= Solution
Use <quasineutrality>, $n_e=Zn_i$. Multiplying the supplied collision time by the electron <plasma frequency> and using the preceding definition gives
$$
\boxed{\omega_p\tau_{ei}=\frac{9.6}{Z\ln\Lambda}N_D.}
$$
Thus $\tau_{ei}\gg2\pi/\omega_p$ requires $N_D\gg(2\pi/9.6)Z\ln\Lambda$; for ordinary $Z$ and $\ln\Lambda\sim1$–$30$, this is a large <plasma parameter>. Many particles then collectively screen a charge, fluctuations in a <Debye sphere> are relatively small, and mean-field <electrostatics> descriptions become meaningful. A large <plasma parameter> is also associated with weak <Coulomb coupling>, well-separated screening and close-collision scales, and collective <plasma oscillations> surviving many oscillations before collisionally relaxing. Roughly, relative counting fluctuations scale as $N_D^{-1/2}$ and the ratio of interaction to thermal <energy> decreases as $N_D$ increases. Small $N_D$ signals that strong correlations can invalidate the simple weakly coupled <plasma> description.
Back to article page
