How big do a fusion reactor and bank of capacitors following it up have to be to power a mass driver into space?
(Hi, please be kind - first poster. Also, didn't know if it'd be allowed to put hard-science on something like this, so going with reality-check for now, but formulae will definitely be appreciated!)
I'm 52 years-old X AE A-XII <PERSON>, and I'm trying to become humanity's first home world builder away from home. I've mostly been pleased with the space transport imperium I inherited from my father, the late <PERSON>, which is providing the basic infrastructure for all of us to finally make Mars into the planet that Earth can't be anymore.
Unfortunately, around the year 2040 many of the resources required for launching my rockets into space have begun to run dry on Earth. It was not an immediate problem as I was able to replace most of them with what I found on the Moon and various asteroids, no thanks to the Western Alliance government, who tried to prevent me for too long from using those resources as required. 912
They have been dealt with now, but I've also been looking for a better way--burning chemicals does seem like an awfully dated thing to be doing.
Recently, after one too many times of "only 20 more years", the first experimental fusion reactor to have achieved a solid sustained net energy output of around 150MW, ITER-III, has been acquired by one of my companies, and I'm now planning on having those people build me a bigger one in order to power a mass driver, which I'll call the Space Slide. Texas seems as good as place as any for such a venture and I have signed a contract to develop the area around Guadalupe Peak and the Salt Basin Dunes east of it, including the outskirts of El Paso, for the purpose.
The first Space Slide is intended to be used to launch the quaint, but still reliable Dragon II capsule, which, at maximum payload capacity, has a mass of twice (20402kg) as much as the original Dragon.
Unfortunately, because I've spent most of my life managing companies, I have no clue of either mathematics and physics and so would like to ask the following questions:
* there's around 140km of distance between El Paso and Guadalupe Peak, which rises to 2667m above sea level. Is this long enough² and tall enough for a mass driver capable of launching well-paying (but otherwise ordinary) humans into space, or is it still too short to keep the g-forces down¹?
* (a) how good is Wikipedia's info of 40MJ/kg (~816GJ for the Dragon II) to get to LEO?
* (b) how much more than that would you need to get to the Moon (given suitable alignment of Earth and Moon and assuming the capsule's thrusters are good enough to compensate sub-optimal alignment)?
... and finally ...
* how big does the fusion reactor have to be³ for (a) and/or (b)?
* assuming it's not feasible to feed directly from the reactor to the mass driver, how big would each capacitor in a chain of super capacitors⁴ along the length of the mass driver have to be and how many of them will be required?
¹: Let's say, 5g max? Does that make sense?
²: Assuming 11.2km/s escape velocity
³: How big, as in, what sustained and/or maximum power output in MW does it have to be capable of, not as in the required footprint (which is probably unknowable from a 2021 perspective, aside from an educated extrapolation of something like Wendelstein 7-X...)
⁴: And also: how close are we in 2021 to being able to build such super capacitors? 199