On particle acceleration and radiation output in stochastic electromagnetic fields

We demonstrate that when charged particles interact with a plane electromagnetic wave which possesses a random amplitude, then the particles are accelerated to high energy because they are pushed along by the wave's Poynting vector. Not only are they so accelerated, as they are carried along by the wave, but also they diffuse at right angles to the direction of the Poynting flux (i.e. in the direction of the wave's electric field). The ultimate energy that such particles can reach is determined when they radiate as much energyper unit time as they receive from the plane wave. For numbers believed typical of the Crab nebula this ultimate energy is of order 10¹⁰ mc ². We have done these calculations to show that turbulent electromagnetic waves are quite efficient in generating high energy particles from low energy particles. Thus when the low frequency coherent waves emitted by a magnetized rotating neutron star are turned into incoherent waves because of wave-plasma interactions in a surrounding nebula, they still accelerate particles to rather high energies. Accordingly, while it obviously takes less time to produce high energy particles with a coherent wave than with a turbulent wave, the calculations given here show that the bulk of the relativistic electrons in the Crab nebula could still be energized by the turbulent remnants of a coherent wave.