IANANP (I an not a nuclear physicist) but I have read a great deal, and your best bet is to read http://nuclearweaponarchive.org/ which is chock full of interesting information, including a comprehensive list of every nuclear detonation, ever. Go read there about how Hydrogen bombs work.
TLDR for that site; there are two major factors in play with an H-bomb. The first is the addition of a fair amount of deuterium (Hydrogen with an extra neutron) around the explosive core. This acts as a large source of potential energy, and after the initial fission reaction is kicked off, the deuterium ignites and fussion occurs, similar to that which happens on the sun: 2 Hydrogens become 1 Helium, and 2 neutrons go flying off.
The Fission reaction has to be managed differently, however, as there needs to be a secondary reflector system in use. This secondary core reflector system captures the X-rays after the initial fission begins. These x-rays are reflected back into the core, causing the implosion to have a second stage. This "second stage" ignites the third stage fuel, and boom. The documentation will call it only 2 stages, though that x-ray reflection device is an essential part of kickstarting fusion.
The first H-Bomb detonation was essentially a A-bomb surrounded by liquid deuterium in a massive cooling system. The cooling system was actually the size of a building. http://nuclearweaponarchive.org/Usa/Tests/Ivy.html
Of interesting side note is the second H-bomb Castle Bravo: http://nuclearweaponarchive.org/Usa/Tests/Castle.html ) included a Lithium-deuteride solid fuel around the detonation device. The detonation was accidentally the largest ever conducted by the United States. It irradiated a huge swath of the Pacific ocean, and it's follow-up test had similar results.
Devices which used Lithium-6 or enriched Lithium instead of Deuterium would also be considered H-bombs, despite their not having Hydrogen. That's why we call them thermonuclear.
This was because of the added Lithium in the solid fuel. You're basically tripling the amount of neutrons available to the fusion reaction, and thus, the detonation was completely out of hand and exceeded calculations by an exponential factor.
Your description also leaves out the strictly optional, but common 3rd stage of a thermonuclear device: the thick Uranium blanket surrounding the entire assembly. Even "depleted" U-238 will undergo fast neutron fission, which the deuterium / tritium fusion reaction produces in extreme abundance. In most TN weapons, most of the explosive yield results from fission of the Uranium blanket, not the fusion reaction. In a "neutron bomb", or "enhanced radiation warhead", neutrons are the desired product rather than explosive yield, so these typically omit the U casing.
Richard Rhodes' "Dark Sun: The Making of the Hydrogen Bomb" provides an excellent description and paper bibliography.
TLDR for that site; there are two major factors in play with an H-bomb. The first is the addition of a fair amount of deuterium (Hydrogen with an extra neutron) around the explosive core. This acts as a large source of potential energy, and after the initial fission reaction is kicked off, the deuterium ignites and fussion occurs, similar to that which happens on the sun: 2 Hydrogens become 1 Helium, and 2 neutrons go flying off.
The Fission reaction has to be managed differently, however, as there needs to be a secondary reflector system in use. This secondary core reflector system captures the X-rays after the initial fission begins. These x-rays are reflected back into the core, causing the implosion to have a second stage. This "second stage" ignites the third stage fuel, and boom. The documentation will call it only 2 stages, though that x-ray reflection device is an essential part of kickstarting fusion.
The first H-Bomb detonation was essentially a A-bomb surrounded by liquid deuterium in a massive cooling system. The cooling system was actually the size of a building. http://nuclearweaponarchive.org/Usa/Tests/Ivy.html
Of interesting side note is the second H-bomb Castle Bravo: http://nuclearweaponarchive.org/Usa/Tests/Castle.html ) included a Lithium-deuteride solid fuel around the detonation device. The detonation was accidentally the largest ever conducted by the United States. It irradiated a huge swath of the Pacific ocean, and it's follow-up test had similar results.
Devices which used Lithium-6 or enriched Lithium instead of Deuterium would also be considered H-bombs, despite their not having Hydrogen. That's why we call them thermonuclear.
This was because of the added Lithium in the solid fuel. You're basically tripling the amount of neutrons available to the fusion reaction, and thus, the detonation was completely out of hand and exceeded calculations by an exponential factor.