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We have a definition problem to handle here first: any bomb that gets its energy from the atomic nucleus (regardless of method) can be referred to as either an atomic bomb or a nuclear bomb.

There are two different processes by which the bomb can extract this energy:

  1. Fission of large unstable nuclei (e.g. Uranium-233, Uranium-235, Plutonium-239) into smaller nuclei.
  2. Fusion of small nuclei (e.g. Deuterium, Tritium) into larger nuclei (e.g. Helium). As Fusion can only happen at very high temperatures (i.e., 10,000,000K) it is often referred to as Thermonuclear Fusion.

Fission explosives are limited in yield by the amount of fuel that can be placed in the core of the device without risking criticality before it is desired to have the device detonate (if this happens the device will most likely just melt and kill anyone nearby). The theoretical highest yield of a pure Fission explosive is roughly 1 MTon, the highest yield pure Fission bomb tested was a US MK-18 airdropped as the Ivy King shot in 1952, with a yield of about 500 KTons. The core of the MK-18 was a hollow sphere containing FOUR CRITICAL MASSES of Oralloy (93.5% enriched Uranium-235). To prevent premature criticality the hollow of that sphere was filled with a boron/aluminum chain to absorb neutrons, that was only removed minutes before release from the bomber (this chain could NOT be put back in to safe the bomb).

Fusion explosives operate on a "Staged" principle: the Primary or 1st stage is a Fission explosive, which emits X-Rays used to compress and heat the Secondary or 2nd stage (the actual Fusion explosive). There is no criticality issue with Fusion, you can make the Secondary almost as big as you want with as much fuel as you want. If that isn't enough for the yield you want, additional Fusion stages can be added that are successively triggered by X-Rays from the previous stage compressing and heating the new stage. There is no theoretical limit on number of stages, and the only practical limit is what can fit in and be carried by the delivery vehicle. The highest yield Fusion bomb tested was the USSR AN602 airdropped as the Tzar Bomba (King of bombs) in 1961, with a yield of about 50 MTons. It was a 3 stage device, capable of a yield of 100 MTons if they had wanted to go all the way.

However, we have a complicating factor, almost no modern nuclear explosive is pure Fission or pure Fusion. It is often much cheaper, smaller, and lighter to build for example a miniaturized Fusion explosive than a pure Fission explosive of the same yield. So, many Fusion (aka Thermonuclear) bombs actually have far lower yield and extent of damage than some Fission bombs.