Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2015 / S19 / 3 / c / Solution

In the cold unmagnetized linear plasma model, the refractive-index relation is $n^2=1-{\omega }_p^2/{\omega }_L^2$, withThe critical density occurs at ${\omega }_p={\omega }_L=2\pi c/{\lambda }_L$. Thusfor ${\lambda }_L=1\mu \mathrm{m}$. The corresponding frequency isA propagating conventional laser wake generally uses an underdense plasma, rather than this cutoff density. Strong relativistic laser motion, collisions or a magnetized plasma modify this simple critical-density condition.