Old Inductor, replace with newer current-production?
Ah... seeing the schematic I think it's a "signal amplifier" for a signal derived from a magnetic sensor, not a "magnetic amplifier". Does that make sense in context we don't have?

The inductor looks like a fairly standard "pot core" - sometimes called Vinkor - and the variability is not achieved by voltage but by the adjustable slug.

In which case you may have to find a similar core and wind a similar inductor. (Assuming you are trying to clone the circuit so you can't just re-use the part - that would be my first choice).

Matching the inductance range and DC resistance will get you close : identifying the core material is likely to be the hardest part. Especially since the cores were often glued together and quite fragile. 

You may have to make measurements of DC resistance and wire diameter. 
That gives you length, via copper resistivity, 
Then approximate turns count via mean winding diameter (say, 50% or 60% of the external diameter)
Then specific inductance ( = 1 Henry /  n^2).

Given external diameter and height (preferably in mm rather than foreign coins :-) that may allow identification of possible core material from old databooks.

And at that point you can search for modern replacement coil formers and cores. The available range will be different, so you'll have to design, wind and test, to get the correct turns count (and approx same DC resistance) with modern materials.

Publish the measurements you make and there may be further help : I knew there was a reason to keep some of my old databooks... 

And you are left with the problem of the correct core adjustment. Are there calibration instructions, or a graph of the expected frequency response of that stage? Or is there an obvious frequency it is designed to amplify (or reject)?

EDIT : Cassette player : bias trap! There is a high amplitude AC bias signal (often also used for erase) that can mess up sensitive audio signals if it gets in the wrong places... but it's usually at the sort of frequency where 1 Henry makes no sense... that can't be it.

Time to look at that capacitor, is that 0.026 uF (26 nf?)







simulate this circuit &ndash; Schematic created using CircuitLab

Approximating the previous stage as a source impedance of 120 ohms (R215) the filter looks like this: and te simulation shows a low pass filter with a massive 20dB peak at its resonant frequency of 1 kHz. I don't know if that makes sense. But if it does, it suggests the alignment procedure should be to tune for maximum amplitude from a 1 kHz input.

The next stages look like they rectify this signal, and perhaps differentiate the rectified signal (C214?) to generate a pulse to switch something on or off when a 1 kHz tone burst is played...

(incidentally one of the PCB photos shows the legend "Rowe AMI" and a search on that name turns up a lot of jukeboxes...)