Pig current limiting

The tank supply I am designing uses a 3-phase pig transformer and a 6 diode
bridge to charge a filter capacitor of 15 uF. After that there is a reactor
that charges the primary capacitor usign resonant charging.

Of course, every time the primary capacitor gets charged the filter (15 uF)
capacitor voltage drops a little down: I need a device to limit the current
used to re-charge the big capacitor.

A suitable resistor will delay too much the recharge (and develop losses
and heat!) and the capacitor will never reach full voltage.

I was thinking to some limiting reactor on the 400VAC (primary) side.

My questions:

- if I use a simple autotransformer, it will limit the voltage but the
current will be still orders of magnitude too high, right?
- what about using a non-linear reactor, one that allows the current to
rise until a value X and then will keep it about to that value. I mean like
a MOT with secondary shorted? Who manufacture/sells these devices?