Boundary Depth Scans

Debye Length Inverse-Density Boundary Scan

Debye length squared is scanned across exact density 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

Density divides the same scale square

The checked source holds scale squared at eighteen square meters and density ratio at six, giving lambda squared of three.

λ2=186=3 m2\lambda^{2}=\frac{18}{6}=3\ \text{m}^{2}
Density inverse sourceScale, density, and lambda squared are checked.sourcefieldsource=6 Cresponse=-4 Cvisible=2 Cscale2=18 m^2density=6lambda2=3 m^2

Tripling density cuts lambda squared by three

The scale column is frozen. The density rows rise from three to nine, so lambda squared falls from six to two.

Snλ2183618631892\begin{array}{c|c|c}S&n&\lambda^{2}\\18&3&6\\18&6&3\\18&9&2\\\end{array}
Density inverse scanThe middle row is the checked source diagram.sourcefieldsource=6 Cresponse=-4 Cvisible=2 Cscale2=18 m^2density=6lambda2=3 m^2

Dense plasma means shorter shielding length

This book tracks lambda squared, not the square root. The exact inverse relation is still visible row by row.

n↑⇒λ2=Sn↓n\uparrow\quad\Rightarrow\quad \lambda^{2}=\frac{S}{n}\downarrow
Shorter shielding boundaryHigher density compresses the shielding scale.sourcefieldsource=6 Cresponse=-4 Cvisible=2 Cscale2=18 m^2density=6lambda2=3 m^2