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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.

An equation is derived that describes the linear response of an underdense inhomogeneous plasma [ω0≫ωp(r), where ω0 and ωp(r) are the laser-carrier and plasma frequencies, respectively] during the propagation of a laser pulse along the axis of a plasma channel with a characteristic width Rch. For a wide channel, i.e., when Rch/λp0>1 (where λp0=2πc/ωp0 is the wavelength of the excited plasma wave and ωp0 is the plasma frequency at the channel axis), the structure of the wake field is studied analytically. It is shown that this structure changes with the distance from the trailing edge of the pulse. As a result, at a certain distance behind the pulse, the fraction of the plasma wave period in which the simultaneous focusing and acceleration of electrons are possible increases by a factor of 2. For a narrow channel (Rch/λp0<1), the structure of the wake field is studied numerically and it is shown that, in this case, the doubling of the phase interval of the wave where the simultaneous focusing and acceleration of electrons are possible also occurs; but, in contrast to a wide channel, a rapid reconstruction of the wake occurs, so that the amplitude of the axial (accelerating) field in the wake decreases while the radial (focusing) field increases with the distance from the pulse trailing edge. The numerical modeling of the laser pulse (90 fs, 2 TW) guiding and the excitation of plasma waves in a narrow plasma channel is carried out and the possibility of reaching GeV energies of accelerated electrons in an experiment is discussed.

This report presents the conceptual design of a new European research infrastructure EuPRAXIA. The concept has been established over the last four years in a unique collaboration of 41 laboratories within a Horizon 2020 design study funded by the European Union. EuPRAXIA is the first European project that develops a dedicated particle accelerator research infrastructure based on novel plasma acceleration concepts and laser technology. It focuses on the development of electron accelerators and underlying technologies, their user communities, and the exploitation of existing accelerator infrastructures in Europe. EuPRAXIA has involved, amongst others, the international laser community and industry to build links and bridges with accelerator science — through realising synergies, identifying disruptive ideas, innovating, and fostering knowledge exchange. The Eu-PRAXIA project aims at the construction of an innovative electron accelerator using laser- and electron-beam-driven plasma wakefield acceleration that offers a significant reduction in size and possible savings in cost over current state-of-the-art radiofrequency-based accelerators. The foreseen electron energy range of one to five gigaelectronvolts (GeV) and its performance goals will enable versatile applications in various domains, e.g. as a compact free-electron laser (FEL), compact sources for medical imaging and positron generation, table-top test beams for particle detectors, as well as deeply penetrating X-ray and gamma-ray sources for material testing. EuPRAXIA is designed to be the required stepping stone to possible future plasma-based facilities, such as linear colliders at the high-energy physics (HEP) energy frontier. Consistent with a high-confidence approach, the project includes measures to retire risk by establishing scaled technology demonstrators. This report includes preliminary models for project implementation, cost and schedule that would allow operation of the full Eu-PRAXIA facility within 8—10 years.