 Solution

Define the plasma parameter as the number in a Debye sphere, $N_D=(4\pi /3)n_e{\lambda }_D^3$; some conventions omit $4\pi /3$. A good classical plasma has many particles in a screening volume, $N_D\gg 1$, and a system size much larger than ${\lambda }_D$, so collective fields dominate individual encounters.

A collision here means cumulative Coulomb deflection that significantly changes a particle's velocity, not necessarily a literal hard-sphere impact. A collisionless description requires the phenomenon's timescale to be short compared with the appropriate collision time, and its length scale short compared with the mean free path. Parametrically $\boxed{{\omega }_p{t}_c\sim N_D/\log \Lambda }$ up to convention-dependent constants, with Coulomb logarithm $\log \Lambda$ representing the range of impact parameters. Many oscillations can then occur before collisional relaxation. The formula itself presupposes the weak-coupling regime.