> IMHO I think "Star Wars" was actually more for defense from an invasion than to knock down missiles. I doubt it would have worked to do either goal; it's only now that we are developing lasers powerful enough to do anything to a distant flying object.
I worked on the Strategic Defense Initiative (the proper name for the project) in the 1980's. It was most certainly for knocking down missiles, all the math depended on it. As far as working or not, very few people understand the concept of "layered defense". SDI had 7 layers: two Boost Phase intercepts, three Midcourse intercepts, and High and Low terminal intercepts. Each layer only has to deal with what the previous layer missed. Assume, because the actual numbers were classified and I don't remember them after 30 years, that each layer is 60% effective, meaning 40% of warheads get through to the next layer. With 7 layers, only one in 610 warheads hits their targets. That kind of number is "survivable". Japan survived two warheads, and the US could survive about 15 or 20, due to being a larger country. This breaks the "Mutually Assured Destruction" concept, because the US would have plenty of undamaged assets to shoot back with.
But you don't need a fully functioning missile defense to apply leverage to the Russians. If you have only two functioning layers, and they are only 40% effective each, only 36% of Russian warheads get through. They have to build 2.78 times as many warheads to destroy their priority target list. The more functioning layers, and the higher their effectiveness, the worse their targeting problem gets, rapidly. The Russians may be deficient in some ways, but they had plenty of good mathematicians. They could see the threat of a layered defense, and they could not afford to build enough missiles to counter it. They could also not build their own SDI system, because Western technology was generally more advanced. So coming to the negotiating table to reduce missile counts was the only viable option, which is exactly what they did in 1991. In that sense, the SDI program helped win the Cold War.
Whether Reagan himself had a technical understanding of the project was irrelevant. That was between DARPA, Congress, and the defense contractors. As a former actor who did westerns, his job was making speeches other people wrote, and looking tough to the Russians. He was a figurehead for the nation. Tons of smart people did the real work.
Getting back to your lasers, we had two kinds as *advanced options* in SDI, airborne and space-based. Airborne were a boost phase system, designed to shoot at ICBMs while the rocket was still firing. That makes them an easy target, rockets have huge thermal signatures for targeting. But also they are fragile. Heat the nozzle of a rocket a few hundred degrees while operating, and it can easily fail, same for shock heating part of the fuel tanks. You don't have to melt them, just cause a gas explosion as the fuel boils, it does the rest. Space-based lasers were upper boost phase or early midcourse. They could get a clearer shot when the rocket was in the upper atmosphere, or starting on the ballistic trajectory. Physically the rocket was approaching the same altitude as the laser, so the distance was smaller. Both involved megawatt class lasers based on chemical combustion energy.
But remember, these were not the baseline, they were advanced options. And the US was making credible progress in laser technology. So it was not a matter of having them ready to use. It was a matter of the Russians believing the nation that beat them to the Moon could develop high powered laser weapons if they put their minds to it. After the Strategic Arms treaties were signed, the push to develop SDI technologies ended, so they have piddled along for the last few decades, and battlefield lasers and railguns are now entering field use. There was no rush because there was no enemy threatening enough.