Confusion is not a good place to be. You don't know what to do next. So, you research the problem. With some luck, you may find some answers and further progress can be made. Or you may hit an impenetrable wall and you are stopped cold.
The laser idea seemed promising, but there are things about it I don't like. Too much conversion of one type of energy to another.
Curved mirrors have been off and on. At times, I like them. At other times, I hate them.
The "power tower" idea seemed good too, but the inefficiency of the thing nixed that idea.
The thought occurred to me to go back to the original inspiration. The temperature at the focal point of a 2 meter mirror is 3500 degrees C. This is much hotter than the original goal of 2700 degrees. What is the problem then? You have to successfully transfer that temperature to a gas which can be expelled out of a rocket nozzle for thrust. If it can be done at 2700 degrees C, it will yield an ISP comparable to a nuclear thermal rocket. That would be an ISP of 850 or so. Quite an improvement over chemical rockets.
How much thrust from a 2 meter apparatus? No more than what is delivered to it as energy. Between 2 or 3 kilowatts is the maximum. How much thrust from a rocket based upon this--- I don't know. The calculations are unknown to me, as are many other things. For example, how to design a rocket is unknown to me. How to design a heat exchanger is unknown to me. How to get the energy to the heat exchanger is unknown to me. And so on and so forth. There are many questions and too few answers.
Now these people in Uzbekistan have a problem with heat. The thing gets too hot and has to be cooled down. For what they are trying to do, they probably can't use liquid hydrogen. So, they are using distilled water.
Now, what if we didn't want to use a crystal to produce a laser. What if we just wanted to heat tungsten and then cool it down through a heat exchange? We are left with a lot of hot hydrogen, which would be useless to this thing on the ground.
But what if we built this in space and did the same thing? The hot hydrogen could be used for thrust in a rocket. Then we could go places in the solar neighborhood. That would be useful. But then you've got a new problem. How to build something this big in space?
As Homer Simpson would say, "d'oh"!
In order to make something big in space, you will need to commit to building big stuff in space. With a commitment, it becomes possible. Without one, you are just whistling Dixie.
This reminds me of another series that I wrote, perhaps the first one I wrote, which was about recycling the et, or External Tank of the Shuttle.
Since the SLS is just an updated version of the Shuttle, why not recycle that tank for each liftoff? Now, there was a study during the Shuttle Era which proposed to do just that. That is, melt down the metals in the external tank and reuse them. Reuse them for what? Why, to make very large mirrors for concentrating solar light so as to produce thrust for a high ISP rocket.
You could melt down the aluminum and spray it on a curved surface- also produced by melted aluminum- in order to make mirrors. Or very large mirrors. You could fabricate support beams to place them on and so forth. Just reuse the metal and make useful things as opposed to dropping the used up tanks into the ocean. What a waste.
Cut away view of the External Tank