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# Langmuir probe VA characteristics measurement of the standard GOLEM tokamak plasma
Aim: to measure VA characteristics on the shot to shot basis.

##Experimental setup

<!--<iframe width="100%" height="100%" src="http://golem.fjfi.cvut.cz/wiki/Experiments/EdgePlasmaPhysics/ParticleFlux/RakeProbe/1114ShotToShotMeasurement/Sessions/1114Intro/latexrsrcs/setup/index?printable" frameborder="0" allowfullscreen></iframe>-->

<img src="/Experiments/EdgePlasmaPhysics/ParticleFlux/RakeProbe/1114ShotToShotMeasurement/Sessions/1114Intro/latexrsrcs/setup/expsetup.png" width="50%">

[Rake probe description](http://golem.fjfi.cvut.cz/wiki/Diagnostics/ParticleFlux/RakeProbe/index)

##Theory

<iframe width="100%" height="100%" src="http://golem.fjfi.cvut.cz/wiki/Experiments/EdgePlasmaPhysics/ParticleFlux/RakeProbe/1114ShotToShotMeasurement/Sessions/1114Intro/latexrsrcs/theory/index?printable" frameborder="0" allowfullscreen></iframe>

###Initial configuration: 

* Date: Afternoon 261114
* LP position of 1st pin from the vessel center $LP_{pos}=107$ mm, 
* $V_{bias}$ off, 
* $R=100$ Ohm:
* LP orientation: pins ahead SouthEast (in the port direction), i.e. probe is oriented perpendicularly to the magnetic field lines
* Discharge setup: --UBt 800 --Ucd 500 --Tcd 10000  --Tres 2000 --pressure 1 --preionization 4 
* Preionization: ECR wave
* $V_{bias}$ measured with 1:100 divider



###Minutes of the experiment:

<table border="1">
<tr><th>Aim</th><th>Shot(s)</th><th>Comments</th></tr>
<tr><td>Reference shot</td><td>[#17717](http://golem.fjfi.cvut.cz/shots/17717)</td><td></td></tr>
<tr><td>Switching on $V_{bias}$ to ~ 10V</td><td>[#17718](http://golem.fjfi.cvut.cz/shots/17718)</td><td>OK, [$V_{bias}$ goes to ~0.1V](http://golem.fjfi.cvut.cz/shots/17718/DAS/1011Papouch_St.ON/)</td></tr>
<tr><td>Lp to position $LP_{pos}$ = 54 mm</td><td>[#17719](http://golem.fjfi.cvut.cz/shots/17719)</td><td>[$I_{sat}$ too high ~ 100 mA](http://golem.fjfi.cvut.cz/shots/17719/DAS/1011Papouch_St.ON/)</td></tr>
<tr><td>Galvanic insulation implemented for V_bias power supply</td><td>[#17720](http://golem.fjfi.cvut.cz/shots/17720)</td><td>Satisfactory, no problem</td></tr>
<tr><td>Since $I_{sat}$ is too high, <br/>Let's decrease R to 50 Ohm</td><td>[#17721](http://golem.fjfi.cvut.cz/shots/17721)</td><td>Better, but still $V_R$ ~9V</td></tr>
<tr><td>Since $I_{sat}$ is still too high, <br/>Let's take out LP to position 68 mm </td><td>#17722 to #17726 fails</td><td></td></tr>
<tr><td></td><td>[#17727](http://golem.fjfi.cvut.cz/shots/17727) OK</td><td>No effect, still $V_R$ ~9V</td></tr>
<tr><td>HS discussion: configuration OK<br/>reverse $V_{bias}$ polarity to -10 V to measure $I_{is}$</td><td>#17728 to #17733 fails</td><td></td></tr>
<tr><td></td><td>[#17734](http://golem.fjfi.cvut.cz/shots/17734) OK</td><td>[Hopefully good result](http://golem.fjfi.cvut.cz/shots/17734/DAS/1011Papouch_St.ON/)</td></tr>
<tr><td>$V_{bias}$ = {-20,-30,-40} V</td><td>[#17735](http://golem.fjfi.cvut.cz/shots/17735),[#17736](http://golem.fjfi.cvut.cz/shots/17736),[#17737](http://golem.fjfi.cvut.cz/shots/17737)</td><td>OK, ready for scan</td></tr>
<tr><td>Scan $V_{bias}$ = {-40,-35,-30,-25,-20,-15,-10,-5,0,1,2,3,4,5,6,7,8,9,10,12} V</td><td>From [#17739](http://golem.fjfi.cvut.cz/shots/17739) to [#17762](http://golem.fjfi.cvut.cz/shots/17762)</td><td>see Figs. 1, 2, 3, 4</td></tr>
</table>


###Final experiment configuration: 

* LP position of 1st pin from the vessel center $LP_{pos}=68$ mm, 
* $V_{bias}$ from -40V (\#17739) to 12V (\#17762), 
* $R=50$ Ohm:
* LP orientation: pins ahead SouthEast (in the port direction) i.e. probe is oriented perpendicularly to the magnetic field lines
* Discharge setup: --UBt 800 --Ucd 500 --Tcd 10000  --Tres 2000 --pressure 1 --preionization 4 
* Preionization: ECR wave
* $V_{bias}$ measured with 1:100 divider
* Length of pin: 2 mm, diameter of the pin: 0.7 mm => pin surface ~ 3.14*0.7*2*10^-6 m^2 ~ 4.4*10^-6 m^2


##Reference shot \#17743

<a href="http://golem.fjfi.cvut.cz/shots/17743/">![](/Experiments/EdgePlasmaPhysics/ParticleFlux/RakeProbe/1114ShotToShotMeasurement/Sessions/1114Intro/Figures/17743/graphpres.png)</a>

Reproducibility of the GOLEM tokamak discharge from \#17739 to \#17762

<a href=Figures/StandardPlasmaI_p_scan/graph.html><img src=Figures/StandardPlasmaI_p_scan/graph.jpg width=50%></a>
<br>$I_{p}$ scan - alltogether ([jpg](Figures/StandardPlasmaI_p_scan/graph.jpg), [svg](Figures/StandardPlasmaI_p_scan/graph.svg),[canvas](Figures/StandardPlasmaI_p_scan/graph.html),[script](Figures/StandardPlasmaI_p_scan/script.page))


##Raw experimental data

<a href=Figures/StandardPlasmaV_bias_scan/graph.html><img src=Figures/StandardPlasmaV_bias_scan/graph.jpg width=50%></a>
<br>Fig.1: $V_{bias}$ scan - alltogether ([jpg](Figures/StandardPlasmaV_bias_scan/graph.jpg), [svg](Figures/StandardPlasmaV_bias_scan/graph.svg),[canvas](Figures/StandardPlasmaV_bias_scan/graph.html),[script](Figures/StandardPlasmaV_bias_scan/script.page))

<a href=Figures/StandardPlasmaV_bias_scan_I_is/graph.html><img src=Figures/StandardPlasmaV_bias_scan_I_is/graph.jpg width=50%></a>
<br>Fig.2: $V_{bias}$ scan - ion side ([jpg](Figures/StandardPlasmaV_bias_scan_I_is/graph.jpg), [svg](Figures/StandardPlasmaV_bias_scan_I_is/graph.svg),[canvas](Figures/StandardPlasmaV_bias_scan_I_is/graph.html),[script](Figures/StandardPlasmaV_bias_scan_I_is/script.page))

<a href=Figures/StandardPlasmaV_bias_scan_I_es/graph.html><img src=Figures/StandardPlasmaV_bias_scan_I_es/graph.jpg width=50%></a>
<br>Fig.3: $V_{bias}$ scan - electron side ([jpg](Figures/StandardPlasmaV_bias_scan_I_es/graph.jpg), [svg](Figures/StandardPlasmaV_bias_scan_I_es/graph.svg),[canvas](Figures/StandardPlasmaV_bias_scan_I_es/graph.html),[script](Figures/StandardPlasmaV_bias_scan_I_es/script.page))

<a href=Figures/StandardPlasmaV_bias_scan_V_bias/graph.html><img src=Figures/StandardPlasmaV_bias_scan_V_bias/graph.jpg width=50%></a>
<br>Fig.4: $V_{bias}$ scan - alltogether $U_{bias}$ ([jpg](Figures/StandardPlasmaV_bias_scan_V_bias/graph.jpg), [svg](Figures/StandardPlasmaV_bias_scan_V_bias/graph.svg),[canvas](Figures/StandardPlasmaV_bias_scan_V_bias/graph.html),[script](Figures/StandardPlasmaV_bias_scan_V_bias/script.page))

##Analysis
### Raw data - VA characteristics at specific time with $10\mu s$ averaging.

<iframe width="420" height="315" src="//www.youtube.com/embed/mhLmCppPm3c" frameborder="0" allowfullscreen></iframe>

### VA characteristics fit

* Inspiration came from [Aasim Azooz: Langmuir probe data analysis code. Mathworks](http://www.mathworks.com/matlabcentral/fileexchange/19312-langmuir-probe-data-analysis-code), see [manual](Analysis/EEDF/TheNewUpdatedLangmuirProbeDataAnalysisProgram.pdf) and from [Nicholas James Behlman: Electron Energy Distribution Measurements in the Plume Region of a Low Current Hollow Cathode. Master thesis at Worcester Polytechnic Institute](https://www.wpi.edu/Pubs/ETD/Available/etd-011210-194717/Funrestricted/nbehlman.pdf)
* VA characteristics is fitted to the function $$I=\exp[a_1 \tanh{(V+a_2)/a_3}]+a_4 $$

<img src="/Experiments/EdgePlasmaPhysics/ParticleFlux/RakeProbe/1114ShotToShotMeasurement/Sessions/1114Intro/Analysis/Figs/19630.jpg">


<iframe width="420" height="315" src="//www.youtube.com/embed/hknP8aa6SAg" frameborder="0" allowfullscreen></iframe>

<iframe width="420" height="315" src="//www.youtube.com/embed/yd54Cy2tFT4" frameborder="0" allowfullscreen></iframe>


[This video in avi format](Analysis/LPsignal.avi)


### Resulting dependeces
* [Directory with files](Analysis/Dpndcs/)
    * [Langmuir fit coefficients](Analysis/Dpndcs/langmuirfit)
    * [Maxwell-Boltzman fit coefficients](Analysis/Dpndcs/maxwellfit)
    * [Druyvesteyn fit coefficients](Analysis/Dpndcs/Dryfit)
    
    <table><tr>
    <td>[Electron saturation current](Analysis/Dpndcs/Ies)<br/>    
    <a href="Analysis/Dpndcs/Ies.jpg"><img src="Analysis/Dpndcs/Ies.jpg"/></a></td>
    <td>[Ion saturation current](Analysis/Dpndcs/Iis)<br/> 
    <a href="Analysis/Dpndcs/Iis.jpg"><img src="Analysis/Dpndcs/Iis.jpg"/></a></td>
    <td>[Electron density](Analysis/Dpndcs/Ne)<br/> 
    <a href="Analysis/Dpndcs/Ne.jpg"><img src="Analysis/Dpndcs/Ne.jpg"/></a></td>
    <td>[Ion density](Analysis/Dpndcs/Ni)<br/> 
    <a href="Analysis/Dpndcs/Ni.jpg"><img src="Analysis/Dpndcs/Ni.jpg"/></a></td></tr><tr>
    <td>[Electron temperature](Analysis/Dpndcs/Te)<br/> 
    <a href="Analysis/Dpndcs/Te.jpg"><img src="Analysis/Dpndcs/Te.jpg"/></a></td>
    <td>[Floating potential](Analysis/Dpndcs/Vf)<br/> 
    <a href="Analysis/Dpndcs/Vf.jpg"><img src="Analysis/Dpndcs/Vf.jpg"/></a></td>
    <td>[Plasma potential](Analysis/Dpndcs/Vp)<br/> 
    <a href="Analysis/Dpndcs/Vp.jpg"><img src="Analysis/Dpndcs/Vp.jpg"/></a></td>
    <td>[$I_{es}/I_{es}$ ration](Analysis/Dpndcs/Ies2Iis)<br/> 
    <a href="Analysis/Dpndcs/Ies2Iis.jpg"><img src="Analysis/Dpndcs/Ies2Iis.jpg"/></a></td>
    </tr></table>
    

    
## Discussion
* The reason for the VA char vanish in the end of the discharge could be fact, that the GOLEM plasma is normally moving up as can be seen here (#11405):

<a href="http://golem.fjfi.cvut.cz/shots/11405/diagnostics/Radiation/0211FastCamera.ON/"><img src="http://golem.fjfi.cvut.cz/shots/11405/diagnostics/Radiation/0211FastCamera.ON/2/CorrectedRGB.png" width="25%"/></a>

Note the rake probe seen in the photo.

## Data access
* [Raw data directory](Analysis/Data/)
    * <#ShotNo>v_r: $V_R$ reflecting current via Langmuir Probe @ $R=50\Omega$
    * <#ShotNo>param_2: abs(Biasing voltage)

* [$10\mu s$ averaged data at specific times directory](Analysis/IndData/)
    * <#Time>raw.dat, where #Time $in <14000,28000> \mu s$ with $10 \mu s$ step in 2 column format: $V_{bias}$, $V_R$.
* [Files in directory, where #Time $\in <14000,28000> \mu s$ with $10 \mu s$ step](Analysis/IndData/)
    * <#Time>raw.dat in 2 column format: $V_{bias} [V]$, $I_{Lprobe} [A]$.
    * <#Time>Bt.dat in 1 single data format: $B_t [T]$.
    * <#Time>d2f.dat: second derivative of the VA characteristics fit (available during plasma life from 17100 to 20800 us).
    * <#Time>eedf.dat: Experimental EEDF (available during plasma life from 17100 to 20800 us).
    * <#Time>fm.dat: Maxwell-Boltzman fit to experimental EEDF (available during plasma life from 17100 to 20800 us).
    * <#Time>fd.dat: Druyvesteyn fit to experimental EEDF (available during plasma life from 17100 to 20800 us).
* [Individual figures directory, where #Time $\in <14000,28000> \mu s$ with $10 \mu s$ step](Analysis/Figs/)
* [Toroidal magnetic field evolution $B_t$ of the \#17743](http://golem.fjfi.cvut.cz/utils/data/17743/toroidal_field)


## Codes used
* [Main code](Analysis/ScriptV1.page)
* [Matlab main script](Analysis/matlscr.m)
* [Latex envelope for nice graphs](Analysis/image.tex)
* [Matlab support descriptions](Analysis/EEDF/)


# References:

* [David Pace:Example of Langmuir Probe Analysis](http://www.davidpace.com/physics/graduate-school/langmuir-analysis.htm)
* [Aasim Azooz: Langmuir probe data analysis code. Mathworks.](http://www.mathworks.com/matlabcentral/fileexchange/19312-langmuir-probe-data-analysis-code) 
* [Nicholas James Behlman: Electron Energy Distribution Measurements in the Plume Region of a Low Current Hollow Cathode. Master thesis at Worcester Polytechnic Institute](https://www.wpi.edu/Pubs/ETD/Available/etd-011210-194717/Funrestricted/nbehlman.pdf)

## EEDF 

* [Annette Meiners @COMSOL: Electron Energy Distribution Function](http://www.comsol.com/blogs/electron-energy-distribution-function/)