First, some background info.
Plasma is mostly transparent to electromagnetic radiation.
The radiation emitted to the plasma is usually described in terms of two polarizations, relative to the magnetic field in the plasma:
- O-mode: Ordinary mode, wave electric field is parallel to the plasma magnetic field, in which the dispersion relation is like that of the unmagnetized plasma. For waves with a frequency above a certain cutoff frequency, the wave does not propagate and is thus reflected.
- X-mode: Extraordinary mode, wave electric field is perpendicular to the plasma magnetic field, and the dispersion relation is... quadratic and has two solutions for the cutoff frequency! We use the upper cutoff, because the lower cutoff is at too a low frequency to probe. The cutoff frequency has a dependency on the plasma magnetic field and on the plasma density. We use some other diagnostic to find the magnetic field profile and then it's a matter of getting the density profile.
Where I work, we use X-mode waves to probe the plasma.
Using X-mode, the cutoff frequency equivalent to zero plasma density is the cyclotron frequency. Zero density is what we find right at the edge of the plasma. Then we just keep increasing the frequency of the probing wave and we can trace the all the successive densities at which we get a cutoff. Sadly, there comes a time when we cross the first harmonic of the cyclotron frequency and that one is absorbed by the plasma... and this messes up the reconstruction of the density profile.
We use 4 different bands to probe the plasma:
- Q-band: 44 - 52GHz
- V-band: 50 - 75GHz
- W-band: 72 - 110GHz
- D-band: 105 - 130GHz
These bands' frequencies are swept in 10micro-seconds (us), all at the same time and using the same antenna.
The wave reflected by the plasma is combined with a reference wave, giving as beat wave.
Some people extract the phase of this wave to estimate the time it took to travel thorough the plasma... but in my place we use the spectrogram
Here's a spectrogram of two bands (in this case, the ones where reflected signal exists):
![[Image: spect_zpsapt2z1nx.png]](https://images.weserv.nl/?url=i191.photobucket.com%2Falbums%2Fz226%2Fpocaracas%2FAF%2Fspect_zpsapt2z1nx.png)
From the spectrogram, I get the first frequency where we have a reflection - in that image, it's at about 52GHz.
I then trace the maximum of the spectrogram, for each probing frequency to get the wave's group delay - that's the white line I plotted - it's not on top of the spectrogram's maximum, because some extra calibration is done there - we know the calibration is correct, because the white line is continuous from one band to the next.
People usually go for the phase because it is proportional to the integral of the refractive index, in frequency, up to the cutoff frequency... well, actually, it's the phase difference that gets measured. And what we want to determine is not only the density, but also the distance from some reference location (we use the back wall for reference by probing before there's any plasma)... it follows this here nice equation for you geeks:
![[Image: eq1_zpsjtlyusr9.png]](https://images.weserv.nl/?url=i191.photobucket.com%2Falbums%2Fz226%2Fpocaracas%2FAF%2Feq1_zpsjtlyusr9.png)
x_c is the position at the cutoff frequency, x_0 is the position at the first cutoff, c is the speed of light, pi is 3.14, w_p is the plasma frequency (which depends on the plasma density), "d phi" is the phase derivative (which is proportional to the group delay) and w is the integral from 0 to cutoff frequency.
Knowing the position of the plasma layer that's reflecting the wave, we can use the dispersion equation to get the density, by also using the "known" magnetic field profile.
Repeat for every probing frequency, up to where there is no reflection and you have a nice density profile:
![[Image: profile_zpso4ureztn.png]](https://images.weserv.nl/?url=i191.photobucket.com%2Falbums%2Fz226%2Fpocaracas%2FAF%2Fprofile_zpso4ureztn.png)
This image has 3 different profiles. Mine, in black.. the one calculated from the signal's phase in cyan and, in pink, the one provided by another diagnostic: High Resolution Thomson Scattering - this one uses lasers and measures how the lasre light gets scattered by the plasma as there's a relation between the intensity of the scattered light (measured perpendicularly to the direction of the probing laser) and both the plasma temperature and density... they know how to discern each of these quantities and provide both temperature and density profiles. Reflectometry cannot produce a temperature profile...
My profile is slightly to the inside of the vacuum vessel, compared to HRTS, because there's a slight error in the magnetic field profile that we use. A mere post-hoc correction of this profile, of the order of 1.6%, overlaps my profile with HRTS's, but I'm evil and like to let everyone know that the guys in charge of the magnetic diagnostics have some work to do!
![[Image: CU7DxT4WEAAx_a1.jpg:large]](https://pbs.twimg.com/media/CU7DxT4WEAAx_a1.jpg:large)
![[Image: extraordinarywoo-sig.jpg]](https://i.postimg.cc/zf86M5L7/extraordinarywoo-sig.jpg)
