Beamed Energy Propulsion or, in brief, BEP, is a part of rocket science. However, you don't need to be a rocket scientist to get its idea, it is very simple, and I will explain it to you in the next several paragraphs.
The essence of rocket science is the principle of reactive motion. Cars on the highway are pushing pavement and move against it, swimmer pushes with his limbs (or fins) the water, and swims. Space has nothing to push from, because space is empty. So rocket pushes off its own exhaust formed by burning hydrogen with oxygen. Of course, since the space is a vacuum, everything (fuel, burner, tanks, cryogenics, combustion chamber) must be carried onboard.
So, the rockets are the only manmade vehicles that push away from their own exhaust and move that way. Rockets have to carry everything needed for motion in space onboard, is a heavy burden and it brings a great downside: price of cargo gets enormously high. If we can only separate the source of energy from a rocket, we will be rewarded with gigantic increase in efficiency!
Energy can be delivered to the rocket from remote external source using light or, say, laser, x-ray, microwave high-power beams. With its mirrors, rocket will collect and focus that beams on its "fuel". Any solid matter can be a fuel. When high-power beam of photons is focused on a solid material, the material evaporates and ionizes instantaneously. The energy density in focused high-power beam exceeds hundreds to millions times one in the heat of burning hydrogen. Thus, beam-driven rocket will remain a rocket, it will be pushing from its own exhaust, but the energy of this exhaust is much higher, and the rocket itself is much lighter, comparing to hydrogen burners.
Driven by a high-power photon beam rocket will be composed of very light focusing mirrors, relatively small (energy efficient) solid propellant and, voila: the rest will be payload! Forget heavy liquefied gases (oxygen and hydrogen), cryogenics, fuel tanks and lines, combustion chambers, etc.: Payload, Propellant and Photons, Period! Arthur Kantrowitz, the founding father of laser propulsion, called it 4P Rule.
So, what is efficiency gain of beam-driven rocket vs. hydrogen burning rocket? Hydrogen burners cost us $10,000 per pound of a payload delivered to low earth orbit. Scientifically-proven calculations have shown that the price of space delivery per pound drops to minute $100 for laser-driven rockets: a hundredfold, revolutionary change in cost!
Laser propulsion, i.e. use of high-power lasers for terrestrial space launches and in-space transportation is the most developed today branch of BEP. Various types of laser propulsion have been demonstrated in field and by many research groups in lab. Microwave propulsion is another relatively well explored part of BEP. Much less is known about potential of x-rays and particle beams for BEP. Overall, beamed-energy propulsion remains a field of future technology, where a lot of interesting development will happen in the next several decades. Still, it is quite clear, that in the future a great part of space transportation will be driven by high-power photonic beams.
