Debye Length Trade Cross-Scan - Plasma Physics: Debye Shielding, Gyromotion, and Collective Oscillations Step by Step

Debye length squared is scanned across scale and 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

Shielding length squared is scale divided by density

The checked source keeps density six and scale squared eighteen, so lambda squared is three square meters.

\lambda^{2}=\frac{18}{6}=3

Density and scale pull lambda squared in opposite ways

The first two rows hold scale fixed while density rises. The last row raises scale at the same density.

\begin{array}{c|c|c}\text{scale sq}&\text{density}&\lambda\text{ sq}\\12&3&4\\12&6&2\\18&6&3\\\end{array}