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Why does a Trap help?
Single-stage acceleration mechanisms operate very far from equilibrium. They therefore have a huge difference in entropy between W and Q, and are therefore inherently inefficient. Likewise environmental conditions are far from equilibrium, and are thus inherently unlikely. The product of these two situations = low density of accelerated particles.
Energy Source * Efficiency * Probability = Power
A trap allows small impulses to be cumulative. The pulses are close to equilibrium and are also likely. Thus a trap = higher density of accelerated particles.