 1.005 ms
0
250
Axial velocity
(m/s)
0
-280
500
2
50
300
19
-3 -1
Tgas (°K)
Potential (V) E-source (10 cm s )
 Power deposition occurs in the cathode
fall by collisions with energetic electrons.
 Gas heating is the primary source of
thrust.
ICOPS2005_RAA_09
 6 sccm Ar
 -300 V
 Power turned on at 1 ms
Iowa State University
Optical and Discharge Physics
EFFECT OF PLASMA ON VELOCITY
Without
discharge
With
discharge
0
250
Axial velocity (m/s)
ICOPS2005_RAA_10
 6 sccm Ar
 -300 V
 Power turned on at 1 ms
Iowa State University
Optical and Discharge Physics
PLASMA CHARACTERISTICS: CURRENT-VOLTAGE
3 sccm
6 sccm
 (10-6 g/cc) power off
5
100
 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
Iowa State University
Optical and Discharge Physics
INCREMENTAL THRUST: MOTIVATION FOR PULSING
 Thrust calculated by:
dm
F
Ve  Ae Pe  Pa 
dt
 Increase in thrust is the rate of
momentum transfer to the
neutrals when the discharge is
switched on.
.
 dm 
 dm 
V

V
 dt  pulse  dt  nopulse
F  
 Meaningful incremental thrust
occurs when plasma power to is
greater than that of the flow
1 2
j .E  v
2
ICOPS2005_RAA_12




6 sccm Ar
-300 V
Power turned on at 1 ms
F calculated close to cathode
Iowa State University
Optical and Discharge Physics
PULSING:
VOLTAGE vs TIME
 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.
ICOPS2005_RAA_13
Iowa State University
Optical and Discharge Physics
PLASMA CHARACTERISTICS : PULSED
0
-280
Potential (V)
2
Ionization
(1019 cm-3 sec-1)
50
Beam electrons
(1019 cm-3 sec-1)
 Plasma reaches steady state
quickly whereas the fluid
does not.
ICOPS2005_RAA_14
425
300
Tgas (°K)
 6 sccm Ar
 -300 V
 1 s pulse
Iowa State University
Optical and Discharge Physics
VARIATION OF [e] AND TGAS WITH BIAS VOLTAGE
-300 V
-400 V
[e] (1011 cm-3) 5
-500 V
-300 V
500
Logscale
 Absence of electrons near cathode fall
due to high fields and gas rarefaction.
 Beam electrons are important to
sustain the plasma.
ICOPS2005_RAA_15
-400 V
-500 V
25
Logscale
Beam electrons (1020 cm-3 sec-1)
1
 6 sccm Ar
 Values shown at the end
of a 1 s pulse
Iowa State University
Optical and Discharge Physics
VARIATION OF VAXIAL AND TGAS WITH BIAS VOLTAGE
-300 V
300
-400 V
420 300
-500 V
600 300
-300 V
900
-400 V
Axial velocity (m/s)
-500 V
0
250
Gas temperature (°K)
 Power deposition varies non-linearly
with applied voltage.
 Gas heating leads to stagnation of flow
upstream of the power deposition zone.
ICOPS2005_RAA_16
 6 sccm Ar
 Values shown at the end
of a 1 s pulse
Iowa State University
Optical and Discharge Physics
EFFECT OF PULSE WIDTH ON THRUST
500 ns
 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.
1 s
.
 dm 
 dm 
V

V
 dt  pulse  dt  nopulse
F  
 6 sccm Ar
 -400 V
ICOPS2005_RAA_17
Iowa State University
Optical and Discharge Physics
EFFECT OF POWER ON THRUST
 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.
 6 sccm Ar
 1 s pulse
.
 dm 
 dm 
F   V 

V
 dt  pulse  dt  nopulse
ICOPS2005_RAA_18
Iowa State University
Optical and Discharge Physics
CONCLUDING REMARKS
 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.
ICOPS2005_RAA_19
Iowa State University
Optical and Discharge Physics