nonlinear dynamics

Nonlinear Dynamics and Chaos in Gas Discharge Tubes

I’ve been procrastinating heavily lately with high voltages and some noble gas tubes lying around. Seen below is some footage I took of a xenon flash tube connected to a high-voltage inverter salvaged from the LCD of a scrap laptop.

As the current provided by the DC-DC converter is by far not enough for a strong (and potentially blinding) discharge, this allowed me to stay still and look at the weak discharge for a long time. Eventually, I got to play a bit with the mini-lightning and noticed that the elecromagnetic fields induced into my body from the noisy environment are radiated back to the flashlamp which causes the discharge to flicker. These flickers reminded me of Chua’s circuit and the various fractal chaotic attractors.  What if one uses an ultra-high speed camera to capture the chaotic trajectory and potentially fractal behaviour of the discharge? Notice how the discharge has a few very stable modes and switches between them before it goes completely at random. Also note that even when in chaos mode, the arc still has a higher probability of following specific paths in space than others, which is another feature of Chua’s and Rössler’s circuits. That behaviour also strongly reminds of chaos diagrams as the ones below:

From order - to sub-order - to chaos

From order – to sub-order – to chaos, source: wikipedia

I dug an intriguing paper from 2015 on “Complex dynamics of a dc glow discharge tube: Experimental modeling and stability diagrams”. The group shows detailed statistical light intensity diagrams from a similar discharge occurring in a Neon sign glow tube. They have also derived the bifurcation diagrams of the glow discharge and have concluded that it somewhat resembles a Hénon chaotic attractor.

Although these kinds of studies have little practical applications, it is worth doing them just for the sake of the coolness of the project. Hmm, I have an old multimode HeNe gas laser tube lying around, maybe I could try hooking it up to a stronger-ish HV source, make it oscillate between modes, place a photodiode at the beam and start capturing intensities to reconstruct its fractal diagram. I am sure lots of experiments have been conducted on this, but still, it is cool and has merit for a potential geeky Christmas project.