If the public believes Hollywood then i don’t think any amount of fliers are going to fix it. To give an idea of how much fuel there is, even in ITER the total amount is about 1 gram, or about 10lt of fuel in a gas state.
Contrary to popular belief there are no neutron bombs. They where proposed but never built. The idea was that the neutrons would be the primary kill mechanism. All bombs so far are optimized for yield, not neutron radiation. Even with the large neutron pulse (and subsequent activation of the surroundings), hydrogen bombs are far less dirty than pure fission weapons of the same yield.
For the Tsar bomb, which in its design configuration was a 50MT bomb. Half of that was from fast neutron induced fission of the 238U tamper/case. This was replaced with lead because of the large amounts of fallout you get with fission. The yield of the tested bomb was 25MT.