Sorry, but this isn't correct. There's no more "instability" in the ignition of a thermonuclear weapon than there is in the sun. The reaction kinetics are different because the reactants and confinement mechanisms are different. That's all. There is nothing fundamentally different about the physics which involves a release of binding energy from the strong nuclear force. The criticality, or runaway, reaction is entirely in the fission part of the bomb.
The "instability" in all the cases you're talking about is all about the containment's ability to confine fuel long enough to fuse; that's all. In a PPI supernova, most of the fuel is not instantaneously consumed by some sort of "instability." In fact, most of the fuel isn't consumed at all. The core is entirely consumed and blows most of the hydrogen/helium atmosphere (about 75% of the star) off into space. The same thing happens in a thermonuclear device. Ablation of the shell and x-ray pressure confines the reactants long enough for significant consumption of the reactants, but there isn't any special magic sauce there that isn't present in the sun. It's just a more energetic reaction because it isn't the P-P chain.
No magic sauce, just feedback. It’s a very general concept, epitomized by the HS auditorium audio feedback, heard as an earsplitting screech. It accounts for supernovae of all sorts, I believe.
As I read the LHC wiki article, this is what they’re trying to achieve, but they’re having trouble getting the microphone close enough to the speakers :-)