IIRC, the first model ate mosfets for breakfast because the photo resistor is way too slow going from illuminated to dark. That leaves the mosfet in a fairly high resistance state for an extended amount of time during which it dissipates a lot of power. You should add some kind of Schmitt trigger inverter that buffers the resistive divider and gives you a clean narrow edge to drive the mosfet gate. A 74HC14 together with a 7805 voltage regulator should give you enough output voltage to drive the mosfet. These chips cost less than a single replacement mosfet and you can drive 6 coils with them.
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I'm guessing you watched the first video, the one with a single coil, which, as you said, doesn't specify those details. However, on a later video ( https://www.youtube.com/watch?v=uNbL3tRZeMQ ), where he makes some improvements to the whole circuit, there are some details mentioned in the description, such as
Input voltage: 24V
Number of coils: 4
Wire Gauge: 24AWG
Coil Current: 13A
Coil ID: 1.1"
Coil OD: 1.4"
Coil Length: 0.5"
Coil turns: 200
The final outer diameter is ~2" due to the addition of steel wire to create a magnetic flux guide or "shell".
FET Type: IRLZ44N
On time: ~8 ms at max. speed
Energy input per pulse: 2.6J
Ball mass: 65 grams
Ball kinetic energy: ~0.52J
I hadn't watched the second video yet. Thank you.