Chokes with magnets can be used to get more ability to handle current.
Take the coil in the first picture and knock off the magnet. It probably saturates at +10A and -10A. Add the magnet and it might work from 0 to +20A or -2 to +18. This does not affect the +/- range but it moves the center over.
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The pictured coils are "linearity coils" from TV sets. I have used the same idea where there is a strong DC current that will never go negative.