Somehow I had the impression that in the 1950s, the government and the press (at the government's behest) were much more secretive about how the H-bomb would work, but I found the Popular Science article surprisingly informative. We say thermonuclear weapon rather than H-bomb these days, but I didn't see anything in the article that seemed inaccurate compared to what's known publicly today.
The H-bomb design described in that article is that of the "Classical Super." It shows a fission bomb embedded in a larger mass of fusion fuel. The A-bomb is supposed to act as a spark to ignite the fusion fuel, which then burns to completion from its own fusion energy. This is the same sort of schematic explanation of H-bombs that I saw in popular science books and encyclopedias as a child in the 1980s.
The Classical Super design does not work. The Richard Rhodes book Dark Sun describes it such:
George Gamow found a way to dramatize how unpromising Teller’s Super had proven to be. John McPhee reports the story as Los Alamos physicist Theodore Taylor remembered it. "One day, at a meeting of people who were working on the problem of the fusion bomb . . . Gamow placed a ball of cotton next to a piece of wood. He soaked the cotton with lighter fuel. He struck a match and ignited the cotton. It flashed and burned, a little fireball. The flame failed completely to ignite the wood, which looked just as it had before—unscorched, unaffected. Gamow passed it around. It was petrified wood. He said, ‘That is where we are just now in the development of the hydrogen bomb.’"
The secret of a working H-bomb, not published in unclassified form until 1979 [1], is the Teller-Ulam design [2] using "radiation implosion." The atomic bomb is not placed to heat the fusion fuel but to enormously compress it. The A-bomb is kept separate from the fusion fuel but contained within a shared space. For a detailed unclassified description of how this works, see section 4.4 of the Nuclear Weapons FAQ, "Elements of Thermonuclear Weapon Design":
https://nuclearweaponarchive.org/Nwfaq/Nfaq4-4.html
But that 1950 Popular Science article was still accurate for the date, since the Teller-Ulam design wasn't conceived until 1951.
[1] And that after the government tried to suppress publication: https://en.wikipedia.org/wiki/United_States_v._Progressive,_....
[2] Independently discovered in the USSR as Sakharov's Third Idea: https://en.wikipedia.org/wiki/Andrei_Sakharov
