First, I am here for guidance not to pontificate so please add to my post and correct any and all mistakes and misconceptions.
Awesome comprehensive reference reflecting state of the art in the late 80s: 300+ pages I haven't finished it yet:
https://apps.dtic.mil/dtic/tr/fulltext/u2/a192102.pdfOK so tons of individuals have built railguns and these railguns all have a few things in common:
1) Relatively small, high cost capacitor bank power supply
2) Terrible efficiency below 1%
3) Because of 1 and 2, really weak projectiles
The most powerful individual railguns that appear to have been built are on the order or 30kj of input energy (edit: apparently sam barros had one with 100kJ). Even 10% of that in terms of kinetic energy would be pretty impressive, on the order of a high power hunting rifle. Unfortunately from firing demonstrations it's clear that the actual projectile energy these designs deliver is on the order of 100 joules or less: somewhere between a small-bore air rifle and a .22. Man I live in Texas, surely we can do better.
In order to make an AWESOME railgun one or more of the above issues needs to be solved. First the pulse power supply:
While it's possible to find relatively large high power capacitors for salvage this leaves you at the mercy of what's available. Usually salvage cap lots are significantly limited in number. So you may be able to assemble a modest bank for relatively little money, but you probably won't be able to build a huge one. Conversely, if you want to build a big bank, you can buy as many capacitors as you want from the production market but this is extremely expensive with even a 100Kj bank costing on the order of several 10s of thousands of dollars. Maybe it's possible to find a physics lab scrapping their trashcan sized caps but this strikes me as especially impractical.
Building your own capacitors for any reasonable bank size is not an option (correct me if I'm wrong).
Building your own high energy inductor IS a realistic option and it is probably possible to create an inductor storing on the order of 1MJ energy for a few thousand dollars. I'd settle for 100kj. The material of choice would probably be aluminum.
So the inductor should probably be the choice of energy storage for amateurs who want to build a badass railgun--NOT capacitors unless you are so lucky as to come across a reasonably priced, gigantic salvage lot.
Charging the inductor is an open question. Since the charge time is on the order of 100x longer than the discharge, maybe it's possible to use a relatively small bank of high C-rate lithium polymer.
Now the second part, increasing firing efficiency.
Why could amateur railguns be so inefficient? A few guesses:
--Improper dimensions and geometry of rails and projectile
--Not taking skin effect into account, leading to much more energy wasted thru resistive heating than expected
--Pulse width too short (cap bank left to its own devices can easily dump all the energy nearly 2 orders of magnitude faster than it takes the projectile to leave the rails even with short rails). This could be tuned with an inductor in series with the cap bank (but we don't want a cap bank, we want POWER)
--Friction. Even if you have a loose-fitting projectile and rely on plasma to bridge the gap your projectile could still be intermittently spot-welding or sticking to the rails. I don't know how much loss this would be responsible for but maybe a high pressure low temperature gas could help. Totally speculative.
--Reliance on single-stage rails. It's known that adding additional lateral rails in series can increase efficiency. I don't know how important this is or even what such a design would look like in practice. I think this one is mostly irrelevant for the time being since it should be possible to achieve efficiencies higher than <1% even with a single pair of rails.
Action plan:
--Obtain solid grasp on what makes an efficient railgun
--Figure out muzzle energy level desired (let's say 5kj, on the order of a 12G shotgun slug)
--Figure out what efficiency is reasonable with all realistic optimizations
--Design inductor capable of delivering (muzzle energy / efficiency), inductor supply
--Design switching for inductor charge and discharge
--Design rails and supporting structure, projectile and electrical interconnects
--Design loading / injection system
Anyway if you read all that maybe you have something to add. Let's make amateur railguns BADASS instead of pitiful exercises in wasting money and energy.