Electron dynamics in the fields associated with a transverse magnetic (TM) wave propagating inside a rectangular waveguide is analytically studied. The relativistic momentum and energy equations for an electron are solved, which was injected initially along the propagation direction of the microwave. Expressions of the acceleration gradient and deflection angle are obtained. In principle, it is shown that the electron can be accelerated in this condition and there is no deflection when the electron is injected from the centre of the waveguide front. However, it is found that the acceleration gradient and deflection angle depend strongly on the parameters of the microwave (intensity, frequency, etc.) and the dimensions of the waveguide.

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A two-dimensional particle in cell code has been used to demonstrate the formation mechanism of a periodic nanograting structure in the hydrogen plasma. By using a linearly polarized, ultrafast laser beam with a wavelength of 800 nm, an incidence angle of 0• , and an intensity of 10 16 W/cm 2 -µm 2 , the periodic nanograting structure was clearly self-organized at the boundary between a preformed and dense plasma at t = 600 fs. The bidirectional surface plasma wave plays a significant role together with the oscillating two-stream instability in producing the periodic nanograting structure.

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