You can control the sequence by having the rail separated into different sections, and use the armature to connect each area as it spreads. The other option is to use a timing circuit.
You don't really need a sequence; railguns just require a steady current. That can be accomplished by putting an inductor in series with the capacitors.
To stop the projectiles, I'll probably use a steel backplate put up against a wall. The lab I work in is below ground, so if it penetrates the wall it'll just hit dirt.
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