Theory of wakefield in a transversely inhomogeneous plasma waveguide

Plasma wakefield acceleration is one of the advanced and perspective technology for charged particle accelerators, particularly for future linear colliders and accelerator-based light sources for fundamental and applied research. Such wakefield accelerators provide acceleration gradients ∼GV/m and higher. Despite the progress, there are important tasks and problems that need to be overcome. One of them is a problem of transportation of accelerating bunches, especially the positron bunches. This was a main motivation of the studies presented in the paper. One possible way to solve this problem is to excite an accelerating field that simultaneously has focusing properties. Suitable electrodynamic structures for this purpose include, in particular, plasma waveguides. The paper presents theoretical studies of wakefield generation by a relativistic electron bunch in a cylindrical waveguide filled with transversely inhomogeneous plasma. The transversely inhomogeneous plasma is described as a set of three partial regions (one region is tubular plasma and two regions are plasma background) having different densities. Analytical expressions have been derived for the excited radial and axial electric field components, and for the azimuthal magnetic field component. The dispersion of the plasma waveguide under study, as well as the transverse profile of the electromagnetic field components of the transverse magnetic-eigenwaves, resonant with the bunch, have been investigated. Longitudinal and transverse amplitude distribution structures of the axial and radial wakefields have been determined. Spectrum analysis of the longitudinal and transverse wakefields has been performed with the result, that their frequency content has been determined. The results of the numerical analysis based on the developed theory demonstrated that the bunch-excited wakefield in such a waveguide provides radially stable acceleration of electron and positron bunches.