Plasma Resistivity

Unlike ordinary conductors, plasma resistivity decreases with increasing temperature — hotter plasmas are better conductors. This is because Coulomb collisions become rarer at higher thermal speeds.

Spitzer Resistivity

The Spitzer resistivity is the classical result for fully ionized plasma:

$\eta_{\text{Spitzer}} \approx 5.2 \times 10^{-5} \frac{Z \ln\Lambda}{T^{3/2}} \quad [\Omega \cdot \text{m}]$

where:

• (T) is in Kelvin
• (Z) is the ion charge number
• (\ln\Lambda \approx 10\text{–}20) is the Coulomb logarithm, accounting for the range of impact parameters in Coulomb collisions

The (T^{-3/2}) scaling means that a plasma at fusion temperatures ((\sim 10^8) K) has resistivity (\sim 10^{10}) times lower than at 10,000 K.

Electrical Conductivity

The plasma conductivity is simply:

$\sigma = \frac{1}{\eta}$

At fusion temperatures, plasma conductivity rivals that of copper.

Mean Free Path

The electron-ion collision frequency is:

$\nu_{ei} = 2.91 \times 10^{-12} \frac{n \ln\Lambda}{T^{3/2}}$

The electron mean free path between collisions is:

$\lambda_{\text{mfp}} = \frac{v_{\text{th}}}{\nu_{ei}}, \quad v_{\text{th}} = \sqrt{\frac{k_B T}{m_e}}$

At fusion temperatures and densities, (\lambda_{\text{mfp}}) can be enormous — electrons travel hundreds of kilometers between collisions.