We derive relativistic resistive magnetohydrodynamics for a two-component ultrarelativistic plasma directly from kinetic theory. Starting with the Boltzmann-Vlasov equation and using the 14-moment approximation in the Landau frame, we obtain coupled evolution equations for the charge diffusion four-current and the shear-stress tensor. Benchmarking against the usual Israel-Stewart type relaxation form shows that this simplified description is accurate for small viscosity to entropy ($\eta /s$) ratio, vanishing magnetic field, and not so strong electric field. Outside this regime the dynamics depart in a controlled way, i.e., strong electric fields introduce nonlinear backreaction that delays and reduces current peaks, and a sizable shear stress is produced even without a flow profile.

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• High-energy-density plasmas
• Magnetohydrodynamics
• Relativistic heavy-ion collisions
• Magnetically confined plasmas
• Hydrodynamic models
• Relativistic magnetohydrodynamics