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"How precise does the detonation timing have to be to achieve a successful implosion?"

Probably pretty precise, but radiation-induced damage to the conductors of wiring won't be large enough to affect it.

Think about it for a minute---the only mechanism for radiation damage is for the radiation to displace electrons from their "normal" bonds and orbits. In silicon chips and similar devices, and in wiring insulation, some (or most) of those electrons get trapped and cannot return to their "normal" state. BUT, because wiring is conductive throughout its volume, any "displaced" electron (or another conductance band electron) "zips" into the displacement location as soon as the inducing radiation ceases, thus eliminating the "damage". To cause irreversible radiation damage in conducting wires requires HUGE radiation fluxes.

"Think about it for a minute---the only mechanism for radiation damage is for the radiation to displace electrons from their "normal" bonds and orbits."

That's incorrect. Electron radiation is comparably tame (though it could do the deed if a particular electron caused a spontaneous neutron emission such as what we see when Be is mixed with Po-210). Neutrons are also being radiated, and they have to go *somewhere*. The heavier your shielding, the fewer such neutrons go somewhere that interrupts your design...but no matter how thick your shielding, not all neutrons are ever fully shielded.

Neutrons that hit atoms in your wiring *will* impact your wiring, be it heat, resistence, or other potential changes. The fewer neutrons that hit your wiring, the less serious the impact, of course, but neutron emission over time increases the odds of adverse impacts.

The longer the time, the less escapes damage. This factors in to how often you replace the wiring, the electronics, the conventional explosives, the pits, the cores, and the triggers in your weapon. Certainly the less shielding that you have (e.g. a suitcase nuke), the more frequent you have to serve up high quality maintenance.