Dear Donggyu Jang,

I think Stark broadening at these densities is rather challenging.

A simple method to gain information is the usage of Langmuir probes. They are cheap and easy to apply. In you case you are just facing 2 caveats. You have to ensure that your measurement is not influenced by your inductive coupling - that should be possible by appropriate electronic filters and you have to figure out your ionisation state distribution.

A second possibility is the usage of an interforometer (Mach-Zehnder type). There the technical effort is higher but the measurement result should be more precise.

Without any further analysis it think these two methods are more promising.

Best regards,

Hans Werner Müller

What do you mean by "Stark-broadening tables from 10^14 /cm³"? - you measure the Stark-broadening of the H line and calculate ne from that. This should also work with densities around 10^13 /cm³. There are lots of papers dealing with this subject, for example:

• Laux C O, Spence T G, Kruger C H and Zare R N (2003)

Plasma Sources Sci. Technol. 12 125

• Belostotskiy S G, Ouk T, Donnelly V M, Economou D J and

Sadeghi N (2010) J. Appl. Phys. 107 053305

Dear Donggyu Jang,

I think Stark broadening at these densities is rather challenging.

A simple method to gain information is the usage of Langmuir probes. They are cheap and easy to apply. In you case you are just facing 2 caveats. You have to ensure that your measurement is not influenced by your inductive coupling - that should be possible by appropriate electronic filters and you have to figure out your ionisation state distribution.

A second possibility is the usage of an interforometer (Mach-Zehnder type). There the technical effort is higher but the measurement result should be more precise.

Without any further analysis it think these two methods are more promising.

Best regards,

Hans Werner Müller

Hans Werner made a good point. I'd like to add one more point: if you are using Langmuir probes in these density regime be carefull not to go too high with your sweeping voltage (especially in the electron saturation region) as I have seen sometimes sparking, which goes hand in hand with momentarily high currents on the probe. Such currents can do severe damage to the electronics that is connected to the probe - so start with low sweeping voltage of only a few volts and go up, if necessary, in small steps.

Mach-Zehnder-Interferometry is also a good idea, but you should be sure that your electron density is not much lower than 10^12 - 10^13 /cm^3. This is because interferometric measurement techniques work with differences in the refraction index of your plasma and this goes with the electron density. So, if the density is too low, your results might get quite erroneous.

Good luck with your measurements.

Dear Donggyu Jang,

Stark broadening around 1e13 is, indeed, borderline but definitely not impossible. Find attached one additional paper showing that when the fitting is done with care, you can go as low as 5e12 cm^-3 with your Stark broadening measurements.

Hope this helps, good luck with measurements.

Article Hβ Stark broadening in cold plasmas with low electron densit...

stark boarden or shift is quite challenge even in the range of 10^16 cm-3;

For this measurement, you have to fullfill the LTE conditions.

I once measured the electron density inside a femtosecond laser induced filamentation using three different methods: line boarden, MZ interferometry and the so-called in-axis holographic recording (shadowgraphy).

you can refer to the papers:

M. Centurion et.al., Opt. Lett. 29, 772 (2004).http://dx.doi.org/10.1364/OL.29.000772

J. Liu et.al., Appl. Phys. Lett. 99, 151105 (2011); http://dx.doi.org/10.1063/1.3650709

http://aei.ucsd.edu/LIB/REPORT/UCSD-ENG/UCSD-ENG-114.pdf

Good luck with the measurement.

Just to add to this,

We are operating a CO2 interferometer(10.4micron) with an FPGA backend that has an error of 10^17m-2  before averaging, which is about what you would have, correct? So in principle 10^13cm-3 is not impossible to do.

However in your case I would increase the wavelength, so say you go to a mm wave rf-source you will get a much better measurement even because the plasma phase shift in creases linearly with the wavelength. You could potentially measure down below 10^10cm-3. This wouldn't be an optical system anymore, but it should provide you with more reliable measurements.

If you are stuck with an Infrared Laser source another alternative is  using a multi-pass Mach-Zehnder setup, i.e. just pass the laser beam multiple times through the plasma, which gives you a higher phase shift and thus an easier measurement. But even for that I would increase the wavelength, if you have the choice.

The obvious benefit of interferometric methods is, that it is not influencing the plasma.

Best regards.

Why don't you try Doppler broadening or a convolution of Doppler with Stark broadening.Look Griem's plasma spectroscopy text-book  Chaps.4-5

You can use curling probe for high density plasma.

 I appreciate all of you to take care of my inquiry. I'll read recommended paper for Stark broadening. The probe is simpler method but Should I worry that probe itself interrupt plasma? Is there any method to estimate the degree of  interruption? I was considering microwave interferometry using Gunn diode. But even at 10^13 cm^(-3) electron density, 100 mm plasma will give me phase shift of 9 radian at ~ 90 GHz. This is already exceeding 2*pi. Can I get precise phase shift even the value is over than 2*pi in CW interferometry?

One of the best books on the subject: W. Lochte-Holtgreven, Ed. Plasma diagnostics. Wiley, NY, 1968.

Article Plasma Diagnostics. W. Lochte-Holtgreven, Ed. North-Holland,...

Dear Donggyu Jang,

most interferometers in plasma physics fight with fringe jumps. Usually the time history of the phase shift signal is then used for correction.

Probes will always influence your plasma. If they will disturb the plasma significantly is often quite close to religious discussions. It might be tested by having one probe inside the plasma while inserting a second one. If the signals stay the same the influence of a probe on the plasma is with rather high propability rather small (as long as we can neglect effects not depending on the probe number or size).

Good luck with finding your solution,

Hans Werner Müller

There is nothing intrinsically borderline about Stark.  Your task is to find a line with  a)significant Stark broadening that is at least comparable to Doppler (else it will be hard to extract a  reliable density) and  b) has enough intensity. I am not sure what the temperature is, but a high n-line, either from Argon or some impurity (such as hydrogen) may be usable. 

An example for n=10**13 and hydrogen Balmer lines is

E. Stambulchik, S. Alexiou, H. R. Griem, and P. C. Kepple

Stark broadening of high principal quantum number hydrogen Balmer lines in low-density laboratory plasmas

Phys. Rev. E 75, 016401 (2007)

In general spectroscopic diagnostics are preferable to probes.

If your plasma is not uniform (generally it is so), particularly if you have radially distributed temperature and electron density you will observe integrated broadening of the line of interest looking across the plasma column. If your plasma parameter distributions are axially symmetric you could find spatially resolved radial distribution of your stark broadened line from one dimension scan of your plasma image by means of inverse Abel transform. You will have to perform this procedure with all optical or microwave methods to obtain spatially resolved data.