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In a coherent monoenergetic beam of non-interacting particles, the phasevelocity and the particle transport velocity are functions of position, withthe strongest variation being in the focal region. These velocities areeverywhere parallel to each other, and their product is constant in space. Fora coherent monochromatic electromagnetic beam, the energy transport velocity isnever greater than the speed of light, and can even be zero. The phasevelocities (one each for the non-zero components of the electric and magneticfields, in general) can be different from each other and from the energytransport velocity, both in direction and in magnitude. The phase velocities ata given point are independent of time, for both particle and electromagneticbeams. The energy velocity is independent of time for the particle beam, but ingeneral oscillates (with angular frequency 2w) in magnitude and direction aboutits mean value at a given point in the electromagnetic beam. However, thereexist electromagnetic steady beams, within which the energy flux, energydensity and energy velocity are all independent of time.Comment: 9 pages, 12 figure

Phase and transport velocities in particle and electromagnetic beams