Energy dissipation and current decay in this circuit
At my previous job I worked with and programmed a surge generator with a maximum output of 32 kV at 150 kA. Over 16 uS that is about 5 gigawatts of peak power-but very few joules. Our back-feed inductors were 1 foot diameter poly-carbonate tubes 4 feet long with 110 turns of 6 AWG wire. The connections were with 500mcm locomotive cable which is very flexible. At full power I could vaporize a 16 penny nail in a flash of light, almost as loud as a grenade.

My above rant is to point out a few very important things, if your playing the numbers game.


Your 5 mH inductor needs a silicon steel core about the size of a shoe box. Too small of a core and it will saturate and act like a short-circuit.
You will need to wind maybe 40 turns or so of 6 awg stranded wire. Use a good LCR meter and do a 'poke' test until you have enough turns to equal 5 mH.
Your mosfet is going to be a module that you bolt to a heat sink.
I recommend 10 each 40mm MOV's in parallel with a voltage rating 50% higher than your supply voltage. This will keep the kick-back voltage from being so high it arcs across the inductor or blows the mosfet.
The survival of this circuit depends on a precisely controlled 10 uS pulse. If not enough to charge the inductor to maximum current, I would limit the on time to 20 uS at most, or things will start to blow up.
You need a digital or analog controlled power supply that will cost maybe $2,000 USD. Shop for a re-furbished analog type to keep cost down. Your mosfet may cost over $100 USD. It needs to be rated at least 100 amps at twice the supply voltage you use, only because the on time is very short.
You could shop online for such a huge inductor but they are normally custom made. You need a digitally controlled pulse generator to provide a precise 'on' pulse for the mosfet. Maybe shop for a re-furbished model for less then $1,000 USD.
If you scale back to 20 amps both components and cost become much lower. No reason why you cannot re-scale the math to fit a 20 amp circuit, then extrapolate the results as if you had used 200 amps.
I see nothing wrong with your calculations. It is the building and implementation of something so powerful that great damage could occur if your mosfet 'on' time is just a few uS too long.
Once you get this setup working it is best to test it using a dual channel oscilloscope with high-voltage probes connected in differential mode. Oscilloscopes are Earth grounded and you do NOT want to connect its probe grounds to your test setup.


EDIT: A few more important things about your test:

A) Your iron core inductor may saturate. You can compensate for this by wrapping the iron core in thick mastic tape or kapton tape to create a space between the core and the wire. You could use a air core but it would be huge. See my first paragraph.

B) You should seal your windings with epoxy cement or they will 'jump' when you apply so much current.

C) You have no time-constant without a capacitor. I suggest you use the power supply just to charge up a capacitor of 33uF to 100uF (rated twice the expected surge voltage), then dump the charge (with the power supply off) using the mosfet module. Now you will have a time constant of 2 pi LC - the MOV clamp voltage. It should create a decaying ring wave lasting several mS. This way you protect your power supply as well.

D) I suspect you will need 1,000 to 3,000 VDC on the capacitor to push 200 amps through the windings. Use a shunt resistor and oscilloscope to check the current intensity and decay. You can put 450 VDC capacitors in series with 1 Meg bleed/balance resistors to get the capacitance you need without buying very expensive laboratory grade capacitors with that voltage rating.