Debye Length Scale Proportionality Scan - Plasma Physics: Debye Shielding, Gyromotion, and Collective Oscillations Step by Step

Debye length squared is scanned across exact scale squares. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Scale square raises lambda square at fixed density

The checked source keeps density ratio at three. Scale squared nine therefore gives lambda squared three.

\lambda^{2}=\frac{9}{3}=3\ \text{m}^{2}

Changing scale alone changes lambda square linearly

Density stays fixed in every row. Raising scale squared from six to fifteen raises lambda squared from two to five.

\begin{array}{c|c|c}S&n&\lambda^{2}\\6&3&2\\9&3&3\\15&3&5\\\end{array}

Scale and density are separate knobs

This is the companion to the density scan. One knob multiplies the numerator; the other divides it.

S\uparrow\quad\Rightarrow\quad \lambda^{2}=\frac{S}{n}\uparrow