When, if ever, should K_nu = K_c^{-3} be preferred for collisional scaling with reduced speed of light?

Determine whether there exist plasma problems for which setting the collision-frequency scaling prefactor K_{\nu \alpha \beta} = K_{c}^{-3} in particle-in-cell simulations with an artificially reduced speed of light is preferable to K_{\nu \alpha \beta} = K_{c}^{-4}, specifically in the context of choosing to match collisional dynamics to electrostatic (plasma-frequency) scales rather than electromagnetic (cyclotron/skin-depth) scales.

Background

To reduce computational cost, many PIC simulations use an artificially reduced speed of light and adjust the elementary charge so ion-scale dynamics are preserved. This alters the separation between electrostatic and electromagnetic scales. The authors introduce a species-dependent scaling factor K_{\nu \alpha \beta} to tune collisionality and show that choosing K_{\nu \alpha \beta} = K_{c}^{-4} preserves collisional dynamics relative to electromagnetic scales, matching collision frequencies to cyclotron scales and mean free paths to gyroradii/skin depths.

They note, however, that matching to electromagnetic scales modifies electrostatic-scale behavior: collision frequencies relative to the plasma frequency increase by K_c^{-1} and mean free paths relative to the Debye length decrease by K_c. For problems dominated by electrostatic physics, they caution that reduced-c scaling may be inappropriate and explicitly state uncertainty about whether any problems would favor the alternative choice K_{\nu \alpha \beta} = K_{c}^{-3}, which would instead align collisional dynamics with plasma-frequency scales.