Re: I think _I_ can explain it (and it's not that hard)
Well, I actually CAN explain it, and its not that hard. But it MAY require that you part with some treasured, but unsubstantiated, notions about electromagnetic phenomena, or anyway at least ONE widely-held belief. But before I tell you what that belief is, let me mention that several of the most revered physicists of all time did not hold that belief. The list includes Michael Faraday and James Clerk Maxwell, in part because they did their famous work before quantum theory came into existence. There are also a few more recent physicists who also do not cling to the aforementiond belief, but I don't want to name names because I may misremember them.
The belief I am talking about is that all EM energy is ambiguous about whether it is in the form of waves or particles, namely photons. Nope, sorry, not true. Radio waves, including microwaves, generally DO NOT involve photons at radio frequencies. WBZ, in Boston, or WBT, in Charlotte, NC, generate purely WAVE signals, at 1030 KHz and 1100 KHz, respectively. No photons need apply, though all are welcome if they find an opportunity to absorb the requisite amount of energy (E=hf is the familiar formula for the energy of a single photon at frequency f Hz, replacing the usual "nu" of physics notation, since "f" is more familiar to engineers, but more importantly available on my keyboard and useable in ASCII text-only mode). In which case the same amount of energy, as a minimum, would have to be lost by some means from the wave.
So, the microwave generator used by those experimenting with these not-so-surprising EM propulsion systems merrily draws energy from some very conventional source, runs it through some ingenious device which produces a microwave signal - electric current oscillating back and forth along a wire - and couples this oscillating current to a conductive structure designed to launch analog waves, satisfying Maxwell''s equations, into space. These waves are WELL-KNOWN to carry momentum, and the exact amount of it can be calculated correctly (albeit a bit mystically) by assuming that the ENERGY in the EM waves REALLY IS EQUIVALENT to an amount of mass given by the most famous of Einstein's equations, at least to the general public, namely the familiar "E=mc^2", the ^2 being the standard ASCII alphabet representation of "squared", or raised to the second power.
Now, one of the main hindrances to more rapid advance in physics, IMO, is the rather "comprehension-free" form that a lot of the modern theory takes, this EM propulsion technology being a rather good example. So, folks, including some real physicists with real PhDs in that subject, I'm sorry to have to say, get your mind around the fact that EM waves DO carry momentum. This fact is NOT exotic, and in fact is dutifully explained in even Undergraduate physics texts such as the extremely highly respected one by Griffiths, used in the Junior year (3rd-year Undergraduate) Physics curriculum at many American schools. So now Conservation of Momentum indeed says that a thrust will be developed, in accordance with Newton's laws, by launching the microwaves out the back, either directly from the antenna or by bouncing waves off the surrounding structure and out through the opening at the back. The thrust should be accurately predicted by Newton's famous formula, most usefully put in the relativistically-correct form F=dp/dt, where p is the momentum, and dp/dt refers to the rate at which it is being blasted out in the backward direction, but the reaction force -- the thrust -- is of course going to push in the opposite direction -- you know, "equal and opposite"? This is nothing new - same as throwing rocks, or chemical molecules, out the back of a rocket engine, except that the momentum does not involve actual mass, but EM wave energy per unit time, converted to mass by dividing energy by the speed of light squared. Ask any science-oriented high-school student if you have trouble with the algebra! :^). As for optimization, it will be mostly a matter of finding better and better ways to narrow the beam width, as only the energy component in the backward direction contributes to propulsion - the lateral components of the beam of course cancel out, at best, and any actual forward components would SUBTRACT from the propulsive effect.
NOW do you understand what is going on? Anyway, all but the "mysterious" part about exactly how the wave energy is able to make the leap, physically, from obviously real energy that can burn things, light flashbulbs, and even kill people in the beam, if it's zillions of times more intense than the beams from these engines, to acting as if it had real mass instead of just "equivalent" mass in terms of an innocent little equation that came out of Einstein's work?
As I said above, coming to actual COMPREHENSION, in a practical sense, of such matters is what the next generation of physicists need to master, to bring us the next wave of advances in physics!