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An explosive booster acts as a bridge between a low energy explosive and a low sensitivity (but typically high energy) explosive such as TNT. It increases the explosive shockwave from an initiating explosive to the degree sufficient to detonate the secondary charge.
An initiator such as a shock tube, cannon fuse (or even a conventional detonator) does not deliver sufficient shock to detonate charges comprising TNT, Composition B, ANFO and many other high explosives. Therefore, some form of "booster" is required to amplify the energy released by the detonator so that the main charge will detonate.
Tetryl was once a very popular chemical for booster charges, particularly during World War II, but has been largely superseded by other compositions e.g. a small cylinder or pellet of phlegmatized RDX or PETN (slightly larger than the actual detonator) into which the detonator itself is inserted.
Note: booby traps and improvised explosive devices frequently use plastic explosive as the booster charge, for example, some C4 or Semtex stuffed into the empty fuze pocket of a 120mm mortar shell. This is because any standard detonator will initiate plastic explosive as is.
When encountered in connection with artillery shells or air dropped bombs, a booster charge is sometimes referred to as the "gaine". See detonators.
At a purely technical level, a sufficiently large detonator would initiate high explosives without the need for a booster charge. However, there are very good reasons why this method is never used. Firstly, there is a major safety issue i.e. detonators are (like all primary explosives) much more sensitive to shock, heat and friction than an explosive booster. Therefore, minimising the amount of primary explosive that users must store or carry greatly reduces the likelihood of serious accidents. An additional economic reason for using explosive booster charges is that chemical compounds used in detonators (e.g. lead styphnate) are comparatively expensive to produce and encapsulate when compared to the manufacturing costs of explosive boosters.