I could run it at a higher frequency (100kHz) to minimize the inductor size.
The problem designing the inductor will be the peak current.
At 40 amps average the peak will be around 63 amps, plus switching ripple on top of that.
Absolute current peak may be something like 80 amps, which is not in itself a problem.
But then you need to think about skin effect in the inductor.
At 100 Khz the thickest wire you can use is about 0.4mm diameter which will carry about 360mA per strand.
At 20 Khz about 0.9mm wire can be used that will carry about 1.8 amps per strand.
The required inductance will be so low that only one or two turns may be required.
Core saturation is obviously important, and also core loss for heating reasons.
After thinking about all this for a while, If I was doing something like this myself, I would probably use a short length of copper tube with several powdered iron toroids slipped over it, and run it at a much lower switching frequency.
I have not done any calculations on this, but from past experience I might start with 10mm OD copper tube with perhaps 0.7mm wall thickness.
That should easily carry the high frequency current with negligible heating.
Then slip one powdered iron toroid over it and calculate what the core saturation and losses were at 80 amps, for one toroidal core by itself, and how much inductance I ended up getting.
With a bit of messing about, it should be possible to slip several (?) suitable toroids over the tube to meet all of my requirements.
With this type of very low inductance very high current, its physically much easier to wrap the core around the wire, than wrap the wire around a core.
Also keep an open mind about switching frequency.
Your copper pipe may make several tens of Khz possible.
But permiability and core loss of readily available (cheaper) cores may force a much lower switching frequency, which is not really a problem.
What I am saying is, select the switching frequency to suit the magnetics you can build, rather than starting off selecting some impractically high switching frequency and then getting into real grief trying to make it work.