The properties of the eigenmodes of a capillary tube are examined in the context of ultrashort intense laser pulse guiding. The dispersion relation for the eigenmodes of a cylindrical hollow waveguide is derived and the family of eigenmodes EH(nus) is shown to be a solution of the wave equation up to the first order under the condition k(0)a >>1, where k(0) is the light wave number and a the capillary tube radius. The expressions of the fields for the eigenmodes are given at zero and first order of a small parameter equal to the ratio of the perpendicular to longitudinal wave number and the absorbed intensity at the wall is estimated.

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The dynamics of a guided laser pulse propagation and wakefield generation in plasma channels, ionizing gases and gas filled capillaries is investigated. The efficient generation of a regular wakefield over long distances suitable for laser wakefield accelerators is demonstrated. The different schemes of electron bunch injection and compression to provide monoenergetic electron acceleration to high energies are analysed. A possibility of effective multistage acceleration of short electron bunches with low emittance and energy spread is demonstrated. The analytical results are confirmed by the results of numerical modelling.