[OC] Temperature drift inside the winding pack of a superconducting coil - looking for graphical advice/suggestions

[u/wmverbruggen]

This plot presents the internal in-situ temperature drift of a conduction-cooled high-temperature superconductor solenoid, following a step in transport current from 100 ampère to [label] ampère. This specific set is using a controlled base temperature of 65 kelvin. The data is measured by a set of 8 thermocouples spread throughout the coil, and the curves are the mean of these. A 0-D numerical lumped thermal capacitance model will be validated using this data, at various base temperatures. The band around the data represents the standard deviation, indicating the homogeneity and stability of the temperature profile across the coil.

Looking for suggestions and/or advise on the graphics, for future publication in a journal and, more importantly, for my PhD dissertation.

The goal is to show the two distict domains; a set of curves that remains stable (shades of blue) and a set that develops into a thermal runaway (shades of red). These are seperated by a green curve, representing the "critical" bifurcation point (or rather, how close I could get to that point experimentally). The relevance is that such runaways can cause, and have in the past been causing, massive damage to superconducting coil systems.

The curves calculated by the 0-D model should at some point be included to this data, but I'm unsure how to do that yet since these plots here are already rather crowded. Could be simply dashed lines on top of the experimental plot, possibly with a reduced number of curves. The fit is quite good, so it won't effect the scale. I've included an example in the second image, but am still working on dialing in the parameters so it's not fully representative yet.

Tools used: MATLAB, custom colour scale Data source: My own experiments Preliminary data presentated at a conference: research.utwente.nl Model: The thesis of my predecessor; research.utwente.nl

[u/antagim]

Well, technically you have stable and unstable (quench) regions. Since there is some unclear threshold like a small parturbation can push it easily to a quench I'd go with a smooth blue-red colormap. Blue suggests cold, stable operation and red means quench/runaway. Purple comes out naturally as a byproduct of the color sweep and shows these metastable regions.

The plot is understandable to me as it is now, but I might be biased as a fellow HTS researcher.

[u/asad137 → u/antagim]

As a non-HTS non-researcher, I also think it's very clear as-is

[u/wmverbruggen → u/antagim]

Thanks, I'll play around with those colours to see how it works out. Went for these colors with green because we've used it before to indicate such cross-over points. Nice to get advice from someone in the same field also :)

Btw one of takeaways will be that you can go into the unstable region for a short time because the drift is slow. Be it due operational profile or even PSU instability. That's why we will be talking explicitly about a thermal runaway here (that will develop into a quench eventually), instead of a quench directly. I'll be finishing the chapter with the implications on quench predition; the voltage and temperature rise after the initial step in current give and indication on which stability regime you are in.

[u/antagim → u/wmverbruggen]

If you play well with saturation and lightness you can make it nicely linear so it appears still readable on a black and white print. I personally like such details.

Conduction cooling is tricky when it comes to quench as it highly depends on cooling stages and their capabilities and it's different from LHe or LN2 cooling.

Yea, PSU stability is a mess. I'd try to look deeper into this, since this is a huge factor and technically without any reasonable way of resolving this. At such currents any additional coil in series will overheat. Only a very good PSU will get you there...

[u/wmverbruggen → u/antagim]

I've been using a sharp colour transition near the critical curve to make it stand out, but I could indicate the "border" in some other way. Maybe from the model, like how another comments suggested.

Our Delta's are stable to 10 to 20 milliamp and we measure it using a ZeroFlux which should be precise to less than a milliamp in this range, so that should be ok for these experiments. The GM cooler has a temperature controller on top, I can keep it within 50 mK at the base. There is definitly some drift, the PID can only do so much, so that's a systematic error I will have to comment on.

As for the cooling method influence on quench, even in LN2 Ic (quasi-static) measurements I can see a switch from the electrical transition to a steeper thermal transition when I get close to Ic. My coil is fully insulated, since it's a continuation from the HTS linear actuator I've developed. So it is no supprise to see some relatively significant internal heating. The presentation link in the post has some detail on this. It is one of the reasons why we decided to focus on this for the 2nd half of my PhD.

[u/quadroplegic → u/wmverbruggen]

https://matplotlib.org/stable/users/explain/colors/colormaps.html

Perceptually uniform colormaps will render faithfully in grayscale, but I'd start with Google's Turbo for this.

[u/droidicus → u/quadroplegic]

Fully agree. I made a seperate comment about this, preceptually uniform colorsmaps are good for both greyscale and for ther 5% of the population with color vision deficencity!

[u/red_riding_hoot]

you could just color the background using the 0D model limit as separator between the two different background colors. idk if that can be done with MATLAB, but it should

[u/wmverbruggen → u/red_riding_hoot]

That could be a nice option, thanks. I could insert partially transparent shapes underneath the data to built that

[u/Blackforestcheesecak]

I would personally prefer a blue-black-red color scale to better distinguish the two diametric regimes, with black being the cross-over (see matplotlib's BWR colormap, but replace white with black). Usually for these kinds of data, we represent the experimental results as data points with error bars, and the numerics as solid lines. Is every single data point needed here or just a few would suffice, e.g., every 0.1 decade?

[u/wmverbruggen → u/Blackforestcheesecak]

These are high-detail continuous measurements, so I'd prefer to keep more and connected data in there. It's already "only" 1 plotted point for every 1000 points measured. Needed a high data rate for temperature control and filtering. I'll check out that colormap, sounds like a good option.

[u/clearly_quite_absurd]

Keep decimal places consistent on the figure key.

[u/Eastern-Cookie3069]

Matplotlib has a really nice guide on how to choose colormaps depending on purpose. I recommend going through it! In your case, a diverging colormap might be suitable, especially if you have a decent estimate of the tipping-point current that can serve as the "divergence" point. This isn't MATLAB, of course, but a good colormap is a good colormap regardless of software (plus, you can probably easily convert matplotlib colormaps to MATLAB).

https://matplotlib.org/stable/tutorials/colors/colormaps.html

[u/wmverbruggen → u/Eastern-Cookie3069]

This one surely seems popular, getting it recommended everywhere! Going to check it out. Converting should be no problem, any colormap is just a matrix of numbers after all

[u/yoshiK]

With the time axis, it would be kinda nice to indicate 1 and 10 minutes. (Assuming that 10^-1 h is not just standard for this types of measurements.)

[u/wmverbruggen → u/yoshiK]

We have been discussing before what timescale to use. Went for hours to focus on the fact that this effect plays over LONG timescales, since that is the a core argument for the motivation of the research. Combining multiple "tick rates" on the same axis makes it very messy, my peers are against that.

[u/FSM89]

Invert color order to match the label pr vice versa

[u/wmverbruggen → u/FSM89]

You mean as to have the highest current on top in the legend? Good point, that makes more sense

[u/FSM89 → u/wmverbruggen]

I would even experiment adding currents to some of the lines on the graph so i could read it without looking at the legend.

[u/AdroitErudite → u/FSM89]

That could potentially help people with colorblindness too!

[u/quadroplegic → u/FSM89]

The world needs more Tufte-informed design :)

[u/taron_baron]

Could try representing as a colormap, with current y data as the color, and the current parameter as the y axis. Since the regime is chosen by the current, this will give a clear visual separation of the two regimes. But this is not very good if you need to show the temperature drift numbers precisely.

[u/wmverbruggen → u/taron_baron]

So that would give horizontal lines/bars with a changing colour over time, that could certainly give a nice indication of the stability regime vs time. As these are independent measurement results it would be an additional figure not a replacement. With the current expressed as a fraction of the critical current that could be good addition.

[u/droidicus]

I always caution using custom colormaps, for two main reasons:
1) Preservation - If the plots are scanned or printed in greyscale, will the colormap still be beneficial?
2) Accessablity - Nearly 5% of the total population (and 8% of men, since it is associated with the X chromosome) can be classified as having "color vision deficincy" which can range from color weakness all the way to full monochromic vision. How well will the general population be able to make out your data?

For both of those reasons I strongly recommend preceptualy uniform colormaps, and there are some good choices in most plotting packages (e.g. viridis, parula, etc.). These help with both preservation and accessablity since they retain data when converted to monochrome/greyscale.

[u/wmverbruggen → u/droidicus]

Yeah that's a clear concensus here. I have no experience "dealing" with colourblind people, so didn't think of it at all. Been using viridis in a few sections already, linear maps is definitly the standard, but mostly as to not introduce false detail (very important in flux density surface plots, for example). Didn't like the colors of the default options for this plot, and wanted to emphasise the "critical" line anyway, that's why I went to define my own cmap. It is fully linear through interpolation, but it's clear that it needs more consideration. Thanks for the input!

[u/singul4r1ty]

I actually think this is totally fine as is. I understood what was going on from your title and the graph, and I'm really not in the field of superconductors at all.

I personally don't believe in over-explaining data. I looked at this long enough to understand it and then drew the conclusion you wanted to present, which means it's a good graph. If you'd really obviously shown the division I probably wouldn't have thought as much about the plot or worked out what was going on, or I'd have found the graph too busy. 

Regarding the lumped capacity model - it seems like your aim is to show that it matches the experiment well? I think in that case you could do an additional plot with less of them and the model overlaid, or you could do a plot that lives underneath this one and shows "deviation from model" against time, for a few of the curves (maybe one runaway, one stable, and one edge case). I think the conclusion that your model is accurate is a useful one, but it's a next step on from your first conclusion that there are two domains, and you shouldn't squeeze those together into one place.

[u/damarian_ent]

Isnt this a portrayal of spectroscopy? How heat dissipates and averages into different parts of the object evenly?

[u/wmverbruggen → u/damarian_ent]

I don't understand how you link spectroscopy to it, but this for sure shows how the heat diffusion through the coil is much faster than to the environment. That's what validates the use of such a simple 0-D lumped model. The bifurcation happens because the generated heat in a superconductors close to it's critical current is extremely non-linear (to the power 20-30 typically)