A collective-oscillation density-mass-ratio scan varies density or particle mass across rows, showing how the plasma-frequency scale follows sqrt(n / m) row by row. The arithmetic is exact only for the stated densities, masses, charges, oscillation ratios, and rows in the ideal cold-plasma model. Real plasmas add collisions, nonuniform fields, distribution functions, boundary/sheath effects, calibration, finite precision, and measurement uncertainty.
Plasma frequency squared is scanned across exact density and mass ratios. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
The checked oscillation square starts from a ratio
The diagram pins normalized constant twelve, density ratio three, and mass ratio six. The square frequency is therefore six.
ω2=12⋅63=6s−2
Density and mass ratio pull opposite directions
The first row is the checked source. Doubling density doubles omega squared; halving mass ratio doubles it again.
n366m663ω261224
The square frequency follows density over mass
The lesson stays with omega squared so every row remains exact. That is enough to see the collective frequency trend.