Past exam of the short options paper shared by Parts A and B of the physics course of the University of Oxford / 2019 / S16 / 3 / a / Solution

Linearize the electron Boltzmann distribution, $n_e(\varphi )\simeq n_{e0}[1+e\varphi /(k_{B}T)]$, about a uniform fixed-ion background. Poisson's equation gives ${\nabla }^2\varphi =\varphi /{\lambda }_D^2$, where the electron Debye length isDefine the plasma parameter as the number of electrons in a Debye sphere:Some authors omit $4\pi /3$ in this definition. Mobile ions alter the total screening length by contributing their own susceptibility; the electron-only convention is used consistently here.