This is getting quite off-topic PropulsionDisk. Maybe we should follow the discussion in the Science questions thread since how an electric circuit works is not the main issue to get to Proxima Centauri. Anyways I respond here one last time (let's migrate if you want to keep it going ok?).

But now that brings up other questions, how do you make electrons? is it with a "external electric source" and if so what is that?

How do you make electrons? Well first you have to create the universe. No, really. Electrons aren't created, they are fundamental particles that have been here since the birth of matter.

In the case of a circuit you don't bring electrons from an outside source (at least in principle), you just use the electrons embeded in the copper wire. There is no external electric source in terms if by that you mean an electron source. A typical circuit has external energy inputs like the one provided by the chemical reactions inside the battery to generate an electromotive force and other elements so that voltage is mantained. Electrons were on the wire even before the circuit itself was assembled, they were in the copper even before they copper was mined and extracted from the Earth's crust.

The important thing in electromechanics is how to get the voltage, the energy, the current, but not the electrons. You are looking at electric circuits as if they were a particle accelerator but they are not. You don't have a reservoir of electrons an shoot them through the wire, you have electrons in the wire, from start to end, and you play with potential energy to make them flow. You can see that in the videos I posted before (I know they are slow but this is well explained in my opinion).

The water flow from a mountain analogy has some limitations, though.

This is also a very important point PropulsionDisk. Analogies are just that. They only get parts of the behaviour of a system and translate them to more common everyday systems so that we can use them as comprehension tools, but they are always limited. There are a lot of mechanical analogues for electricity and each of those has regions where they are usefull an regions where they become a source of wrong assumptions. If I told you that a snowman is an analogy of a real human being, then the anology could work for a certain field inside anatomy but it can't work as a medical model for example; a snowman has a "nose", has lateral symetry, has human size, has a head, a torso etc... so we could gain confidence with the analogy to the point we confuse it with the actual human and ask if human beings die slowly as the Sun evaporates them. No humans are not like that but it's true that humans have a head in analogy to the snowman. That is an abuse of the analogy and there you have a person who has forgotten that this is just an analogy and not the actual mathematical model that describes human beings.

The hydraulic analogy article in wikipedia has a section where they map the limitations of the analogy precisely. I've tried to use the analogy were it makes sense and there is a reciprocal for a concept in electricity, but keep that in mind PropulsionDisk, electricity has nothing to do with rivers in reality and your last question invites me to think you just abused the analogy. You don't need electrons coming from outside as water in a river because in electricity the electrons are there in the wire from beggining to end. Also you don't need the electrons to "flow from the top of the mountain" to the bottom to make the current complete the entire circuit end therefore make it work. In reality electrons move at millimeters per hour speeds (extremely slow if you take into accountthat electricity is a close-to speed of light influence) but they are able to light a bulb a thousand kilometers away just in a fraction of a second, because the electric signal is carried by the electric field under the voltage applied (different electrons located across the entire wire respond to that field) and it is not carried by the electrons that are in one end of the wire moving to the other end (in fact electrons flow in the opposite direction of current making it weirder). It's strange I know. But that's how it works. No water analogy will ever describe in full detail and coherence the real behaviour of electricity and that's the reason electricity is an entirely separate phenomena in nature and not the same as a "fluid substance that behaves weird", which was an actual hypothesis back in the good old days and is now regarded as pseudoscience.

Maybe that's the big filter. (Fermi paradox.)

we could even imagine onboard antimatter plant instead of a storage.

Stellarator:

Maybe that's the big filter. (Fermi paradox.)

I find that unlikely, since a civilization advanced enough to make quantities of antimatter sufficient to deal any real damage to their planet would also have sophisticated space-travel capabilities and the required magnetic storage facilities, logically making the antimatter in planetary-orbit or on a moon.  This is just a question of logistics - antimatter is VERY hard to make. Don't be fooled by the fact that we've made ~400 antihydrogen atoms, along with several other antiparticles. These experiments cost astounding amounts of energy for a few nanograms of the stuff. With current technology today (and into the predictable future), antimatter will not reach production levels wherein it can pose as a menace to civilization. By the time it does, assuming we survive until then, humanity (and by following the Law of Mediocrity, most other alien civilizations at our level as well) should be adequately equipped to contain it.

SpaceEngineer:Pure antimatter is bad fuel for starship. You want to have 1 petawatt of thrust power on engine with 75% efficiency? Say hello to 500 gigawatts of deadly gamma-ray radiation, which will be emitted from the reaction zone. Annihilation produces 2/3 of charged pions, which can be used to produce thrust in a magnetic nozzle, while 1/3 of neutral pions cannot be deflected and will beam to all directions, including ship itself. These neutral pions decays to gamma quants shortly, so you must have extremely massive gamma ray protection, and put engines very far away from your payload.

More here.

The better way we can use antimatter in ship propulsion is by using antiproton-induced nuclear fusion. This is "easy" way to achieve fusion temperatures in the fuel pellet. Also, amounts of antimatter needed to be stored onboard the ship is some nanograms instead of 40% of ship's mass in case of a pure antimatter rocket. This is much more easy technologically, we could even imagine onboard antimatter plant instead of a storage.