We have developed explicit analytic expressions for the electron and ion electrical-conductivity tensors of a fully ionized two-component plasma. We assume the plasma is nondegenerate, nonrelativistic, and subject to electric and magnetic fields. The conductivity tensors give the Pedersen, Hall, and Birkeland currents of the electrons and ions as functions of the electric field, magnetic field, and plasma parameters. (By definition, the electron and ion Pedersen currents are those that flow in the direction of the component of E that is perpendicular to B. The electron and ion Hall currents flow in the $-\mathbf{E}\times \mathbf{B}$ and $\mathbf{E}\times \mathbf{B}$ directions, respectively. The electron and ion Birkeland currents flow in the direction of the component of E that is parallel to B.) We derive the conductivity tensors from Lorentz-force, kinetic, modified-two-fluid, and standard-two-fluid models of a plasma. The Lorentz-force model is based on the electron and ion Lorentz-force equations, and the probability distribution of random collisions. The kinetic model is based on the electron and ion Boltzmann equations in the relaxation-time approximation. The modified-two-fluid model is derived from the kinetic model, and differs from the well-known standard-two-fluid model. The Lorentz-force, kinetic, and modified-two-fluid models are in agreement and, in the steady state, predict the following: In the collisionless limit $({\omega }_{ce}\tau \to \infty ,$ ${\omega }_{ci}\tau \to \infty )$, the electron and ion Pedersen currents $\to 0$, whereas the electron and ion Hall currents dominate. In the collisional limit $({\omega }_{ce}\tau \to 0$, ${\omega }_{ci}\tau \to 0)$, the Pedersen currents dominate, whereas the Hall currents $\to 0$. (The quantities ${\omega }_{ce}$ and ${\omega }_{ci}$ are the electron- and ion-cyclotron frequencies, respectively; τ is the interparticle momentum-transfer collision time.) The results are consistent with elementary physical considerations. The standard-two-fluid model predicts instead that, in the steady state, the Pedersen currents are identically 0, and the Hall currents dominate, for all values of ${\omega }_{ce}\tau$ and ${\omega }_{ci}\tau$ (when $\mathbf{B}\ne 0$). The discrepancies with the Lorentz-force, kinetic, and modified-two-fluid models are caused by the collision terms of the standard-two-fluid model.

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• High-energy-density plasmas
• Plasma discharges in vacuum
• Magnetized plasma
• Pulsed-power accelerators
• First-principles calculations in plasma physics
• Plasma kinetic theory
• Two-fluid & multi-fluid model