Weibel Instability in Collisionless Plasmas Across Astrophysical and Laboratory Shocks

We present a systematic cold‐fluid analysis of the purely transverse Weibel (current‐filamentation) instability across four regimes: non‐relativistic (NR) single‐species, NR multi‐species, relativistic single‐species and relativistic multi‐species (electron–positron and electron–proton). Beginning from the linearized fluid equations, we derive the dispersion relations in each regime and extract scaling laws for and . The main contributions are: (i) explicit regime‐transition criteria in the parameter space; (ii) contour maps of relativistic suppression and mass‐ratio dependence serving as diagnostic charts and (iii) an assessment of where the purely transverse mode dominates over competing instabilities. Relativistic corrections suppress by up to 40% above , peaking near . For the tabletop laser experiment of Bai et al., the predicted ion skin depth agrees with the observed filament spacing to within 2%, and is consistent with the measured under kinetic suppression. Two MMS burst‐mode bow shock crossings confirm from FGM/FPI PySPEDAS data. A multi‐environment scatter plot spanning 21 orders of magnitude in , from laser‐plasma to young SNR scales, shows all points within a factor of 3 of the 1:1 line.