Motion of relativistic particles in standing wave fields

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Abstract
The motion of relativistic particles in the field produced by two circularly polarised, electromagnetic plane waves travelling in opposite directions is studied. The Klein-Gordon equation is used, i.e. spin effects are neglected, and only motion along the beam direction is considered. If the electromagnetic beam carry opposite polarisation, the particle energy shows a band structure. The transmission of a plane particle wave through a long device is calculated. Transmission occurs only if the particle energy corresponds to an allowed energy band. For other energies the particles are totally reflected. For equal polarisation a similar structure emerges for the particle momentum along the beam direction. The observation of the band structure poses serious experimental problems.

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