I think a plan for building a prototype is starting to crystallise

stator coils will be placed in pairs (to balance the force acting on the piston) around the loop.  Hall effect sensors will precede each stator pair and the stators will be connected to a H bridge so that polarity can be reversed.

I foresee the density of stator coils increasing the further round the track. As the pressure increases,  more torque(?) will be needed to move the piston around. Although increasing power to the later coils my work as well.

Issues

Most of the information I'm coming across is for x pole rotating motors. this 'motor' is going to be different in a few respects.

1. Normal motors  tend to have little distance between the stator coils. Obviously a bigger gap would indicate the motor could be smaller, so you never come across ones with larger gaps. This means I don't really have a good idea what the optimum distance between stator coils might be.  My motor has the advantage that I can tune the distance between the coils but I'm no really sure whether I'll need 2, 20 or 200?

2. in a normal motor, relatively few hall effect sensors (HES) will give you a good idea of where the motor is in it's cycle. In this motor, the piston is going to be pushing against a rapidly increasing pressure all the time, not only that but at some point the exhaust valve is going to open and at that point the pressure will essentially stop increasing so we can't really predict where the piston is going to be.

The three solutions that I can think of are:

A. Add a pressure sensor at the exhaust valve. from this we can calculate how fast the piston will travel and potentially get away without any HES (although we would need them at start up?) the issue is you still need to know where the pistons are when you turn the motor on, and if anything were to go wrong, the piston/cylinder head would get out of sync and you wouldn't know about it, and there would be no way to recover the situation.

B. Use HES is pairs to calculate the current speed, this could be combined with a pressure sensor so you can work out when pressure stops increasing and work out how fast the piston is travelling and how fast it is likely to continue travelling.

C. Use one HES for each stator pair. this is sort of my preferred option but not knowing how many stators I'll need gives me pause.

3. the whole Newtons cradle thing. This video gives be some confidence that the whole newtons cradle thing will work with just magnetic force. there is some 'bounce' but relatively little. somehow I need to get it to work reliably with a cylinder head that is being held strongly enough to withstand a high pressure but then be pushed out of the way when hit by the cylinder. I have the option of  turning off the stator holding the cylinder head in place, but then there is nothing to stop the old cylinder flying off.. I could add stators in the run up to the cylinder head to slow down/speed up the approaching piston to the right speed.

Ideally the cylinder head stator would just be permanent magnets that is just not quite powerful enough to hold the cylinder head in place against the max air pressure + the piston hitting it. But I can't see it being that simple. With issues 1 and 2 above I'm not sure I'm going to be able to read and control the the speed of the income piston well enough, and I don't know how much wiggle room I'll have with that speed.