A comparison of emissive probe techniques for electric ...doeplasma.eecs.umich.edu/files/Web_Sheehan_JP_2010_12_03.pdfLangmuir probe Better electric field resolution than optical techniques*

Plasma Science CenterPredictive Control of Plasma Kinetics

A comparison of emissive probe techniques for electric potential

measurements in a Hall thruster plasma

J. P. Sheehan*, Y. Raitses**,N. Hershkowitz*, I. Kaganovich**,

and N. J. Fisch***University of Wisconsin – Madison

[email protected]

http://cae.wisc.edu/~sheehan

** Princeton Plasma Physics Laboratory


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Outline

I. MotivationII. Emissive probe basicsIII.Techniques

A. Separation pointB. Floating point in the limit of large emissionC. Inflection point in the limit of zero emission

IV.Experimental setupV. Comparison resultsVI.Discussion


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Outline





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Emissive probes measure the plasma potential

● Electrons are emitted when the probe is biased below Vp, but not when biased above

● They can only measure Vp, not any other parameter

● Can be used where Langmuir probe cannot

● Beams● Temperature fluctuations● Non-steady state

● Much smaller uncertainty than Langmuir probe

● Better electric field resolution than optical techniques*

*V. P. Gavrilenko. Laser-spectroscopic methods for diagnostics of electric elds inplasma (review). Instruments and Experimental Techniques, 49(2):149-156, 2006.


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Motivation● Emissive probe is a useful diagnostic for

determining plasma potential, but underutilized● Three different emissive probe techniques in

active use● The different techniques yield different values of

plasma potential● Theoretical consideration for the floating

potential of an emitting surface, but no experiments


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Outline





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A basic emissive probe

● Loop of tungsten wire

● Wire diameter: 0.025mm – .25mm

● Current through wire heats it to thermionic emission

● Probe can be biased

● This is just one of many designs


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Φw ~TeΦ(x)

For Xe and γ =0 Φw ≈ 5.27Te

ew Tee em

Tn Φ−=Γπ2

MTn eion =Γ

eEM Γ=Γ γ

11e ionγ

Γ = Γ−

( )

−−≈Φ γ

π1

2ln

mMTew

ΓEM can be due to secondary electron emission or thermionic emissionIf γ →1: The walls act as an effective energy sink.

Effects of electron emission on plasma-wall sheath (Fluid theory): the plasma potential at the floating emissive wall is above the wall potential

** G. D. Hobbs and J. A. Wesson. Heat flow through a Langmuir sheath in presence of electron emission. Plasma Physics, 9(1):85, 1967.


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Current-voltage (I-V) characteristic trace of Langmuir probe (Vp = 0)

Ion SaturationCurrent

ExponentialElectronCollection

ElectronSaturationCurrent

OrbitalMotionCurrent


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Electron emission I-V characteristic ignoring space charge effects (Vp = 0)

Temperature Limited Emission

Exponential Reduction Region

Zero Emission


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Emissive probe I-V trace ignoring space charge effects (Vp = 0)


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Emissive probe I-V trace ignoring space charge effects (Vp = 0)


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Emitted current significantly changes when space charge effects are considered (Vp = 0)

Temperature Limited Emission

Zero EmissionSpace Charge Limited Emission


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Describing the three regions of the emission current I-V relationship

● Temperature limited emission● Given by Richardson-Dushman equation

● Independent of probe bias● Space charge limited emission

● Given by Child-Langmuir law

● Zero emission● All electrons are trapped within wire


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Outline





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The plasma potential is approximated as the point at which cold and hot I-V traces separate

Francis F. Chen. Electric probes. In Richard H. Huddlestone and Stanley L.Leonard, editors, Plasma Diagnostic Techniques, page 184. Academic Press, NewYork, 1965.


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Separation point technique based on overly simplified theory

● Assumes there is temperature limited emission below the plasma potential and zero emission above the plasma potential

● Real data shows additional features● Cold and hot traces are not coincident above plasma

potential creating crossing point rather than separation point● Space charge effects modify the emissive I-V trace● There is high uncertainty in identify the separation (or

crossing) point● Theory suggests the technique is valid for any plasma

parameters that do not destroy the probe (typically ne < 10

12 cm-3)


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Real I-V traces differfrom the ideal description


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Outline


A. Separation pointB. Floating point in large emissionC. Inflection point in the limit of zero emission



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How the floating point in large emission method operates in theory

R. F. Kemp and J. M. Sellen. Plasma potential measurements by electron emissive probes. Review of Scientific Instruments, 37(4):455, 1966.

● As emission increases the floating potential approaches the plasma potential

● Valid for a wide range of densities: 105 < ne < 1012 cm-3


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In real data, the floating potential never quite corresponds to the

potential at the knee


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The potential profile near an emitting surface

L. Dorf, Y. Raitses and N. J. Fisch, Review of Scientific Instruments 75 (5), 1255-1260 (2004).

G. D. Hobbs and J. A. Wesson. Heat ow through a Langmuir sheath in presenceof electron emission. Plasma Physics, 9(1):85, 1967.


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Why sheath potential dropof ~Te is reasonable

● Use Child-Langmuir law

● je ~ electron saturation current● d ~ Debye length


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More careful analysis alsoyields the ~Te result

● 1967 paper by Hobbs and Wesson* show this result analytically from Poisson's equation

● Schwager** using PIC simulations determined the potential drop from bulk to cathode to be 1.5Te

● This difference is usually acknowledged by those using this technique for thrusters or fusion

*G. D. Hobbs and J. A. Wesson. Heat flow through a Langmuir sheath in presence of electron emission. Plasma Physics, 9(1):85, 1967.**L. A. Schwager. Effects of secondary and thermionic electron-emission on the collector and source sheaths of a finite ion temperature plasma using kinetic-theory and numerical-simulation. Physics of Fluids B-Plasma Physics, 5(2):631-645, 1993.


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Outline





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Qualitative logic of the inflection point in the limit of zero emission

● For a cold probe, an inflection point exists at the plasma potential

● As emission increases, the inflection point becomes more negative

● By measuring the inflection point at numerous (~5) low emissions (Iemit < Ie,sat) the plasma potential can be determined by linearly extrapolating to zero emission

● Valid from vacuum to large densities: 0 < ne < 1013 cm-3

● Requires less emission, so less risk of probe melting in high density plasmas

J. R. Smith, N. Hershkowitz, and P. Coakley. Inflection-point method of interpreting emissive probe characteristics. Review of Scientific Instruments, 50(2):210, 1979.


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Multiple I-V traces at low emissions


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To find the inflection point, differentiate the I-V trace


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The plasma potential is the inflection point in the limit of zero emission current


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Takamura's theoretical description of emissive probe I-V trace

● Assumptions:● Cold ions (Ti = 0)● Maxwellian plasma electrons● Cylindrical collector● Planar emitter● Emitted electrons have

negligible energy● Predicts floating potential

saturation at ~Te below Vp● Useful for understanding the

inflection point's dependance on emission current

M. Y. Ye and S. Takamura, Physics of Plasmas 7 (8), 3457-3463 (2000).


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Theory shows that the inflection point extrapolated to zero emission is Te/10 below Vp

Theory Experiment


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Explanation of why emission current scale is so low in Takamura theory

● Theoretical emitted current derived in planar conditions

● Experiments show that smaller probe radius gives a steeper slope in emission versus inflection point graph

● Therefore, the planar case would be expected to have a much lower emission current scale

J. R. Smith, N. Hershkowitz, and P. Coakley. Inflection-point method of interpreting emissive probe characteristics. Review of Scientific Instruments, 50(2):210, 1979.


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Outline





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3kW HTX Hall Thruster


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Parameters of Hall thruster plasma● Te ~ 10 to 60 eV

● ne ~ 109 to 1010 cm-3

● Neutral density ~ 1012 to 1013 cm-3

● Outer diameter: 123mm (~4.8 in)● Inner diameter: 73mm (~2.9 in)● Anode bias: 250 – 450 V● Working gas: Xenon● Mean free paths of electrons, ions, and neutrals are larger than the

thruster size (~12cm diameter, ~2.5cm width)● B field maximum ~ 100G● B field at measurement locations ~50G


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Close up of probe and translator


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Construction of emissive probe

● Emitting wire is thoriated tungsten● Boron nitride greatly reduces secondary electron emission● Additional wires ensure good electrical and mechanical

contact● There are many other ways to make emissive probes


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Simple emissive probe circuit● The probe filament is heated by a

variable power supply● The current from the probe is

determined by measuring the voltage across the current shunt resistor

● The bias power supply sweeps the probe bias

● Adjust the probe bias by half of the heater voltage

● There are many variations of this circuit, but these four pieces are common to all of them


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Hall thruster in operation


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Outline





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Additional method compared: inflection point of Langmuir probe I-V trace

● Not an emissive probe technique

● At the plasma potential there is an inflection point as the I-V trace transitions from exponential electron collection to electron saturation

● Functions similarly to the inflection point in the limit of zero emission, though the mechanism is different.


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Method for comparing different emissive probe techniques

● Data was taken at various positions and discharge parameters

● For meaningful comparisons, the results of the different methods at the same position and discharge parameters were compared

● Since the temperature varied greatly, each data point is normalized to the temperature of the plasma from which the data was taken


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Comparison to floating point method


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Comparison to separation point method


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Outline





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Uncertainty• Floating point method uncertainty from

identifying start of plateau region and is typically ~0.1Te

• Warm inflection point method uncertainty from identifying correct peak of dI/dV curve and is typically ~0.5Te

• Inflection point in the limit of zero emission uncertainty comes principally from uncertainty in linear fit and is typically ~0.1Te

• Separation point uncertainty due to large region over which separation occurs and is typically ~0.3Te

• There is an additional uncertainty of ~2V due to the voltage drop across the filament

Warm Inflection Point

Hot Inflection Point


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Conclusions about emissive probe techniques

● There will never be a perfect way to know the plasma potential, only approximations based on measurements

● The inflection point methods give a better measure of the plasma potential than the floating point method

● The separation point technique does not give a consistent or accurate measure of the plasma potential

● Results from experiments are consistent with a virtual cathode forming around a highly emitting surface

● This experiment suggests that a highly emitting surface floats at ~2Te below the plasma potential


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Technique recommendations


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Acknowledgments● This work was supported by US Department of

Energy grants No. DE-AC02-09CH11466 and No. DE-FG02-97ER54437 and the Fusion Energy Science Fellowship

● Special thanks to Martin Griswold and Lee Ellison for all of their help


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Questions?

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A comparison of emissive probe techniques for electric ...doeplasma.eecs.umich.edu/files/Web_Sheehan_JP_2010_12_03.pdfLangmuir probe Better electric field resolution than optical techniques*