Well we all know that a certain inductance will have a certain impedance at a certain frequency. That is relatively simple to calculate. But, inductors can saturate, which means that they are pretty much just a resistive load with no inductance. But how do we know?

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One time I used a spare Variac as a variable inductor. This worked very well with my LCR meter, and varied inductance with the turn of the dial (surprise). When I hooked this up to a small fluorescent tube for use with a choke, I kept manually shorting the output across the filaments as a sort of manual fluorescent starter. I started with maximum inductance, and then slowly incrementally decreased the inductance until something happened. Well boy, did something happen.

The tube struck, but was very dim. So, naturally, I moved the dial to vary the brightness. While very slowly turning the dial, it was getting towards the point of being normal brightness when suddenly *BUZZZZZ*, the lamp lit up super super bright for a split second and luckily blew the 5A fuse on my Variac before it could severely damage the tube. It was almost as if I just suddenly crossed a needle-thin threshold of saturation.

I checked the inductance of the variable choke, and the impedance was within spec for a ballast for that particular tube, but obviously it wasn’t going to work because it was saturating. How do I predict when something will saturate?

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Thanks!

There are multiple ways.
One of the simplest is to use a variable DC source, a low value resistor as a current sensor and a switch, all connected in series.
Connect a (digital) oscilloscope that resistor to record the current rising up at the moment you turn ON the switch, set it so it is triggered by the rising current. You need some quality switch not glitching that much and you may add a freewheeling diode parallel to the measured inductor so it will clamp the voltage spike when you open the switch. The best would be, if the oscilloscope allows you to save the waveform data (in csv or so), it allows you to do a lot of postprocessing in tools like Excell or so.
An ideal inductor will yield linear ramp on the current, the slope governed by an equation:
 di/dt = Vdc / L

Now if the coil has a series resistance, it will turn into the current following an "exponential" settling shape, the same shape as "charging RC", the slope is governed by an equation

di/dt = (Vdc - i * R) / L

Now if we take an inductor with  feromagnetic core, the inductance L is not constant, but it is a function of the current "i", so the equation will become

di/dt = (Vdc - i*R) / L(i)

Assuming the voltage source, as well as the resistances in the circuit are constant and known and the voltage is large enough to allow you to pass the currents of interrest before it stabilizes (so Vdc/R is bigger than the current range you want to measure)

And the way, how the inductance depends on the current, so the "L(i)" is what we are after:

L(i) = (Vdc - i*R) / (di/dt)

Now from the oscilloscope measurement you get the record of the current over time, so "i(t)", so once you have it as a series of numbrs in an Excell or Calc or like tool, you can do the math there.
Most finicky is the way how you extract the "di/dt".
The simplest is to calculate differences equal distance before and after:
di/dt = (i(t + delta) - i(t - delta)) / (2 * delta)
where you select the "delta" so it is still small vs the nonlinearities in the ramp, but big enough to suppress the influence of the noise.
Graph the resulting "L(i)" and play with the "delta" so you get reasonable result (the saturation knee well visible, but a reasonably clean trace).

From that you will see the complete curve.
Now with that, your maximum AC rms current avoiding saturation is the I(SaturationKnee) / sqrt(2)...

@RRK
Well alright then. I do not currently possess an oscilloscope, and even if I did, that still sounds complicated. I just thought about this:

Obtain desired impedance
Plug inductor into a dim bulb tester on a variac
Ramp up to desired voltage drop while watching current
If all goes well, bypass dim bulb tester, if not, then it wont work
Voila!

Would this work reliably?