Hotter Plasma Lengthens Shielding Length - Condensed Matter and Plasma Physics Step by Step

The Debye length grows as sqrt(T), because hotter particles have more thermal energy to resist being pulled into the shielding cloud. Heat the plasma and the screening cloud spreads out, so the field reaches farther before it is cancelled. The scaling holds for the stated temperature and an ideal collisionless plasma; real plasmas have temperature gradients, non-Maxwellian tails, and diagnostic uncertainty.

At fixed density, a larger scale gives a longer shielding square. 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 cooler reference has a shorter square length

Scale squared 12 over density ratio 3 gives 4 square meters.

\lambda_{\text{cool}}^{2}=4\ \text{m}^{2}

A hotter scale lengthens shielding

At the same density ratio 3, scale squared 18 gives length squared 6 square meters.

\lambda_{\text{hot}}^{2}=\frac{18}{3}=6\ \text{m}^{2}