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.

开发了一个理论模型来描述由于径向会聚几何形状中的等离子体流不稳定性而形成的微结构。在激光尾场加速器中通过实验发现了径向辐条形式的微结构。获得一组耦合线性常微分方程的特征值并计算复波数以给出局部增长率。使用对两个反向传播的会聚/发散等离子体环进行的细胞内粒子 (PIC) 模拟证实了这些预测。模拟一致地证明了具有不同数量密度的两个反向传播环之间的相互作用的不稳定增长。从 PIC 模拟获得的增长率与半分析模型的增长率非常吻合。