A comparison of emissive probe techniques for electric potential measurements in a Hall thruster plasma

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 sheehan2@wisc.edu http://cae.wisc.edu/~sheehan ** Princeton Plasma Physics Laboratory

Outline I. Motivation II. Emissive probe basics III.Techniques A. Separation point B. Floating point in the limit of large emission C. Inflection point in the limit of zero emission IV.Experimental setup V. Comparison results VI.Discussion 2

Emissive probes measure the plasma potential 4 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 in plasma (review). Instruments and Experimental Techniques, 49(2):149-156, 2006.

Motivation Emissive probe is a useful diagnostic for determining plasma potential, but underutilized Three different emissive probe techniques in active use 5 The different techniques yield different values of plasma potential Theoretical consideration for the floating potential of an emitting surface, but no experiments

A basic emissive probe 7 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

Effects of electron emission on plasma-wall sheath (Fluid theory): the plasma potential at the floating emissive wall is above the wall potential Te Φ w Te Γe = n e 2π m Γ EM = γ Γ e Te Γ ion = n M Φw ~Te Φ(x) For Xe and 5.27Te γ =0 Φw M (1 γ ) Φ w Te ln 2π m 1 Γe= Γ ion 1 γ ΓEM can be due to secondary electron emission or thermionic emission If γ 1: The walls act as an effective energy sink. 8 ** G. D. Hobbs and J. A. Wesson. Heat flow through a Langmuir sheath in presence of electron emission. Plasma Physics, 9(1):85, 1967.

Current-voltage (I-V) characteristic trace of Langmuir probe (Vp = 0) Orbital Motion Current Ion Saturation Current Exponential Electron Collection Electron Saturation Current 9

Electron emission I-V characteristic ignoring space charge effects (Vp = 0) Zero Emission Exponential Reduction Region Temperature Limited Emission 10

Emissive probe I-V trace ignoring space charge effects (Vp = 0) 11

Emissive probe I-V trace ignoring space charge effects (Vp = 0) 12

Emitted current significantly changes when space charge effects are considered (Vp = 0) Space Charge Limited Emission Zero Emission Temperature Limited Emission 13

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 Zero emission 14 Given by Child-Langmuir law All electrons are trapped within wire

The plasma potential is approximated as the point at which cold and hot I-V traces separate 16 Francis F. Chen. Electric probes. In Richard H. Huddlestone and Stanley L. Leonard, editors, Plasma Diagnostic Techniques, page 184. Academic Press, New York, 1965.

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 17 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 < 1012 cm-3)

Real I-V traces differ from the ideal description 18

Outline I. Motivation II. Emissive probe basics III.Techniques A. Separation point B. Floating point in large emission C. Inflection point in the limit of zero emission IV.Experimental setup V. Comparison results VI.Discussion 19

How the floating point in large emission method operates in theory As emission increases the floating potential approaches the plasma potential Valid for a wide range of densities: 10 5 < ne < 1012 cm-3 20 R. F. Kemp and J. M. Sellen. Plasma potential measurements by electron emissive probes. Review of Scientific Instruments, 37(4):455, 1966.

In real data, the floating potential never quite corresponds to the potential at the knee 21

The potential profile near an emitting surface G. D. Hobbs and J. A. Wesson. Heat ow through a Langmuir sheath in presence of electron emission. Plasma Physics, 9(1):85, 1967. 22 L. Dorf, Y. Raitses and N. J. Fisch, Review of Scientific Instruments 75 (5), 1255-1260 (2004).

Why sheath potential drop of ~Te is reasonable 23 Use Child-Langmuir law je ~ electron saturation current d ~ Debye length

More careful analysis also yields the ~Te result 24 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.

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 26 emissive probe characteristics. Review of Scientific Instruments, 50(2):210, 1979.

Multiple I-V traces at low emissions 27

To find the inflection point, differentiate the I-V trace 28

The plasma potential is the inflection point in the limit of zero emission current 29

Takamura's theoretical description of emissive probe I-V trace Assumptions: Cold ions (Ti = 0) Maxwellian plasma electrons Cylindrical collector Planar emitter 30 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).

Theory shows that the inflection point extrapolated to zero emission is Te/10 below Vp Theory 31 Experiment

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 32 emissive probe characteristics. Review of Scientific Instruments, 50(2):210, 1979.

3kW HTX Hall Thruster 34

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 35

Close up of probe and translator 36

Construction of emissive probe Emitting wire is thoriated tungsten Boron nitride greatly reduces secondary electron emission 37 Additional wires ensure good electrical and mechanical contact There are many other ways to make emissive probes

Simple emissive probe circuit 38 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

Hall thruster in operation 39

Additional method compared: inflection point of Langmuir probe I-V trace 41 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.

Method for comparing different emissive probe techniques 42 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

Comparison to floating point method 43

Comparison to separation point method 44

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 46 Warm Inflection Point Hot Inflection Point

Conclusions about emissive probe techniques 47 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

Technique recommendations 48

Acknowledgments 49 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

Questions? 50