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The earliest ones all did.

Early atomic bombs used an internal initiator/neutron source to start the chain reaction. This was composed of beryllium and polonium and somewhat resembled a golfball in appearance. It was placed in the center of the bomb and when crushed by the shock from the chemical explosives, the two elements mixed, alpha particles from the polonium decay released neutrons from the beryllium which started the chain reaction.

These had a problem though: the polonium decays fairly rapidly, meaning these initiators/neutron sources had to be replaced about every 138 days to keep the bombs reliable. As the stockpile grew this became a major maintenance issue.

In the middle 1950s the US switched to external initiators/neutron sources to start the chain reaction. These are operated electrically and use tritium in a miniaturized particle accelerator to initiate a small fusion reaction reaction and a pulse of neutrons. The maintenance issues were effectively eliminated as these initiators/neutron sources only had to be replaced about every 12 years, a period of time longer than many weapons were even kept in the stockpile before being replaced by newer designs.

Some atomic bombs do use a beryllium neutron reflector on the inside of the depleted uranium tamper to improve efficiency, but this is not absolutely necessary for the bomb to work. To know whether a given bomb uses this or not would require access to classified design information.

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