I read this book as a kid: The Millennial Project: Colonize
the Galaxy in 8 Easy Steps
. It's a great book for inspiration, and as a general strategy for colonizing the solar system the overall approach
the author suggests is much more thought out than anything I've seen elsewhere.
One thing he brings up, though, is basically what your picture suggests, if I'm reading it right:
at each major space travel "destination", you have what is essentially a giant double-barreled shotgun, except with an "in" and an "out barrel.
Outgoing spacecraft are propelled out of the "out" barrel by using a pulsed electromagnet -- ie, the "out barrel" is a giant rail gun -- and the
vehicle is sent off to whereever its going.
the "in" barrel does the same thing in reverse: one of the nifty things about electromagnetism is that a moving magnetic field induces electrical
current in wire (which is how generators work), and thus if you have a long enough incoming barrel you can drain off the incoming vessel's kinetic
energy by way of the induced current it makes.
since there's not much to slow you down in space -- not a lot of gas for friction, not too many strong gravity fields in deep space -- a vessel will
retain most of its kinetic energy over the course of its journey, meaning that with reasonably efficient power reclamation facilities in the
"incoming vessels" you could probably get back 80% or more of the energy originally given to the vessel you're slowing down. what this means is
that on travels between destinations that have these stations, the total network is pretty energy efficient -- most of the energy put into going one
way can be reused to send the ship back the other way, or to send another ship back home -- and for conventional propulsion (ie, chemical-based or
nuclear-based) there's no equivalent way to reclaim your kinetic energy on landing.
So, it's a very good idea, mainly because of the energy efficiency of a network of such propulsion devices. There are some engineering problems:
a) you can't really use a permanent magnet for your initial propulsion, because the ones that exist aren't sufficiently powerful; you need
electromagnets that you can "pulse" power into, but unfortunately how to deliver large amounts of electrical current in very short amounts of time
is a very difficult problem. there's been lots of research into it -- mainly for projects like railguns, which have both military and industrial
applications -- but my understanding is that we're still a long ways off from being able to pulse enough power for space travel purposes, even if we
assume we're starting from space.
b) this approach is really only that useful for trips to places you've already been; once the technology is there an electromagnetic push is still a
better way to get going in a particular direction, but you'll still need to build in some kind of other propulsion devices to maneuver once you get
there. without those, you're just riding a big bullet...
c) likewise, you'd still need some kind of propulsion onboard for course adjustments or unforeseen difficulties
d) lastly, EMP pulses can totally ruin electronic and computer equipment, even if the stuff isn't turned on (ie, it's not like in the matrix where
you just turn off the ship and you're ok). so, if you got this approach working you'd have to shield all your onboard electronics and computer
systems, and while not overly difficult it's a big hassle and adds weight and bulk to your ship.
all of these are just obstacles, and not reasons why EMP propulsion like you're suggesting can't work. if you'd like some really outside-the-box
ideas on space travel and colonization, take a look at that book; it's very inspirational, even if a bit dated (and even though it doesn't take into
account, say, the idea of a space elevator becoming feasible, which is looking more and more likely in our lifetimes if the funding and motivation are
there for it).