= Solution
Linearize the electron <Boltzmann distribution>, $n_e(\phi)\simeq n_{e0}[1+e\phi/(k_BT)]$, about a uniform fixed-ion background. <Poisson's equation> gives $\nabla^2\phi=\phi/\lambda_D^2$, where the electron <Debye length> is
$$
\lambda_D=\sqrt{\frac{\epsilon_0k_BT}{n_ee^2}}.
$$
Define the <plasma parameter> as the number of <electrons> in a <Debye sphere>:
$$
\boxed{N_D=\frac{4\pi}{3}n_e\lambda_D^3=\frac{4\pi}{3}\frac{\epsilon_0^{3/2}(k_BT)^{3/2}}{e^3n_e^{1/2}}.}
$$
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.
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