Power Supply for two 50V/12.5A Solenoids
A transformer is probably the simplest option. It doesn't need to be exactly "110 in 50 out". Transformers are ratiometric, so you just need about 2:1. I would get a 110 to 230v transformer and run it in reverse. 110 * (110/230) = 52.6v. I saw some cheap, high power transformers that fit the bill on ebay.

You almost definetly can't hook up 4 atx power supplies in series, because they're probably grounded.

You may be able to use a smaller power supply, plus a cap bank. You're correct the supply will probably trip almost instantly if you overdraw it, even with a bunch of caps. The reason is that for the caps to provide power, the voltage has to drop. If the supply is any good, it's going to fight that drop and basically take the whole load itself.

The way to counteract this is to place a beefy current limiting resistor between the power supply and the caps.







simulate this circuit &ndash; Schematic created using CircuitLab

Calculating the exact resistor is actually kind of tricky. But you can just buy a handful of 1 ohm power resistors and figure it out by trial and error. You could also play around with a circuit simulation, but you'll need to know the coils inductance. I think if you click on this schematic it'll bring up circuit labs, which has a simulation feature.