I am currently building my first coilgun. I already have MOSFETs rated at 100V, and 50V 470uF capacitors I can wire in series to obtain 100V. I know this voltage will not result in a very high velocity projectile. What I am wondering is if I can switch the charging circuit between multiple capacitors, charging them separately, and then discharge them in series which would result in a higher total voltage. By doing this I would only need to buy one high-voltage switching element. Is this feasible, or am I way off here? What would such a circuit look like?
If you were programming, your way of thinking would be called premature optimisation. And that always tends to end badly.
You need to reconfigure the caps to charge them?
This is almost always a bad idea. It's far better to configure the caps permanently at the voltage you want to use them at, and then charge them at that voltage. It saves excess series inductance and resistance, and switch components, and nasty expensive mistakes.
If you don't have a charger for the requisite voltage, it is really worth buying one, or learning how to build one of the right voltage.
You need more than 100V for a high velocity projectile?
It depends on the coil inductance. If you have already built the coils, then yes, maybe. If you haven't built the coils yet, then you could change the coil design before you build them, to reduce the inductance to use the lower voltage.
Balancing. When you put caps in series, you must balance them. Initially, after a fast charge, their voltages are determined solely by the capacity ratios. If you leave them charged, then eventually leakage current will redistribute the charge and leave the voltages solely determined by the leakage currents.
Leakage current - Use a resistor of a low enough value across each capacitor to swamp the varying leakage current between them, and will also provide a fixed default discharge path so they will be safe some time after switching off. Typical leakage currents are unspecified (max currents usually are), so may take wildly different values and vary with time.
Capacity - Check their values are more or less equal in the series string. Electrolytics are notorious for poor tolerances. If you have (let's say) a +20% and -10% tolerance in series, that's 560uF in series with 423uF. When they charge from the same current, the voltage will split in that ratio (OK, in the inverse of that ratio), so you will not be able to charge the string to the full expected voltage without overvolting the smaller capacitors. Note, this is not an argument for charging in parallel, then switching to series, as the lower capacity caps will then be vulnerable to premature reverse voltage on discharge. You can match up capacitors without actually measuring C if you want to by putting several in series, charge the string to some reasonable low voltage, then quickly measure the voltage on each with a DMM.