Scramjet launchers (and air breathing launchers in general) have been looked at extensively, for decades. They don't make any sense. The math just doesn't work. Here's an insightful post from the Old Usenet that illustrates the difficulty:
https://web.archive.org/web/20220131115058/http://www.island...
When reading that, remember that LOX is 20x the density of LH2 (or 17x the density of "slush hydrogen").
"Rockets, not air-breathing planes, will be tomorrow's spaceships"
(New Scientist, 2009)
https://web.archive.org/web/20101017031109/https://www.newsc...