I am looking for physics-based measurements that can be performed in the edge plasma (upstream, not at the divertor) that yield the separatrix position or some boundary for it. Some of the methods I am working on:
- measure the profile of plasma potential, find the peak
- measure density or ion saturated current fluctuation, find zero skewness (inner boundary)
- measure the profile of electron temperature, electron density, heat flux etc., fit it with a "broken" double exponential and find the breaking point (outer boundary)
- measure the profile of poloidal velocity (cross-correlation of poloidally spaced probes, Er x B drift etc.) and find the zero
Some of the methods I have found (some thanks to the answers below):
- in H-mode, fit the pedestal Te or ne profile with the tanh function and find its center (can optionally be corrected for some fraction of the SOL width) [G. Porter, Physics of Plasmas 5, 1410 (1998)]
- (specific to field reversed configurations with a weak external plasma source) modulate the plasma source at a known frequency and measure the floating potential profile with a Langmuir probe; the region where the frequency amplitude goes down suddenly is the magnetic separatrix [answer by S. Cohen below]
- assuming pressure balance along the field line, map divertor pressure measurements to upstream (at the divertor, the strike point position is known, e.g. Eich function fit, maximum heat flux etc.) and match it to upstream pressure profile (this can also be done with the floating potential, electron temperature, heat flux...) [C. K. Tsui, Physics of Plasmas 24, 062508 (2017)]
- develop some really specialised probes [K. Uehara et al, 2006 Jpn. J. Appl. Phys. 45 L630]
- use the power balance criterion (AKA Stangeby's two-point model) to calculate the separatrix temperature, then find it on any measured Te profile [H J Sun et al 2017 Plasma Phys. Control. Fusion 59 105010]
I am open to any suggestions, links to previous research, or your personal experience (whether you've encountered the problem of not knowing exactly where the separatrix is, whether you think it's worth addressing etc.).
I am looking to answer the same question for FRCs. The method we tried, and which was partially successful, was to modulate the SOL ( density? potential?) at about 10 kHz ( using a capacitively-coupled, 10-kHz modulated RF plasma source "feeding" the SOL) and looking to see the radial extent of the 10kHz oscillations/modulations (and their harmonics) using negatively biased langmuir probes.
Samuel A Cohen Thank you, it's a most interesting take on the subject! If I may ask, where do you insert the RF plasma source and where are your Langmuir probes located? Also, what spatial/radial resolution does this method approximately have? I imagine that it would excel at detecting "magnetic connection" across the poloidal/toroidal angle, and therefore it could be used for mapping or for the correction of mapping. But does this method actually tell you about the position of the last closed flux surface?
Send me your e-mail address and we can have these exchanges off line. You can look up mine at Princeton University.
Assuming you are still interested in the question, are you trying to measure the separatrix at the divertor strike point or at the last closed flux surface?
Your ideas sound good, here are some other ideas:
Slightly different from the double exponential fit - do an Eich function fit to the heat flux Article Inter-ELM power decay length for JET and ASDEX Upgrade: Meas...
In H-mode, modified tanh fits to the midplane n_e and T_e profiles from Thomson or ECE+reflectometry will give a pretty good idea, you can refine it using the divertor heat flux and something like Stangeby's 2 point model to determine T_e,sep
Gas puff imaging / fast visible imaging of ELMs
1-D radial profiles or 2-D images of the divertor strike point - for example, a filtered camera looking at D-alpha
On the Pegasus spherical tokamak at U Wisconsin Madison they have inserted probes directly into the outer-midplane last closed flux surface
MIT has developed some pretty nice Langmuir probes that can survive high heat flux, such as the rail probes and mirror probes.
Dennis P Boyle Dear Dennis, thank you for the reply.
I'm looking for the upstream separatrix position, so the Eich function, while it's very helpful in divertor measurements, is not an option for me.
Are tanh fits only suitable for the pedestal? I'm wondering if there is any way to extend this method also to L-mode.
How does GPI or imaging of ELMs help to detect the separatrix?
Do you know if Pegasus of MIT experiments have applied probe measurements to separatrix detection or equilibrium correction?
Right, the divertor measurements will only help constrain a magnetic reconstruction that maps the midplane to the divertor, not give you anything directly about the midplane. "Kinetic EFITs" are often used in order to most accurately fit the plasma boundary, in which the pressure profile is constrained by high resolution temperature, density, and fast ion measurements, and the current profile is constrained by modelling and q measurements.
Tanh fits are mostly just a useful empirical tool for fitting pedestals; if they can't fit an L-mode profile, they won't be useful - but you can use the breaking point technique.
GPI and ELMs will typically create cold, dense, bright flux tubes at or near the separatrix. With a spatially calibrated camera and proper accounting for the line-integrated emission you should be able to get a pretty good idea of the LCFS. You could probably further refine the analysis by looking at divertor probes/heat flux at the same location as the flux tube to determine if it is actually at the LCFS.
I should clarify that Pegasus used stationary electric and magnetic probes in the outer midplane while the MIT Langmuir probes are either in the divertor or only transiently inserted into the midplane. I believe Pegasus used the probes to constrain reconstructions but I'm not sure about MIT - though I do think the separatrix is apparent in the data. Some of the references here look useful https://scholar.google.com/scholar?hl=en&as_sdt=0%2C31&as_vis=1&q=pegasus++tokamak+internal+magnetic+probes&btnG=
You can measure the radiation with bolometer array. It can also tell us the plasma temperature and density profile.
Guanghui Zhu Thank you for the suggestion. Could you please elaborate it? I'm not sure how I can infer the separatrix position from radiation distribution or temperature and density profiles. In both cases, I think that I'd have to make some additional assumption, such as "upstream separatrix temperature is 70 eV" supported by the two-point model.
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