Breaking symmetry in propagation of radially and azimuthally polarized high power laser pulses in underdense plasma

Propagation of relativistically intense azimuthally or radially polarized laser pulses (RPP) in underdense plasmas is demonstrated to be unstable, via 3D particle-in-cell simulation and disregarding the Kerr non-linearity. Strong pulse filamentation occurs for RPP in transversely uniform plasma with an increment, $\Gamma$, close to the well-known one depending on acceleration, $\alpha$, and modulated density gradient length, $L$, as $\Gamma \approx (\alpha/L)^{1/2}$. In deep plasma channels the instability vanishes. Electron self-injection and acceleration by the resulting laser pulse wake is explored.
Comment: The paper need to be written in a more proper way