Weibel instability in regularized kappa distributed plasmas with anisotropy regularization parameters

Space plasmas are generally in a state of non-thermodynamic equilibrium, and their velocity distributions often exhibit prominent suprathermal tail, which can be accurately described by the kappa distribution. The standard Kappa distribution suffers from the divergence of velocity moments for small kappa parameters, whereas the regularized Kappa distribution introduces an exponential cutoff factor to achieve convergence of all-order velocity moments while retaining the core characteristic of the power-law tail, making it more consistent with realistic space plasma environments. Based on the linear Vlasov–Maxwell equations and superstatistics formulas, we derive the dispersion relation of the Weibel instability under the regularized bi-Kappa distribution, obtain the marginal instability condition, and analyze the effects of the kappa parameters, the cutoff parameters, and thermal speeds on the growth rate of the instability. The results demonstrate that the anisotropy of regularization parameters greatly alters the instability onset conditions, which differ from those for Maxwellian and standard bi-Kappa plasmas.