To make progress, physicists use coarse approximations that, while not exactly accurate, are good enough for what we need to accomplish: all pulleys are frictionless, and all chickens are spheres. In this paper, Marceau et al. find that the usual approximations of Maxwell’s equations aren’t good enough for solving the important problem of electron acceleration, and they show that by solving the equations exactly, they can double the usual energy transfer efficiency.
Fast electrons are used in particle colliders, and are also useful for microscopy. Usually electrons are sped up with electromagnets and superconductors, which is expensive. It also takes a long distance to accomplish, so electron accelerators tend to be rather huge. Finding a way to make a compact electron accelerator that could be used in tabletop experiments would be a big step forward. One idea is to use focused laser pulses to transfer energy to stationary electrons.
Think of the electron as a surfer floating in the ocean. If a wave comes along, she hops on her surfboard and feels an acceleration toward the shore. Bigger waves cause more acceleration, which is like turning up the laser power on the electron. Previous studies have shown that about half of the theoretical energy gain limit can be reached using the standard approximations of Maxwell’s equations. The wave reaches the surfer, but most of it just passes through her without speeding her up very much.
But if she were to start swimming along with the wave to match its speed, she could be in a position to catch more of its energy. Marceau et al. say that they can mimic this kind of action by using extremely short laser pulses. Each pulse is only about five cycles long – that is, it’s so short that light can only oscillate about five times within the pulse. The first couple of small oscillations get the electron moving forward a bit so it can be ready to extract energy from the later oscillations, like two or three “pre-waves” to start the surfer moving before the big one hits.
They also use tightly focused laser pulses, which can be generated by very powerful lenses or mirrors, and which can’t be modeled unless exact versions of Maxwell’s equations are used. Using these tricks, they bump the energy transfer up to about 80% of the theoretical maximum, doubling previous efforts.
Scientists use approximations to solve problems quickly because there are just too many problems to solve. In this paper, the authors show that if you know exactly where to look, the more difficult, exact solutions can have a big payoff.
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