You should use a U shaped core, as those classic red and blue magnets, find a core made of silicon steel, like the one mains transformers are made of. A lamination for toroidal cores could be ideal, as a tape you could cut strips from. EI cores are easier to find, you could cut one E in half and get two squarish U to build this, the size will depend on what you try to archive, and the size of the magnet you want to move, so the field is wide enough for the magnet to fit in. Try at least twice the lenght of the magnet for your gap, maybe three times.
Then you should use a full bridge to make current flow in both senses. If you just make the current flow during the entire cycle the number of turns of the coil will be huge for 10Hz and the current at 1kHz will be very low, so I suggest using constant pulse width and change the timing between pulses, I hope that make sense...
If using 500μs pulses (full width at 1kHz as max freq) you should do the math for your core and the voltage to get the numbers of turns, so the core doesn't saturate. That's just as an air gapped transformer primary, you could fine the equations around. If the core saturates it will just start heating and the power delivered to the field wont rise any further at that point.
If you are more the experimental kind of guy, you could try that experimentally to find the apropiate number of turns, making a random coil on the core, taking it slowly to saturation, where the current starts to increase much higher than the voltage, measure the current and count turns, and then keep that value constant. Add as many turns as you need for the core to be just about to saturate at 500μs, with 180V applied and then you go.
JS
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