Microstructure formation in radially counterstreaming electron flows

A theoretical model is developed to describe the formation of microstructures due to plasma streaming instabilities in radially convergent geometries. Microstructures in the form of radial spokes are found experimentally in laser wakefield accelerators. The eigenvalues of a set of coupled linear ordinary differential equations are obtained and the complex wavenumbers calculated to give the local growth rates. The predictions are confirmed using particle-in-cell (PIC) simulations carried out for two counter-propagating converging/diverging plasma annuli. The simulations consistently demonstrate unstable growth for interactions between two counterpropagating annuli with different number densities. The growth rates obtained from the PIC simulations agree well with the growth rates from the semi-analytical model. The theory presented in this paper can provide powerful insight into converging plasma beams found in space and laboratory scale plasma