The 100 megaton version of Tsar Bomba was only a design. The biggest one tested was 50 megatons, because anything more powerful would have been too large and/or too heavy to carry, and the pilots would not have had enough time to get to a safe distance before detonation.
"The bomb, weighing 27 tonnes, was so large (8 metres (26 ft) long by 2 metres (6.6 ft) in diameter) that the Tu-95V had to have its bomb bay doors and fuselage fuel tanks removed. The bomb was attached to an 800 kilogram parachute, which gave the release and observer planes time to fly about 45 kilometres (28 mi) away from ground zero. The fireball reached nearly as high as the altitude of the release plane and was seen almost 1,000 kilometres (620 mi) from ground zero. The subsequent mushroom cloud was about 64 kilometres (40 mi) high (nearly eight times the height of Mount Everest). The base of the cloud was 40 kilometres (25 mi) wide. All buildings in the village of Severny (both wooden and brick), located 55 kilometres (34 mi) from ground zero within the Sukhoy Nos test range, were completely destroyed."
The Tsar Bomba was a 100 MT bomb, period. It was capable of being used in 50 MT configurations but there was absolutely, positively zero chance that the 100 MT configuration would not work. Additionally, the 100 MT version would not have been a significantly different weight or size.
The reason for the 50 MT / 100 MT difference is that such weapons use a mix of fission and fusion reactions. In a thermonuclear weapon you can use natural Uranium (U-238) as a jacket around the fusion fuel capsule. While U-238 doesn't normally participate in a fission chain reaction it will fission when under high neutron flux and as it turns out fusion bombs generate enormous amounts of neutrons. Thus typical thermonuclear weapons leverage the fusion reactions to drive fission reactions and boost yield enormously, resulting in most of the energy from a "thermonuclear" weapon ultimately coming from fission reactions.
The downside of this is that fission reactions are very dirty. And in the case of the Tsar Bomba design that meant that testing the design at a full 100 MT yield would result in 50 MT worth of nuclear fission fallout being spread across the Soviet Union (and ultimately the world of course). Which is rather quite a lot of fallout. By replacing the jackets around the 3rd stage fusion fuel capsules with different materials that do not undergo fission the result is that the fusion reactions still proceed, and the bomb still releases 50 MT of energy, but very little energy comes from fission (the primary, parts of the secondary and the spark plugs in the tertiary stages), massively reducing fallout.
The part about the pilots not having enough time to get to a safe distance from a 100 MT explosion is true, but aside from that had the Soviets wanted to they could have done a 100 MT test of Tsar Bomba quite readily.
Thanks for the correction, and the explanation. I recalled reading the following in the Wikipedia article, but forgot about it as I was writing the comment, while trying to juggle several other things.
"The initial three-stage design was capable of yielding the power of approximately 100 Mt, but would have caused too much radioactive fallout. To limit fallout, the third stage and possibly the second stage had a lead tamper instead of a uranium-238 fusion tamper (which greatly amplifies the reaction by fissioning uranium atoms with fast neutrons from the fusion reaction). This eliminated fast fission by the fusion-stage neutrons, so that approximately 97% of the total energy resulted from fusion alone (as such, it was one of the "cleanest" nuclear bombs ever created, generating a very low amount of fallout relative to its yield). There was a strong incentive for this modification since most of the fallout from a test of the bomb would have ended up on populated Soviet territory."
Also, if you have the time, I'd like your opinion on what I said about atmospheric focusing.
Atmospheric focusing is a pretty inefficient process, on top of the existing inefficiencies of massive nuclear weapons it's probably not worthwhile to use as a weapon. It's a lot easier to send conventional bombs or bullets to Finland if you want to break windows there than to use multi-megaton bombs thousands of miles away.
The main reason you build big bombs is (aside from the arms race / show boating aspect) to destroy important targets with inaccurate delivery systems. The other reason to build big bombs is to intentionally create fallout, which could be used in a "doomsday" weapon, possibly as a MAD deterrent. If you exploded a 1,000 MT nuke on a containership in international waters off the coast of Europe or North America and you took advantage of the prevailing winds you could do devastating damage to the population, agriculture, etc.
Just to add a little on to what you wrote, seems like there's also a part where anything much over 50 MT just blows the rest of the energy out into space, so there seems to be a cap on how big one can be?
Big bombs are extremely inefficient at directing damage at targets. Their main benefit is that they don't have to be aimed accurately. If you lob a 10 MT bomb at a capital city, metropolis, or military base and you miss by a mile you will still almost certainly destroy it.
The advent of accurately targeted MIRVed weapons makes big bombs obsolete. Instead of lobbing one 10 MT bomb near a target you attack a lot of smaller targets with smaller bombs.
I'm not an expert here, but my opinion is that there is no limit on the megatons, or if there is, it's substantially higher than 50. The reason I believe this comes partly from one sentence in the Wikipedia article: "Atmospheric focusing caused blast damage at even greater distances, breaking windows in Norway and Finland." That focusing reminds me of the practice of shaping conventional explosives. The focusing from the Tsar Bomba test was accidental, meaning that they did not design it into the bomb, but if you were to, for example, design a nuclear explosion to work in conjunction with techniques which allow for precise, large-scale control of weather, you could effectively create a nuclear shaped charge which would focus the explosion downwards or outwards, thereby allowing you to increase the expected yield, as delivered to the target, whereby dissipation into space would not be a real concern. This is just off the top of my head, and I'm guessing that no one's tried it, mostly either due to lack of need, or lack of ability to do grand nuclear experiments.
a little bit farther is something much more disturbing, at least for me:
"The device was trillions of times more powerful per unit volume in comparison to the material in the sun's fusion core (about 25% of the sun's radius) and it would take about 10 million years for an equivalent volume of the sun's core to produce the same amount of energy as came from within the bomb's casing."
It's a confusing metric because stellar fusion is actually extremely slow. The power density of the sun's core is about 0.3 watts/liter, which wikipedia compares to the metabolic heat density of reptiles:
Much more interesting is the fact that, during the few dozen nanoseconds the bomb spent exploding, it produced over 1% of the power output of the entire Sun.
"The bomb, weighing 27 tonnes, was so large (8 metres (26 ft) long by 2 metres (6.6 ft) in diameter) that the Tu-95V had to have its bomb bay doors and fuselage fuel tanks removed. The bomb was attached to an 800 kilogram parachute, which gave the release and observer planes time to fly about 45 kilometres (28 mi) away from ground zero. The fireball reached nearly as high as the altitude of the release plane and was seen almost 1,000 kilometres (620 mi) from ground zero. The subsequent mushroom cloud was about 64 kilometres (40 mi) high (nearly eight times the height of Mount Everest). The base of the cloud was 40 kilometres (25 mi) wide. All buildings in the village of Severny (both wooden and brick), located 55 kilometres (34 mi) from ground zero within the Sukhoy Nos test range, were completely destroyed."
http://en.wikipedia.org/wiki/Tsar_Bomba