The Chapman-Enskog Divergence Problem in Plasma Transport: Structural Limitations and a Practical Regularization Approach

We calculate transport coefficients from the Chapman--Enskog expansion with BGK collision operators, obtaining exactly κ= 5nT/2mν, and show that maximum entropy closure yields identical results when applied with the same collision operator. Through structural arguments, we suggest that this $1/ν$ divergence extends to other local collision operators of the form L = νL̂, making the divergence fundamental to the Chapman--Enskog approach rather than a closure artifact. To address this limitation, we propose a phenomenological effective collision frequency ν_ = ν√1 + ² motivated by gradient-driven decorrelation, where is the Knudsen number. We verify that this regularization maintains conservation laws and thermodynamic consistency while yielding finite transport coefficients across all collisionality regimes. Comparison with exact solutions of a bounded kinetic model shows similar functional form, providing limited validation of our approach. This work provides explicit calculation of a known divergence problem in kinetic theory and offers one phenomenological regularization method with transparent treatment of mathematical assumptions versus physical approximations.