Debye Length Trade Cross-Scan - Condensed Matter and Plasma Physics Step by Step

A Debye-length cross-scan trades density and temperature across rows, showing how the shielding length moves via lambda_D = sqrt(epsilon_0 * k_B * T / (n * e^2)). The arithmetic is exact only for the stated densities, temperatures, and rows in the ideal Maxwellian plasma model. Real plasmas add collisions, sheath boundaries, nonuniform density, temperature spread, diagnostics calibration, and measurement/source uncertainty.

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}